Coexistence of collapse and stable spatiotemporal solitons in multimode fibers
Shtyrina, Olga V.; Fedoruk, Mikhail P.; Kivshar, Yuri S.; Turitsyn, Sergei K.
2018-01-01
We analyze spatiotemporal solitons in multimode optical fibers and demonstrate the existence of stable solitons, in a sharp contrast to earlier predictions of collapse of multidimensional solitons in three-dimensional media. We discuss the coexistence of blow-up solutions and collapse stabilization by a low-dimensional external potential in graded-index media, and also predict the existence of stable higher-order nonlinear waves such as dipole-mode spatiotemporal solitons. To support the main conclusions of our numerical studies we employ a variational approach and derive analytically the stability criterion for input powers for the collapse stabilization.
Moving stable solitons in Galileon theory
International Nuclear Information System (INIS)
Masoumi, Ali; Xiao Xiao
2012-01-01
Despite the no-go theorem Endlich et al. (2011) which rules out static stable solitons in Galileon theory, we propose a family of solitons that evade the theorem by traveling at the speed of light. These domain-wall-like solitons are stable under small fluctuations-analysis of perturbation shows neither ghost-like nor tachyon-like instabilities, and perturbative collision of these solitons suggests that they pass through each other asymptotically, which maybe an indication of the integrability of the theory itself.
Stable rotating dipole solitons in nonlocal media
DEFF Research Database (Denmark)
Lopez-Aguayo, Servando; Skupin, Stefan; Desyatnikov, Anton S.
2006-01-01
We present the first example of stable rotating two-soliton bound states in nonlinear optical media with nonlocal response. We show that, in contrast to media with local response, nonlocality opens possibilities to generate stable azimuthons.......We present the first example of stable rotating two-soliton bound states in nonlinear optical media with nonlocal response. We show that, in contrast to media with local response, nonlocality opens possibilities to generate stable azimuthons....
Exact soliton-like solutions of perturbed phi4-equation
International Nuclear Information System (INIS)
Gonzalez, J.A.
1986-05-01
Exact soliton-like solutions of damped, driven phi 4 -equation are found. The exact expressions for the velocities of solitons are given. It is non-perturbatively proved that the perturbed phi 4 -equation has stable kink-like solutions of a new type. (author)
International Nuclear Information System (INIS)
Atkinson, James; Nijhoff, Frank; Hietarinta, Jarmo
2008-01-01
We construct N-soliton solutions to the equation called Q3 in the recent Adler-Bobenko-Suris classification. An essential ingredient in the construction is the relationship of (Q3) δ=0 to the equation proposed by Nijhoff, Quispel and Capel in 1983 (the NQC equation). This latter equation has two extra parameters, and depending on their sign choices we get a 4-to-1 relationship from NQC to (Q3) δ=0 . This leads to a four-term background solution, and then to a 1-soliton solution using a Baecklund transformation. Using the 1SS as a guide allows us to get the N-soliton solution in terms of the τ-function of the Hirota-Miwa equation. (fast track communication)
International Nuclear Information System (INIS)
Bullough, R.K.
1978-01-01
Two sorts of solitons are considered - the classical soliton, a solitary wave which shows great stability in collision with other solitary waves, and the quantal, that is quantised, soliton. Solitons as mathematical objects have excited theoreticians because of their wide ranging applications in physics. They appear as solutions of particular nonlinear wave equations which often have a certain universal significance. The importance of solitons in modern physics is discussed with especial reference to; nonlinearity and solitons, the nonlinear Schroedinger equation, the sine-Gordon equation, notional spins and particle physics. (U.K.)
International Nuclear Information System (INIS)
Ji Mingjun; Lue Zhuosheng
2005-01-01
By using the further extended tanh method [Phys. Lett. A 307 (2003) 269; Chaos, Solitons and Fractals 17 (2003) 669] to the Broer-Kaup system with variable coefficients, abundant new soliton-like solutions and multi-soliton-like solutions are derived. Based on the derived multi-soliton-like solutions which contain arbitrary functions, some interesting multi-soliton structures are revealed.
(2+1)-dimensional stable spatial Raman solitons
International Nuclear Information System (INIS)
Shverdin, M.Y.; Yavuz, D.D.; Walker, D.R.
2004-01-01
We analyze the formation, propagation, and interaction of stable two-frequency (2+1)-dimensional solitons, formed in a Raman media driven near maximum molecular coherence. The propagating light is trapped in the two transverse dimensions
On soliton solutions of the Wu-Zhang system
Directory of Open Access Journals (Sweden)
Inc Mustafa
2016-01-01
Full Text Available In this paper, the extended tanh and hirota methods are used to construct soliton solutions for the WuZhang (WZ system. Singular solitary wave, periodic and multi soliton solutions of the WZ system are obtained.
Stable optical soliton in the ring-cavity fiber system with carbon nanotube as saturable absorber
Li, Bang-Qing; Ma, Yu-Lan; Yang, Tie-Mei
2018-01-01
Main attention focuses on the theoretical study of the ring-cavity fiber laser system with carbon nanotubes (CNT) as saturable absorber (SA). The system is modelled as a non-standard Schrödinger equation with the coefficients blended real and imaginary numbers. New stable exact soliton solution is constructed by the bilinear transformation method for the system. The influences of the key parameters related to CNTs and SA on the optical pulse soliton are discussed in simulation. The soliton amplitude and phase can be tuned by choosing suitable parameters.
Soliton solutions in a diatomic lattice system
International Nuclear Information System (INIS)
Yajima, Nobuo; Satsuma, Junkichi.
1979-04-01
A continuum limit is considered for a diatomic lattice system with a cubic nonlinearity. A long wave equation describing the interaction of acoustic and optical modes is obtained. It reduces, in certain approximations, to equations having coupled wave solutions. The solutions exhibit trapping of an optical mode by an acoustic soliton. The form of the trapped optical wave depends on the mass ratio of adjacent particles in the diatomic lattice. (author)
Topological soliton solutions for some nonlinear evolution equations
Directory of Open Access Journals (Sweden)
Ahmet Bekir
2014-03-01
Full Text Available In this paper, the topological soliton solutions of nonlinear evolution equations are obtained by the solitary wave ansatz method. Under some parameter conditions, exact solitary wave solutions are obtained. Note that it is always useful and desirable to construct exact solutions especially soliton-type (dark, bright, kink, anti-kink, etc. envelope for the understanding of most nonlinear physical phenomena.
Pure soliton solutions of some nonlinear partial differential equations
International Nuclear Information System (INIS)
Fuchssteiner, B.
1977-01-01
A general approach is given to obtain the system of ordinary differential equations which determines the pure soliton solutions for the class of generalized Korteweg-de Vries equations. This approach also leads to a system of ordinary differential equations for the pure soliton solutions of the sine-Gordon equation. (orig.) [de
Exact, multiple soliton solutions of the double sine Gordon equation
International Nuclear Information System (INIS)
Burt, P.B.
1978-01-01
Exact, particular solutions of the double sine Gordon equation in n dimensional space are constructed. Under certain restrictions these solutions are N solitons, where N <= 2q - 1 and q is the dimensionality of space-time. The method of solution, known as the base equation technique, relates solutions of nonlinear partial differential equations to solutions of linear partial differential equations. This method is reviewed and its applicability to the double sine Gordon equation shown explicitly. The N soliton solutions have the remarkable property that they collapse to a single soliton when the wave vectors are parallel. (author)
Soliton-type solutions for two models in mathematical physics
Al-Ghafri, K. S.
2018-04-01
In this paper, the generalised Klein-Gordon and Kadomtsov-Petviashvili Benjamin-Bona-Mahony equations with power law nonlinearity are investigated. Our study is based on reducing the form of both equations to a first-order ordinary differential equation having the travelling wave solutions. Subsequently, soliton-type solutions such as compacton and solitary pattern solutions are obtained analytically. Additionally, the peaked soliton has been derived where it exists under a specific restrictions. In addition to the soliton solutions, the mathematical method which is exploited in this work also creates a few amount of travelling wave solutions.
Classification of the line-soliton solutions of KPII
International Nuclear Information System (INIS)
Chakravarty, Sarbarish; Kodama, Yuji
2008-01-01
In the previous papers (notably, Kodama Y 2004 J. Phys. A: Math. Gen. 37 11169-90, Biondini G and Chakravarty S 2006 J. Math. Phys. 47 033514), a large variety of line-soliton solutions of the Kadomtsev-Petviashvili II (KPII) equation was found. The line-soliton solutions are solitary waves which decay exponentially in the (x, y)-plane except along certain rays. In this paper, it is shown that those solutions are classified by asymptotic information of the solution as |y| → ∞. The present work then unravels some interesting relations between the line-soliton classification scheme and classical results in the theory of permutations
Classification of the line-soliton solutions of KPII
Chakravarty, Sarbarish; Kodama, Yuji
2008-07-01
In the previous papers (notably, Kodama Y 2004 J. Phys. A: Math. Gen. 37 11169-90, Biondini G and Chakravarty S 2006 J. Math. Phys. 47 033514), a large variety of line-soliton solutions of the Kadomtsev-Petviashvili II (KPII) equation was found. The line-soliton solutions are solitary waves which decay exponentially in the (x, y)-plane except along certain rays. In this paper, it is shown that those solutions are classified by asymptotic information of the solution as |y| → ∞. The present work then unravels some interesting relations between the line-soliton classification scheme and classical results in the theory of permutations.
New types of exact solutions for a breaking soliton equation
International Nuclear Information System (INIS)
Mei Jianqin; Zhang Hongqing
2004-01-01
In this paper based on a system of Riccati equations, we present a newly generally projective Riccati equation expansion method and its algorithm, which can be used to construct more new exact solutions of nonlinear differential equations in mathematical physics. A typical breaking soliton equation is chosen to illustrate our algorithm such that more families of new exact solutions are obtained, which contain soliton-like solutions and periodic solutions. This algorithm can also be applied to other nonlinear differential equations
Optical soliton solutions for two coupled nonlinear Schroedinger systems via Darboux transformation
International Nuclear Information System (INIS)
Zhang Haiqiang; Li Juan; Xu Tao; Zhang Yaxing; Hu Wei; Tian Bo
2007-01-01
In nonlinear optical fibers, the vector solitons can be governed by the systems of coupled nonlinear Schroedinger from polarized optical waves in an isotropic medium. Based on the Ablowitz-Kaup-Newell-Segur technology, the Darboux transformation method is successfully applied to two coupled nonlinear Schroedinger systems. With the help of symbolic computation, the bright vector one- and two-soliton solutions including one-peak and two-peak solitons are further constructed via the iterative algorithm of Darboux transformation. Through the figures for several sample solutions, the stable propagation and elastic collisions for these kinds of bright vector solitons are discussed and the possible applications are pointed out in optical communications and relevant optical experiments.In addition, the conserved quantities of such two systems, i.e., the energy, momentum and Hamiltonian, are also presented
Brane Inflation, Solitons and Cosmological Solutions: I
Energy Technology Data Exchange (ETDEWEB)
Chen, P.
2005-01-25
In this paper we study various cosmological solutions for a D3/D7 system directly from M-theory with fluxes and M2-branes. In M-theory, these solutions exist only if we incorporate higher derivative corrections from the curvatures as well as G-fluxes. We take these corrections into account and study a number of toy cosmologies, including one with a novel background for the D3/D7 system whose supergravity solution can be completely determined. Our new background preserves all the good properties of the original model and opens up avenues to investigate cosmological effects from wrapped branes and brane-antibrane annihilation, to name a few. We also discuss in some detail semilocal defects with higher global symmetries, for example exceptional ones, that occur in a slightly different regime of our D3/D7 model. We show that the D3/D7 system does have the required ingredients to realize these configurations as non-topological solitons of the theory. These constructions also allow us to give a physical meaning to the existence of certain underlying homogeneous quaternionic Kahler manifolds.
Two-Dimensional Spatial Solitons in Nematic Liquid Crystals
International Nuclear Information System (INIS)
Zhong Weiping; Xie Ruihua; Goong Chen; Belic, Milivoj; Yang Zhengping
2009-01-01
We study the propagation of spatial solitons in nematic liquid crystals, using the self-similar method. Analytical solutions in the form of self-similar solitons are obtained exactly. We confirm the stability of these solutions by direct numerical simulation, and find that the stable spatial solitons can exist in various forms, such as Gaussian solitons, radially symmetric solitons, multipole solitons, and soliton vortices.
Topological and non-topological soliton solutions to some time
Indian Academy of Sciences (India)
Topological and non-topological soliton solutions to some time-fractional differential equations ... These equations have been widely applied in many branches of nonlinear ... Department of Engineering Sciences, Faculty of Technology and ...
A study on relativistic lagrangian field theories with non-topological soliton solutions
International Nuclear Information System (INIS)
Diaz-Alonso, J.; Rubiera-Garcia, D.
2009-01-01
We perform a general analysis of the dynamic structure of two classes of relativistic lagrangian field theories exhibiting static spherically symmetric non-topological soliton solutions. The analysis is concerned with (multi-) scalar fields and generalized gauge fields of compact semi-simple Lie groups. The lagrangian densities governing the dynamics of the (multi-) scalar fields are assumed to be general functions of the kinetic terms, whereas the gauge-invariant lagrangians are general functions of the field invariants. These functions are constrained by requirements of regularity, positivity of the energy and vanishing of the vacuum energy, defining what we call 'admissible' models. In the scalar case we establish the general conditions which determine exhaustively the families of admissible lagrangian models supporting this kind of finite-energy solutions. We analyze some explicit examples of these different families, which are defined by the asymptotic and central behaviour of the fields of the corresponding particle-like solutions. From the variational analysis of the energy functional, we show that the admissibility constraints and the finiteness of the energy of the scalar solitons are necessary and sufficient conditions for their linear static stability against small charge-preserving perturbations. Furthermore, we perform a general spectral analysis of the dynamic evolution of the small perturbations around the statically stable solitons, establishing their dynamic stability. Next, we consider the case of many-components scalar fields, showing that the resolution of the particle-like field problem in this case reduces to that of the one-component case. The study of these scalar models is a necessary step in the analysis of the gauge fields. In this latter case, we add the requirement of parity invariance to the admissibility constraints. We determine the general conditions defining the families of admissible gauge-invariant models exhibiting finite
Exact multi-line soliton solutions of noncommutative KP equation
International Nuclear Information System (INIS)
Wang, Ning; Wadati, Miki
2003-01-01
A method of solving noncommutative linear algebraic equations plays a key role in the extension of the ∂-bar -dressing on the noncommutative space-time manifold. In this paper, a solution-generating method of noncommutative linear algebraic equations is proposed. By use of the proposed method, a class of multi-line soliton solutions of noncommutative KP (ncKP) equation is constructed explicitly. The method is expected to be of use for constructions of noncommutative soliton equations. The significance of the noncommutativity of coordinates is investigated. It is found that the noncommutativity of the space-time coordinate has a role to split the spatial waveform of the classical multi-line solitons and reform it to a new configuration. (author)
International Nuclear Information System (INIS)
Mihalache, D.; Mazilu, D.; Lederer, F.; Malomed, B.A.; Crasovan, L.-C.; Kartashov, Y.V.; Torner, L.
2005-01-01
The existence and stability of solitons in Bose-Einstein condensates with attractive interatomic interactions, described by the Gross-Pitaevskii equation with a three-dimensional (3D) periodic potential, are investigated in a systematic form. We find a one-parameter family of stable 3D solitons in a certain interval of values of their norm, provided that the strength of the potential exceeds a threshold value. The minimum number of 7 Li atoms in the stable solitons is 60, and the energy of the soliton at the stability threshold is ≅6 recoil energies in the lattice. The respective energy versus norm diagram features two cuspidal points, resulting in a typical swallowtail pattern, which is a generic feature of 3D solitons supported by quasi-two-dimensional or fully dimensional lattice potentials
Soliton solutions of some nonlinear evolution equations with time ...
Indian Academy of Sciences (India)
Abstract. In this paper, we obtain exact soliton solutions of the modified KdV equation, inho- mogeneous nonlinear Schrödinger equation and G(m, n) equation with variable coefficients using solitary wave ansatz. The constraint conditions among the time-dependent coefficients turn out as necessary conditions for the ...
Inverse scattering transform method and soliton solutions for Davey-Stewartson II equation
International Nuclear Information System (INIS)
Arkadiev, V.A.; Pogrebkov, A.K.; Polivanov, M.C.
1989-01-01
The inverse scattering method for Davey-Stewartson II (DS-II) equation including both soliton and continuous spectrum solutions is developed. The explicit formulae for N-soliton solutions are given. Note that our solitons decrease as |z| -2 with z tending to infinity. (author). 8 refs
Guo, Boling; Wang, Yu-Feng; Liu, Nan
2018-01-01
This book provides an up-to-date overview of mathematical theories and research results on solitons, presenting related mathematical methods and applications as well as numerical experiments. Different types of soliton equations are covered along with their dynamical behaviors and applications from physics, making the book an essential reference for researchers and graduate students in applied mathematics and physics.
Liu, Nan; Wen, Xiao-Yong
2018-03-01
Under consideration in this paper is the Kaup-Newell (KN) lattice equation which is an integrable discretization of the KN equation. Infinitely, many conservation laws and discrete N-fold Darboux transformation (DT) for this system are constructed and established based on its Lax representation. Via the resulting N-fold DT, the discrete multi-dark soliton solutions in terms of determinants are derived from non-vanishing background. Propagation and elastic interaction structures of such solitons are shown graphically. Overtaking interaction phenomena between/among the two, three and four solitons are discussed. Numerical simulations are used to explore their dynamical behaviors of such multi-dark solitons. Numerical results show that their evolutions are stable against a small noise. Results in this paper might be helpful for understanding the propagation of nonlinear Alfvén waves in plasmas.
Seed and soliton solutions for Adler's lattice equation
International Nuclear Information System (INIS)
Atkinson, James; Hietarinta, Jarmo; Nijhoff, Frank
2007-01-01
Adler's lattice equation has acquired the status of a master equation among 2D discrete integrable systems. In this paper we derive what we believe are the first explicit solutions of this equation. In particular it turns out to be necessary to establish a non-trivial seed solution from which soliton solutions can subsequently be constructed using the Baecklund transformation. As a corollary we find the corresponding solutions of the Krichever-Novikov equation which is obtained from Adler's equation in a continuum limit. (fast track communication)
Soliton solutions for ABS lattice equations: I. Cauchy matrix approach
Nijhoff, Frank; Atkinson, James; Hietarinta, Jarmo
2009-10-01
In recent years there have been new insights into the integrability of quadrilateral lattice equations, i.e. partial difference equations which are the natural discrete analogues of integrable partial differential equations in 1+1 dimensions. In the scalar (i.e. single-field) case, there now exist classification results by Adler, Bobenko and Suris (ABS) leading to some new examples in addition to the lattice equations 'of KdV type' that were known since the late 1970s and early 1980s. In this paper, we review the construction of soliton solutions for the KdV-type lattice equations and use those results to construct N-soliton solutions for all lattice equations in the ABS list except for the elliptic case of Q4, which is left to a separate treatment.
Soliton solutions of coupled nonlinear Klein-Gordon equations
International Nuclear Information System (INIS)
Alagesan, T.; Chung, Y.; Nakkeeran, K.
2004-01-01
The coupled nonlinear Klein-Gordon equations are analyzed for their integrability properties in a systematic manner through Painleve test. From the Painleve test, by truncating the Laurent series at the constant level term, the Hirota bilinear form is identified, from which one-soliton solutions are derived. Then, the results are generalized to the two, three and N-coupled Klein-Gordon equations
Baryons as solitonic solutions of the chiral sigma model
International Nuclear Information System (INIS)
Bentz, W.; Hartmann, J.; Beck, F.
1996-01-01
Self-consistent solitonic solutions with baryon number one are obtained in the chiral quark sigma model. The translational invariant vacuum is stabilized by a Landau ghost subtraction procedure based on the requirement of the Kaellacute en-Lehmann (KL) representation for the meson propagators. The connection of this ghost free model (KL model) to the more popular Nambu-Jona-Lasinio (NJL) model is discussed in detail. copyright 1996 The American Physical Society
International Nuclear Information System (INIS)
Ventura, J.
1983-01-01
An introductory and partial discussion on the conceptual news and the multiple consequences which originate from the existence of solitons is presented. Preliminary calculations related with the helium superfluid theory are discussed. (L.C.) [pt
Soliton solutions of the (2 + 1)-dimensional Harry Dym equation via Darboux transformation
International Nuclear Information System (INIS)
Halim, A.A.
2008-01-01
This work introduces solitons solutions for the (2 + 1)-dimensional Harry Dym equation using Darboux transformation. The link between the (2 + 1)-dimensional Harry Dym equation and the linear system associated with the modified Kadomtzev-Patvishvili equation is used. Namely, soliton solutions for the linear system associated with the later equation are produced using Darboux transformation. These solutions are inserted in the mentioned link to produce soliton solutions for the (2 + 1)-dimensional Harry Dym equation
Travelling solitons in the parametrically driven nonlinear Schroedinger equation
International Nuclear Information System (INIS)
Barashenkov, I.V.; Zemlyanaya, E.V.; Baer, M.
2000-01-01
We show that the parametrically driven nonlinear Schroedinger equation has wide classes of travelling soliton solutions, some of which are stable. For small driving strengths stable nonpropagating and moving solitons co-exist while strongly forced solitons can only be stable when moving sufficiently fast
Soliton-like solutions to the ordinary Schroedinger equation
Energy Technology Data Exchange (ETDEWEB)
Zamboni-Rached, Michel [Universidade Estadual de Campinas (DMO/FEEC/UNICAMP), Campinas, SP (Brazil). Fac. de Engenharia Eletrica e de Computacao. Dept. de Microondas e Optica; Recami, Erasmo, E-mail: recami@mi.infn.i [Universita Statale di Bergamo, Bergamo (Italy). Facolta di Ingegneria
2011-07-01
In recent times it has been paid attention to the fact that (linear) wave equations admit of soliton-like solutions, known as Localized Waves or Non-diffracting Waves, which propagate without distortion in one direction. Such Localized Solutions (existing also for K-G or Dirac equations) are a priori suitable, more than Gaussian's, for describing elementary particle motion. In this paper we show that, mutatis mutandis, Localized Solutions exist even for the ordinary Schroedinger equation within standard Quantum Mechanics; and we obtain both approximate and exact solutions, also setting forth for them particular examples. In the ideal case such solutions bear infinite energy, as well as plane or spherical waves: we show therefore how to obtain nite-energy solutions. At last, we briefly consider solutions for a particle moving in the presence of a potential. (author)
Soliton-like solutions to the ordinary Schroedinger equation
International Nuclear Information System (INIS)
Zamboni-Rached, Michel; Recami, Erasmo
2011-01-01
In recent times it has been paid attention to the fact that (linear) wave equations admit of soliton-like solutions, known as Localized Waves or Non-diffracting Waves, which propagate without distortion in one direction. Such Localized Solutions (existing also for K-G or Dirac equations) are a priori suitable, more than Gaussian's, for describing elementary particle motion. In this paper we show that, mutatis mutandis, Localized Solutions exist even for the ordinary Schroedinger equation within standard Quantum Mechanics; and we obtain both approximate and exact solutions, also setting forth for them particular examples. In the ideal case such solutions bear infinite energy, as well as plane or spherical waves: we show therefore how to obtain nite-energy solutions. At last, we briefly consider solutions for a particle moving in the presence of a potential. (author)
Yu, Fajun
2015-03-01
We present the nonautonomous discrete bright soliton solutions and their interactions in the discrete Ablowitz-Ladik (DAL) equation with variable coefficients, which possesses complicated wave propagation in time and differs from the usual bright soliton waves. The differential-difference similarity transformation allows us to relate the discrete bright soliton solutions of the inhomogeneous DAL equation to the solutions of the homogeneous DAL equation. Propagation and interaction behaviors of the nonautonomous discrete solitons are analyzed through the one- and two-soliton solutions. We study the discrete snaking behaviors, parabolic behaviors, and interaction behaviors of the discrete solitons. In addition, the interaction management with free functions and dynamic behaviors of these solutions is investigated analytically, which have certain applications in electrical and optical systems.
Multiple periodic-soliton solutions of the (3+1)-dimensional generalised shallow water equation
Li, Ye-Zhou; Liu, Jian-Guo
2018-06-01
Based on the extended variable-coefficient homogeneous balance method and two new ansätz functions, we construct auto-Bäcklund transformation and multiple periodic-soliton solutions of (3 {+} 1)-dimensional generalised shallow water equations. Completely new periodic-soliton solutions including periodic cross-kink wave, periodic two-solitary wave and breather type of two-solitary wave are obtained. In addition, cross-kink three-soliton and cross-kink four-soliton solutions are derived. Furthermore, propagation characteristics and interactions of the obtained solutions are discussed and illustrated in figures.
Surface solitons in waveguide arrays: Analytical solutions.
Kominis, Yannis; Papadopoulos, Aristeidis; Hizanidis, Kyriakos
2007-08-06
A novel phase-space method is employed for the construction of analytical stationary solitary waves located at the interface between a periodic nonlinear lattice of the Kronig-Penney type and a linear or nonlinear homogeneous medium as well as at the interface between two dissimilar nonlinear lattices. The method provides physical insight and understanding of the shape of the solitary wave profile and results to generic classes of localized solutions having either zero or nonzero semi-infinite backgrounds. For all cases, the method provides conditions involving the values of the propagation constant of the stationary solutions, the linear refractive index and the dimensions of each part in order to assure existence of solutions with specific profile characteristics. The evolution of the analytical solutions under propagation is investigated for cases of realistic configurations and interesting features are presented such as their remarkable robustness which could facilitate their experimental observation.
International Nuclear Information System (INIS)
Xu Guiqiong; Li Zhibin
2005-01-01
It is proven that generalized coupled higher-order nonlinear Schroedinger equations possess the Painleve property for two particular choices of parameters, using the Weiss-Tabor-Carnevale method and Kruskal's simplification. Abundant families of periodic wave solutions are obtained by using the Jacobi elliptic function expansion method with the assistance of symbolic manipulation system, Maple. It is also shown that these solutions exactly degenerate to bright soliton, dark soliton and mixed dark and bright soliton solutions with physical interests
Soliton solutions for a quasilinear Schrodinger equation
Directory of Open Access Journals (Sweden)
Duchao Liu
2013-12-01
Full Text Available In this article, critical point theory is used to show the existence of nontrivial weak solutions to the quasilinear Schrodinger equation $$ -\\Delta_p u-\\frac{p}{2^{p-1}}u\\Delta_p(u^2=f(x,u $$ in a bounded smooth domain $\\Omega\\subset\\mathbb{R}^{N}$ with Dirichlet boundary conditions.
Solitons and separable elliptic solutions of the sine-Gordon equation
International Nuclear Information System (INIS)
Bryan, A.C.; Haines, C.R.; Stuart, A.E.G.
1979-01-01
It is pointed out that the two-soliton (antisoliton) solutions of the sine-Gordon equation may be obtained as limiting cases of a separable, two-parameter family of elliptic solutions. The solitons are found on the boundary of the parameter space for the elliptic solutions when the latter are considered over their usual complex domain. (Auth.)
International Nuclear Information System (INIS)
Ma Songhua; Fang Jianping; Zheng Chunlong
2009-01-01
By means of an extended mapping method and a variable separation method, a series of solitary wave solutions, periodic wave solutions and variable separation solutions to the (2 + 1)-dimensional breaking soliton system is derived.
Energy Technology Data Exchange (ETDEWEB)
Chaudhuri, A. [B.K.C. College, Department of Physics, Kolkata (India); Chaudhuri, S. [University of Burdwan, Department of Physics, Burdwan (India)
2017-11-15
In the paper, magnetostatic solutions of the Einstein-Maxwell field equations are generated from the gravitational two-soliton solutions of a stationary mass. Using the soliton technique of Belinskii and Zakharov (Sov Phys JETP 48:985, 1978, Sov Phys JETP 50:1, 1979), we construct diagonal two-soliton solutions of Einstein's gravitational field equations for an axially symmetric stationary space-time and investigate some properties of the generated stationary gravitational metric. Magnetostatic solutions corresponding to the generated stationary gravitational solutions are then constructed using the transformation technique of Das and Chaudhuri (Pramana J Phys 40:277, 1993). The mass and the dipole moment of the source are evaluated. In our analysis we make use of a second transformation (Chaudhuri in Pramana J Phys 58:449, 2002), probably for the first time in the literature, to generate magnetostatic solutions from the stationary gravitational two-soliton solutions which give us simple and straightforward expressions for the mass and the magnetic dipole moment. (orig.)
On existence of soliton solutions of arbitrary-order system of nonlinear Schrodinger equations
International Nuclear Information System (INIS)
Zhestkov, S.V.
2003-01-01
The soliton solutions are constructed for the system of arbitrary-order coupled nonlinear Schrodinger equations . The necessary and sufficient conditions of existence of these solutions are obtained. It is shown that the maximum number of solitons in nondegenerate case is 4L, where L is order of the system. (author)
International Nuclear Information System (INIS)
Liu, Rong-Xiang; Tian, Bo; Liu, Li-Cai; Qin, Bo; Lü, Xing
2013-01-01
In this paper we investigate a fourth-order dispersive nonlinear Schrödinger equation, which governs the dynamics of a one-dimensional anisotropic Heisenberg ferromagnetic spin chain with the octuple–dipole interaction in condensed-matter physics as well as the alpha helical proteins with higher-order excitations and interactions in biophysics. Beyond the existing constraint, upon the introduction of an auxiliary function, bilinear forms and N-soliton solutions are constructed with the Hirota method. Asymptotic analysis on the two-soliton solutions indicates that the soliton interactions are elastic. Soliton velocity varies linearly with the coefficient of discreteness and higher-order magnetic interactions. Bound-state solitons can also exist under certain conditions. Period of a bound-state soliton is inversely correlated to the coefficient of discreteness and higher-order magnetic interactions. Interactions among the three solitons are all pairwise elastic
International Nuclear Information System (INIS)
Kiknadze, N.A.; Khelashvili, A.A.
1990-01-01
The problem on stability of classical soliton solutions is studied from the unique point of view: the Legendre condition - necessary condition of existence of weak local minimum for energy functional (term soliton is used here in the wide sense) is used. Limits to parameters of the model Lagrangians are obtained; it is shown that there is no soliton stabilization in some of them despite the phenomenological achievements. The Jacoby sufficient condition is discussed
Trullinger, SE; Pokrovsky, VL
1986-01-01
In the twenty years since Zabusky and Kruskal coined the term ``soliton'', this concept changed the outlook on certain types of nonlinear phenomena and found its way into all branches of physics. The present volume deals with a great variety of applications of the new concept in condensed-matter physics, which is particularly reached in experimentally observable occurrences. The presentation is not centred around the mathematical aspects; the emphasis is on the physical nature of the nonlinear phenomena occurring in particular situations.With its emphasis on concrete, mostly experime
Soliton solutions of an integrable nonlinear Schrödinger equation with quintic terms.
Chowdury, A; Kedziora, D J; Ankiewicz, A; Akhmediev, N
2014-09-01
We present the fifth-order equation of the nonlinear Schrödinger hierarchy. This integrable partial differential equation contains fifth-order dispersion and nonlinear terms related to it. We present the Lax pair and use Darboux transformations to derive exact expressions for the most representative soliton solutions. This set includes two-soliton collisions and the degenerate case of the two-soliton solution, as well as beating structures composed of two or three solitons. Ultimately, the new quintic operator and the terms it adds to the standard nonlinear Schrödinger equation (NLSE) are found to primarily affect the velocity of solutions, with complicated flow-on effects. Furthermore, we present a new structure, composed of coincident equal-amplitude solitons, which cannot exist for the standard NLSE.
An infinite number of stationary soliton solutions to the five-dimensional vacuum Einstein equation
International Nuclear Information System (INIS)
Azuma, Takahiro; Koikawa, Takao
2006-01-01
We obtain an infinite number of soliton solutions to the five-dimensional stationary Einstein equation with axial symmetry by using the inverse scattering method. We start with the five-dimensional Minkowski space as a seed metric to obtain these solutions. The solutions are characterized by two soliton numbers and a constant appearing in the normalization factor which is related to a coordinate condition. We show that the (2, 0)-soliton solution is identical to the Myers-Perry solution with one angular momentum variable by imposing a condition on the relation between parameters. We also show that the (2, 2)-soliton solution is different from the black ring solution discovered by Emparan and Reall, although one component of the two metrics can be identical. (author)
International Nuclear Information System (INIS)
Yong Chen; Qi Wang
2005-01-01
In this paper, we extend the algebraic method proposed by Fan (Chaos, Solitons and Fractals 20 (2004) 609) and the improved extended tanh method by Yomba (Chaos, Solitons and Fractals 20 (2004) 1135) to uniformly construct a series of soliton-like solutions and double-like periodic solutions for nonlinear partial differential equations (NPDE). Some new soliton-like solutions and double-like periodic solutions of a (2 + 1)-dimensional dispersive long wave equation are obtained
Multiloop soliton and multibreather solutions of the short pulse model equation
International Nuclear Information System (INIS)
Matsuno, Yoshimasa
2007-01-01
We develop a systematic procedure for constructing the multisoliton solutions of the short pulse (SP) model equation which describes the propagation of ultra-short pulses in nonlinear medica. We first introduce a novel hodograph transformation to convert the SP equation into the sine-Gordon (sG) equation. With the soliton solutions of the sG equation, the system of linear partial differential equations governing the inverse mapping can be integrated analytically to obtain the soliton solutions of the SP equation in the form of the parametric representation. By specifying the soliton parameters, we obtain the multiloop and multibreather solutions. We investigate the asymptotic behavior of both solutions and confirm their solitonic feature. The nonsingular breather solutions may play an important role in studying the propagation of ultra-short pulses in an optical fibre. (author)
Holomorphic Vector Bundles Corresponding to some Soliton Solutions of the Ward Equation
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Zhu, Xiujuan, E-mail: yzzhuxiujuan@sina.com [Jiangsu Second Normal University, School of Mathematics and Information Technology (China)
2015-12-15
Holomorphic vector bundles corresponding to the static soliton solution of the Ward equation were explicitly presented by Ward in terms of a meromorphic framing. Bundles (for simplicity, “bundle” is to be taken throughout to mean “holomorphic vector bundle”) corresponding to all Ward k-soliton solutions whose extended solutions have only simple poles, and some Ward 2-soliton solutions whose extended solutions have only a second-order pole, were explicitly described by us in a previous paper. In this paper, we go on to present some bundles corresponding to soliton-antisoliton solutions of the Ward equation, and Ward 3-soliton solutions whose extended solutions have a simple pole and a double pole. To give some more interpretation of the bundles, we study the second Chern number of the corresponded bundles and find that it can be obtained directly from the patching matrices. We also point out some information about bundles corresponding to Ward soliton solutions whose extended solutions have general pole data at the end of the paper.
General N-Dark Soliton Solutions of the Multi-Component Mel'nikov System
Han, Zhong; Chen, Yong; Chen, Junchao
2017-07-01
A general form of N-dark soliton solutions of the multi-component Mel'nikov system are presented. Taking the coupled Mel'nikov system comprised of two-component short waves and one-component long wave as an example, its general N-dark-dark soliton solutions in Gram determinant form are constructed through the KP hierarchy reduction method. The dynamics of single dark-dark soliton and two dark-dark solitons are discussed in detail. It can be shown that the collisions of dark-dark solitons are elastic and energies of the solitons in different components completely transmit through. In addition, the dark-dark soliton bound states including both stationary and moving cases are also investigated. An interesting feature for the coupled Mel'nikov system is that the stationary dark-dark soliton bound states can exist for all possible combinations of nonlinearity coefficients including positive, negative and mixed types, while the moving case are possible when nonlinearity coefficients take opposite signs or they are both negative.
The soliton solution of the PHI24 field theory in the Hartree approximation
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Altenbokum, M.
1984-01-01
In this thesis in a simple model which possesses at the classical level a soliton solution a quantum-mechanical soliton sector shall be constructed in a Hartree-Fock approximation without application of semiclassical procedures. To this belongs beside the determination of the excitation spectrum of the applied Hamiltonian the knowledge of the corresponding infinitely-much eigenfunctions. The existing translational invariance of a classical soliton solution which implies the existence of a degenerated ground state by presence of a massless excitation is removed by quantum fluctuations. By removing of this degeneration conventional approximation procedures for this sector of the Hilbert space become for the first time immediately possible. (HSI) [de
Energy Technology Data Exchange (ETDEWEB)
Abram, I [Centre National d' Etudes des Telecommunications (CNET), 196 Avenue Henri Ravera, F-92220 Bagneux (France)
1999-02-01
Two of the most remarkable properties of light - squeezing and solitons - are being combined in a new generation of experiments that could revolutionize optics and communications. One area of application concerns the transmission and processing of classical (binary) information, in which the presence or absence of a soliton in a time-window corresponds to a ''1'' or ''0'', as in traditional optical-fibre communications. However, since solitons occur at fixed power levels, we do not have the luxury of being able to crank up the input power to improve the signal-to-noise ratio at the receiving end. Nevertheless, the exploitation of quantum effects such as squeezing could help to reduce noise and improve fidelity. In long-distance communications, where the signal is amplified every 50-100 kilometres or so, the soliton pulse is strongest just after the amplifier. Luckily this is where the bulk of the nonlinear interaction needed to maintain the soliton shape occurs. However, the pulse gets weaker as it propagates along the fibre, so the nonlinear interaction also becomes weakerand weaker. This means that dispersive effects become dominant until the next stage of amplification, where the nonlinearity takes over again. One problem is that quantum fluctuations in the amplifiers lead to random jumps in the central wavelength of the individual solitons, and this results in a random variation of the speed of individual solitons in the fibre. Several schemes have been devised to remove this excess noise and bring the train of solitons back to the orderly behaviour characteristic of a stable coherent state (e.g. the solitons could be passed through a spectral filter). Photon-number squeezing could also play a key role in solving this problem. For example, if the solitons are number-squeezed immediately after amplification, there will be a smaller uncertainty in the nonlinearity that keeps the soliton in shape and, therefore, there will also be less noise in the soliton. This
A perturbation method for dark solitons based on a complete set of the squared Jost solutions
International Nuclear Information System (INIS)
Ao Shengmei; Yan Jiaren
2005-01-01
A perturbation method for dark solitons is developed, which is based on the construction and the rigorous proof of the complete set of squared Jost solutions. The general procedure solving the adiabatic solution of perturbed nonlinear Schroedinger + equation, the time-evolution equation of dark soliton parameters and a formula for calculating the first-order correction are given. The method can also overcome the difficulties resulting from the non-vanishing boundary condition
Arshad, Muhammad; Seadawy, Aly R.; Lu, Dianchen
2017-12-01
In optical fibers, the higher order non-linear Schrödinger equation (NLSE) with cubic quintic nonlinearity describes the propagation of extremely short pulses. We constructed bright and dark solitons, solitary wave and periodic solitary wave solutions of generalized higher order NLSE in cubic quintic non Kerr medium by applying proposed modified extended mapping method. These obtained solutions have key applications in physics and mathematics. Moreover, we have also presented the formation conditions on solitary wave parameters in which dark and bright solitons can exist for this media. We also gave graphically the movement of constructed solitary wave and soliton solutions, that helps to realize the physical phenomena's of this model. The stability of the model in normal dispersion and anomalous regime is discussed by using the modulation instability analysis, which confirms that all constructed solutions are exact and stable. Many other such types of models arising in applied sciences can also be solved by this reliable, powerful and effective method.
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Guo Rui; Tian Bo; Lue Xing; Zhang Haiqiang; Xu Tao
2010-01-01
For the propagation of the ultrashort pulses in an inhomogeneous multi-component nonlinear medium, a system of coupled equations is analytically studied in this paper. Painleve analysis shows that this system admits the Painleve property under some constraints. By means of the Ablowitz-Kaup-Newell-Segur procedure, the Lax pair of this system is derived, and the Darboux transformation (DT) is constructed with the help of the obtained Lax pair. With symbolic computation, the soliton solutions are obtained by virtue of the DT algorithm. Figures are plotted to illustrate the dynamical features of the soliton solutions. Characteristics of the solitons propagating in an inhomogeneous multi-component nonlinear medium are discussed: (i) Propagation of one soliton and two-peak soliton; (ii) Elastic interactions of the parabolic two solitons; (iii) Overlap phenomenon between two solitons; (iv) Collision of two head-on solitons and two head-on two-peak solitons; (v) Two different types of interactions of the three solitons; (vi) Decomposition phenomenon of one soliton into two solitons. The results might be useful in the study on the ultrashort-pulse propagation in the inhomogeneous multi-component nonlinear media. (electromagnetism, optics, acoustics, heat transfer, classical mechanics, and fluid dynamics)
Soliton-like solutions to the GKdV equation by extended mapping method
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Wu Ranchao; Sun Jianhua
2007-01-01
In this note, many new exact solutions of the generalized KdV equation, such as rational solutions, periodic solutions like Jacobian elliptic and triangular functions, soliton-like solutions, are constructed by symbolic computation and the extended mapping method, with the auxiliary ordinary equation replaced by a more general one
Relativistic solitons and pulsars
Energy Technology Data Exchange (ETDEWEB)
Karpman, V I [Inst. of Terrestrial Magnetism, Ionosphere, and Radio-Wave Propagation, Moscow; Norman, C A; ter Haar, D; Tsytovich, V N
1975-05-01
A production mechanism for stable electron bunches or sheets of localized electric fields is investigated which may account for pulsar radio emission. Possible soliton phenomena in a one-dimensional relativistic plasma are analyzed, and it is suggested that the motion of a relativistic soliton, or ''relaton'', along a curved magnetic-field line may produce radio emission with the correct polarization properties. A general MHD solution is obtained for relatons, the radiation produced by a relativistic particle colliding with a soliton is evaluated, and the emission by a soliton moving along a curved field line is estimated. It is noted that due to a number of severe physical restrictions, curvature radiation is not a very likely solution to the problem of pulsar radio emission. (IAA)
Vertex dynamics in multi-soliton solutions of Kadomtsev–Petviashvili II equation
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Zarmi, Yair
2014-01-01
A functional of the solution of the Kadomtsev–Petviashvili II equation maps multi-soliton solutions onto systems of vertices—structures that are localized around soliton junctions. A solution with one junction is mapped onto a single vertex, which emulates a free, spatially extended, particle. In solutions with several junctions, each junction is mapped onto a vertex. Moving in the x–y plane, the vertices collide, coalesce upon collision and then split up. When well separated, they emulate free particles. Multi-soliton solutions, whose structure does not change under space–time inversion as |t| → ∞, are mapped onto vertex systems that undergo elastic collisions. Solutions, whose structure does change, are mapped onto systems that undergo inelastic collisions. The inelastic vertex collisions generated from the infinite family of (M,1) solutions (M external solitons, (M − 2) Y-shaped soliton junctions, M ⩾ 4) play a unique role: the only definition of vertex mass consistent with momentum conservation in these collisions is the spatial integral of the vertex profile. This definition ensures, in addition, that, in these collisions, the total mass and kinetic energy due to the motion in the y-direction are conserved. In general, the kinetic energy due to the motion in the x-direction is not conserved in these collisions. (paper)
Soliton structure in crystalline acetanilide
International Nuclear Information System (INIS)
Eilbeck, J.C.; Lomdahl, P.S.; Scott, A.C.
1984-01-01
The theory of self-trapping of amide I vibrational energy in crystalline acetanilide is studied in detail. A spectrum of stationary, self-trapped (soliton) solutions is determined and tested for dynamic stability. Only those solutions for which the amide I energy is concentrated near a single molecule were found to be stable. Exciton modes were found to be unstable to decay into solitons
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Dai, Chao-Qing; Qin, Zhen-Yun; Zheng, Chun-Long
2012-01-01
Multi-soliton solutions to the modified nonlinear Schrödinger equation (MNLSE) with variable coefficients (VCs) in inhomogeneous fibers are obtained with the help of mapping transformation, which reduces the VC MNLSE into a constant-coefficient MNLSE. Based on the analytical solutions, one- and two-soliton transmissions in the proper dispersion management systems are discussed. The sustainment of solitons and the disappearance of breathers for the VC MNLSE are first reported here. (paper)
Classical solutions in quantum field theory solitons and instantons in high energy physics
Weinberg, Erick J
2012-01-01
Classical solutions play an important role in quantum field theory, high energy physics and cosmology. Real-time soliton solutions give rise to particles, such as magnetic monopoles, and extended structures, such as domain walls and cosmic strings, that have implications for early universe cosmology. Imaginary-time Euclidean instantons are responsible for important nonperturbative effects, while Euclidean bounce solutions govern transitions between metastable states. Written for advanced graduate students and researchers in elementary particle physics, cosmology and related fields, this book brings the reader up to the level of current research in the field. The first half of the book discusses the most important classes of solitons: kinks, vortices and magnetic monopoles. The cosmological and observational constraints on these are covered, as are more formal aspects, including BPS solitons and their connection with supersymmetry. The second half is devoted to Euclidean solutions, with particular emphasis on ...
Manafian, Jalil; Foroutan, Mohammadreza; Guzali, Aref
2017-11-01
This paper examines the effectiveness of an integration scheme which is called the extended trial equation method (ETEM) for solving a well-known nonlinear equation of partial differential equations (PDEs). In this respect, the Lakshmanan-Porsezian-Daniel (LPD) equation with Kerr and power laws of nonlinearity which describes higher-order dispersion, full nonlinearity and spatiotemporal dispersion is considered, and as an achievement, a series of exact travelling-wave solutions for the aforementioned equation is formally extracted. Explicit new exact solutions are derived in different form such as dark solitons, bright solitons, solitary wave, periodic solitary wave, rational function, and elliptic function solutions of LPD equation. The movement of obtained solutions is shown graphically, which helps to understand the physical phenomena of this optical soliton equation. Many other such types of nonlinear equations arising in basic fabric of communications network technology and nonlinear optics can also be solved by this method.
Institute of Scientific and Technical Information of China (English)
张解放; 吴锋民
2002-01-01
We study an approach to constructing multiple soliton solutions of the (3+1)-dimensional nonlinear evolution equation. We take the (3+1)-dimensional Jimbo-Miwa (JM) equation as an example. Using the extended homogeneous balance method, one can find a Backlund transformation to decompose the (3+1)-dimensional JM equation into a linear partial differential equation and two bilinear partial differential equations. Starting from these linear and bilinear partial differential equations, some multiple soliton solutions for the (3+1)-dimensional JM equation are obtained by introducing a class of formal solutions.
International Nuclear Information System (INIS)
Kaya, Dogan; El-Sayed, Salah M.
2003-01-01
In this Letter we present an Adomian's decomposition method (shortly ADM) for obtaining the numerical soliton-like solutions of the potential Kadomtsev-Petviashvili (shortly PKP) equation. We will prove the convergence of the ADM. We obtain the exact and numerical solitary-wave solutions of the PKP equation for certain initial conditions. Then ADM yields the analytic approximate solution with fast convergence rate and high accuracy through previous works. The numerical solutions are compared with the known analytical solutions
Soliton and periodic solutions for higher order wave equations of KdV type (I)
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Khuri, S.A.
2005-01-01
The aim of the paper is twofold. First, a new ansaetze is introduced for the construction of exact solutions for higher order wave equations of KdV type (I). We show the existence of a class of discontinuous soliton solutions with infinite spikes. Second, the projective Riccati technique is implemented as an alternate approach for obtaining new exact solutions, solitary solutions, and periodic wave solutions
Singular solitons and other solutions to a couple of nonlinear wave equations
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Inc Mustafa; Ulutaş Esma; Biswas Anjan
2013-01-01
This paper addresses the extended (G'/G)-expansion method and applies it to a couple of nonlinear wave equations. These equations are modified the Benjamin—Bona—Mahoney equation and the Boussinesq equation. This extended method reveals several solutions to these equations. Additionally, the singular soliton solutions are revealed, for these two equations, with the aid of the ansatz method
Highly stable families of soliton molecules in fiber-optic systems
Moubissi, A.-B.; Tchofo Dinda, P.; Nse Biyoghe, S.
2018-04-01
We develop an efficient approach to the design of families of single solitons and soliton molecules most suited to a given fiber system. The obtained solitonic entities exhibit very high stability, with a robustness which allows them to propagate over thousands of kilometers and to survive collisions with other solitonic entities. Our approach enables the generation of a large number of solitonic entities, including families of single solitons and two-soliton molecules, which can be distinguished sufficiently by their respective profiles or energy levels, and so can be easily identifiable and detectable without ambiguity. We discuss the possible use of such solitonic entities as symbols of a multi-level modulation format in fiber-optic communication systems.
International Nuclear Information System (INIS)
Wu Jianping
2010-01-01
Based on the Hirota bilinear form, a simple approach without employing the standard perturbation technique, is presented for constructing a novel N-soliton solution for a (3+1)-dimensional nonlinear evolution equation. Moreover, the novel N-soliton solution is shown to have resonant behavior with the aid of Mathematica. (general)
Soliton solutions of the quantum Zakharov-Kuznetsov equation which arises in quantum magneto-plasmas
Sindi, Cevat Teymuri; Manafian, Jalil
2017-02-01
In this paper, we extended the improved tan(φ/2)-expansion method (ITEM) and the generalized G'/G-expansion method (GGEM) proposed by Manafian and Fazli (Opt. Quantum Electron. 48, 413 (2016)) to construct new types of soliton wave solutions of nonlinear partial differential equations (NPDEs). Moreover, we use of the improvement of the Exp-function method (IEFM) proposed by Jahani and Manafian (Eur. Phys. J. Plus 131, 54 (2016)) for obtaining solutions of NPDEs. The merit of the presented three methods is they can find further solutions to the considered problems, including soliton, periodic, kink, kink-singular wave solutions. This paper studies the quantum Zakharov-Kuznetsov (QZK) equation by the aid of the improved tan(φ/2)-expansion method, the generalized G'/G-expansion method and the improvement of the Exp-function method. Moreover, the 1-soliton solution of the modified QZK equation with power law nonlinearity is obtained by the aid of traveling wave hypothesis with the necessary constraints in place for the existence of the soliton. Comparing our new results with Ebadi et al. results (Astrophys. Space Sci. 341, 507 (2012)), namely, G'/G-expansion method, exp-function method, modified F-expansion method, shows that our results give further solutions. Finally, these solutions might play an important role in engineering, physics and applied mathematics fields.
Bright-Dark Mixed N-Soliton Solutions of the Multi-Component Mel'nikov System
Han, Zhong; Chen, Yong; Chen, Junchao
2017-10-01
By virtue of the Kadomtsev-Petviashvili (KP) hierarchy reduction technique, we construct the general bright-dark mixed N-soliton solution to the multi-component Mel'nikov system. This multi-component system comprised of multiple (say M) short-wave components and one long-wave component with all possible combinations of nonlinearities including all-positive, all-negative and mixed types. Firstly, the two-bright-one-dark (2-b-1-d) and one-bright-two-dark (1-b-2-d) mixed N-soliton solutions in short-wave components of the three-component Mel'nikov system are derived in detail. Then we extend our analysis to the M-component Mel'nikov system to obtain its general mixed N-soliton solution. The formula obtained unifies the all-bright, all-dark and bright-dark mixed N-soliton solutions. For the collision of two solitons, an asymptotic analysis shows that for an M-component Mel'nikov system with M ≥ 3, inelastic collision takes place, resulting in energy exchange among the short-wave components supporting bright solitons only if the bright solitons appear in at least two short-wave components. In contrast, the dark solitons in the short-wave components and the bright solitons in the long-wave component always undergo elastic collision which is only accompanied by a position shift.
Soliton solutions of the two-dimensional KdV-Burgers equation by homotopy perturbation method
International Nuclear Information System (INIS)
Molabahrami, A.; Khani, F.; Hamedi-Nezhad, S.
2007-01-01
In this Letter, the He's homotopy perturbation method (HPM) to finding the soliton solutions of the two-dimensional Korteweg-de Vries Burgers' equation (tdKdVB) for the initial conditions was applied. Numerical solutions of the equation were obtained. The obtained solutions, in comparison with the exact solutions admit a remarkable accuracy. The results reveal that the HPM is very effective and simple
Exact soliton solutions of the generalized Gross-Pitaevskii equation based on expansion method
Directory of Open Access Journals (Sweden)
Ying Wang
2014-06-01
Full Text Available We give a more generalized treatment of the 1D generalized Gross-Pitaevskii equation (GGPE with variable term coefficients. External harmonic trapping potential is fully considered and the nonlinear interaction term is of arbitrary polytropic index of superfluid wave function. We also eliminate the interdependence between variable coefficients of the equation terms avoiding the restrictions that occur in some other works. The exact soliton solutions of the GGPE are obtained through the delicate combined utilization of modified lens-type transformation and F-expansion method with dominant features like soliton type properties highlighted.
Darboux transformation and soliton solutions for the Boiti-Pempinelli-Tu (BPT) hierarchy
International Nuclear Information System (INIS)
Wang Jiong
2005-01-01
Starting from a spectral problem, we derive the well-known Boiti-Pempinelli-Tu (BPT) hierarchy. An explicit and universal Darboux transformation for the whole hierarchy is constructed. The soliton solutions for the BPT hierarchy are obtained by applying the Darboux transformation
New soliton solution to the longitudinal wave equation in a magneto-electro-elastic circular rod
Directory of Open Access Journals (Sweden)
Aly R. Seadawy
2018-03-01
Full Text Available This paper examines the effectiveness of an integration scheme which called the extended trial equation method (ETEM in exactly solving a well-known nonlinear equation of partial differential equations (PDEs. In this respect, the longitudinal wave equation (LWE that arises in mathematical physics with dispersion caused by the transverse Poisson’s effect in a magneto-electro-elastic (MEE circular rod, which a series of exact traveling wave solutions for the aforementioned equation is formally extracted. Explicit new exact solutions are derived in different form such as dark solitons, bright solitons, solitary wave, periodic solitary wave, rational function, and elliptic function solutions of the longitudinal wave equation. The movements of obtained solutions are shown graphically, which helps to understand the physical phenomena of this longitudinal wave equation. Many other such types of nonlinear equations arising in non-destructive evaluation of structures made of the advanced MEE material can also be solved by this method. Keywords: Extended trial equation method, Longitudinal wave equation in a MEE circular rod, Dark solitons, Bright solitons, Solitary wave, Periodic solitary wave
Yu, Ming-Xiao; Tian, Bo; Chai, Jun; Yin, Hui-Min; Du, Zhong
2017-10-01
In this paper, we investigate a nonlinear fiber described by a (2+1)-dimensional complex Ginzburg-Landau equation with the chromatic dispersion, optical filtering, nonlinear and linear gain. Bäcklund transformation in the bilinear form is constructed. With the modified bilinear method, analytic soliton solutions are obtained. For the soliton, the amplitude can decrease or increase when the absolute value of the nonlinear or linear gain is enlarged, and the width can be compressed or amplified when the absolute value of the chromatic dispersion or optical filtering is enhanced. We study the stability of the numerical solutions numerically by applying the increasing amplitude, embedding the white noise and adding the Gaussian pulse to the initial values based on the analytic solutions, which shows that the numerical solutions are stable, not influenced by the finite initial perturbations.
New soliton solution to the longitudinal wave equation in a magneto-electro-elastic circular rod
Seadawy, Aly R.; Manafian, Jalil
2018-03-01
This paper examines the effectiveness of an integration scheme which called the extended trial equation method (ETEM) in exactly solving a well-known nonlinear equation of partial differential equations (PDEs). In this respect, the longitudinal wave equation (LWE) that arises in mathematical physics with dispersion caused by the transverse Poisson's effect in a magneto-electro-elastic (MEE) circular rod, which a series of exact traveling wave solutions for the aforementioned equation is formally extracted. Explicit new exact solutions are derived in different form such as dark solitons, bright solitons, solitary wave, periodic solitary wave, rational function, and elliptic function solutions of the longitudinal wave equation. The movements of obtained solutions are shown graphically, which helps to understand the physical phenomena of this longitudinal wave equation. Many other such types of nonlinear equations arising in non-destructive evaluation of structures made of the advanced MEE material can also be solved by this method.
Arshad, Muhammad; Seadawy, Aly R.; Lu, Dianchen
2018-01-01
In mono-mode optical fibers, the higher order non-linear Schrödinger equation (NLSE) describes the propagation of enormously short light pulses. We constructed optical solitons and, solitary wave solutions of higher order NLSE mono-mode optical fibers via employing modified extended mapping method which has important applications in Mathematics and physics. Furthermore, the formation conditions are also given on parameters in which optical bright and dark solitons can exist for this media. The moment of the obtained solutions are also given graphically, that helps to realize the physical phenomena's of this model. The modulation instability analysis is utilized to discuss the model stability, which verifies that all obtained solutions are exact and stable. Many other such types of models arising in applied sciences can also be solved by this reliable, powerful and effective method. The method can also be functional to other sorts of higher order nonlinear problems in contemporary areas of research.
International Nuclear Information System (INIS)
Barashenkov, I.V.; Getmanov, B.S.; Kovtun, V.E.
1992-01-01
The scheme for unified description of integrable relativistic massive systems provides an inverse scattering formalism that covers universally all (1+1)- dimensional systems of this kind. In this work we construct the N-soliton solution (over an arbitrary background) for some generic system which is associated with the sl(2,C) case of the scheme and whose reductions include the complex sine-Gordon equation, the massive Thirring model and other equations, both in the Euclidean and Minkowski spaces. Thus the N-soliton solutions for all these systems emerge in a unified form differing only in the type of constraints imposed on their parameters. In an earlier paper the case of the zero background was considered while here we concentrate on the case of the non-vanishing constant background i.e., on the N-kink solutions. (author). 18 refs
Du, Zhong; Tian, Bo; Xie, Xi-Yang; Chai, Jun; Wu, Xiao-Yu
2018-04-01
In this paper, investigation is made on a Kadomtsev-Petviashvili-based system, which can be seen in fluid dynamics, biology and plasma physics. Based on the Hirota method, bilinear form and Bäcklund transformation (BT) are derived. N-soliton solutions in terms of the Wronskian are constructed, and it can be verified that the N-soliton solutions in terms of the Wronskian satisfy the bilinear form and Bäcklund transformation. Through the N-soliton solutions in terms of the Wronskian, we graphically obtain the kink-dark-like solitons and parallel solitons, which keep their shapes and velocities unchanged during the propagation.
Extended Soliton Solutions in an Effective Action for SU(2 Yang-Mills Theory
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Nobuyuki Sawado
2006-01-01
Full Text Available The Skyrme-Faddeev-Niemi (SFN model which is an O(3 σ model in three dimensional space up to fourth-order in the first derivative is regarded as a low-energy effective theory of SU(2 Yang-Mills theory. One can show from the Wilsonian renormalization group argument that the effective action of Yang-Mills theory recovers the SFN in the infrared region. However, the theory contains an additional fourth-order term which destabilizes the soliton solution. We apply the perturbative treatment to the second derivative term in order to exclude (or reduce the ill behavior of the original action and show that the SFN model with the second derivative term possesses soliton solutions.
Dynamical creation of complex vector solitons in spinor Bose-Einstein condensates
International Nuclear Information System (INIS)
Xiong Bo; Gong Jiangbin
2010-01-01
By numerical simulations of the Gross-Pitaevskii mean-field equations, we show that the dynamical creation of stable complex vector solitons in a homogeneous spin-1 Bose-Einstein condensate can be achieved by applying a localized magnetic field for a certain duration, with the initial uniform density prepared differently for the formation of different vector solitons. In particular, it is shown that stable dark-bright-dark vector solitons, dark-bright-bright vector solitons, and other analogous solutions can be dynamically created. It is also found that the peak intensity and the group velocity of the vector solitons thus generated can be tuned by adjusting the applied magnetic field. Extensions of our approach also allow for the creation of vector-soliton chains or the pumping of many vector solitons. The results can be useful for possible vector-soliton-based applications of dilute Bose-Einstein condensates.
Inverse Scattering Method and Soliton Solution Family for String Effective Action
International Nuclear Information System (INIS)
Ya-Jun, Gao
2009-01-01
A modified Hauser–Ernst-type linear system is established and used to develop an inverse scattering method for solving the motion equations of the string effective action describing the coupled gravity, dilaton and Kalb–Ramond fields. The reduction procedures in this inverse scattering method are found to be fairly simple, which makes the proposed inverse scattering method applied fine and effective. As an application, a concrete family of soliton solutions for the considered theory is obtained
Exact soliton-like solutions of the radial Gross–Pitaevskii equation
International Nuclear Information System (INIS)
Toikka, L A; Hietarinta, J; Suominen, K-A
2012-01-01
We construct exact ring soliton-like solutions of the cylindrically symmetric (i.e. radial) Gross–Pitaevskii equation with a potential, using the similarity transformation method. Depending on the choice of the allowed free functions, the solutions can take the form of stationary dark or bright rings whose time dependence is in the phase dynamics only, or oscillating and bouncing solutions, related to the second Painlevé transcendent. In each case the potential can be chosen to be time independent. (paper)
International Nuclear Information System (INIS)
Koeppel, T.; Harvey, M.
1984-06-01
A new numerical method is applied to solving the equations of motion of the Friedberg-Lee Soliton model for both ground and spherically symmetric excited states. General results have been obtained over a wide range of parameters. Critical coupling constants and critical particle numbers have been determined below which soliton solutions cease to exist. The static properties of the proton are considered to show that as presently formulated the model fails to fit all experimental data for any set of parameters
International Nuclear Information System (INIS)
Biswas, Anjan
2009-01-01
In this Letter, the 1-soliton solution of the Zakharov-Kuznetsov equation with power law nonlinearity and nonlinear dispersion along with time-dependent coefficients is obtained. There are two models for this kind of an equation that are studied. The constraint relation between these time-dependent coefficients is established for the solitons to exist. Subsequently, this equation is again analysed with generalized evolution. The solitary wave ansatz is used to carry out this investigation.
Khusnutdinova, K. R.; Stepanyants, Y. A.; Tranter, M. R.
2018-02-01
We study solitary wave solutions of the fifth-order Korteweg-de Vries equation which contains, besides the traditional quadratic nonlinearity and third-order dispersion, additional terms including cubic nonlinearity and fifth order linear dispersion, as well as two nonlinear dispersive terms. An exact solitary wave solution to this equation is derived, and the dependence of its amplitude, width, and speed on the parameters of the governing equation is studied. It is shown that the derived solution can represent either an embedded or regular soliton depending on the equation parameters. The nonlinear dispersive terms can drastically influence the existence of solitary waves, their nature (regular or embedded), profile, polarity, and stability with respect to small perturbations. We show, in particular, that in some cases embedded solitons can be stable even with respect to interactions with regular solitons. The results obtained are applicable to surface and internal waves in fluids, as well as to waves in other media (plasma, solid waveguides, elastic media with microstructure, etc.).
Soliton solution for nonlinear partial differential equations by cosine-function method
International Nuclear Information System (INIS)
Ali, A.H.A.; Soliman, A.A.; Raslan, K.R.
2007-01-01
In this Letter, we established a traveling wave solution by using Cosine-function algorithm for nonlinear partial differential equations. The method is used to obtain the exact solutions for five different types of nonlinear partial differential equations such as, general equal width wave equation (GEWE), general regularized long wave equation (GRLW), general Korteweg-de Vries equation (GKdV), general improved Korteweg-de Vries equation (GIKdV), and Coupled equal width wave equations (CEWE), which are the important soliton equations
Topological and non-topological soliton solutions to some time ...
Indian Academy of Sciences (India)
Department of Engineering Sciences, Faculty of Technology and Engineering, East of ... These equations have been widely applied in many branches ... solutions of nonlinear fractional partial differential equations is one of the most impor-.
Soliton solutions and chaotic motions of the Zakharov equations for the Langmuir wave in the plasma
Energy Technology Data Exchange (ETDEWEB)
Zhen, Hui-Ling; Tian, Bo, E-mail: tian-bupt@163.com; Wang, Yu-Feng; Liu, De-Yin [State Key Laboratory of Information Photonics and Optical Communications, and School of Science, Beijing University of Posts and Telecommunications, Beijing 100876 (China)
2015-03-15
For the interaction between the high-frequency Langmuir waves and low-frequency ion-acoustic waves in the plasma, the Zakharov equations are studied in this paper. Via the Hirota method, we obtain the soliton solutions, based on which the soliton propagation is presented. It is found that with λ increasing, the amplitude of u decreases, whereas that of v remains unchanged, where λ is the ion-acoustic speed, u is the slowly-varying envelope of the Langmuir wave, and v is the fluctuation of the equilibrium ion density. Both the head-on and bound-state interactions between the two solitons are displayed. We observe that with λ decreasing, the interaction period of u decreases, while that of v keeps unchanged. It is found that the Zakharov equations cannot admit any chaotic motions. With the external perturbations taken into consideration, the perturbed Zakharov equations are studied for us to see the associated chaotic motions. Both the weak and developed chaotic motions are investigated, and the difference between them roots in the relative magnitude of the nonlinearities and perturbations. The chaotic motions are weakened with λ increasing, or else, strengthened. Periodic motion appears when the nonlinear terms and external perturbations are balanced. With such a balance kept, one period increases with λ increasing.
International Nuclear Information System (INIS)
Chen Huaitang; Zhang Hongqing
2004-01-01
A generalized tanh function method is used for constructing exact travelling wave solutions of nonlinear partial differential equations in a unified way. The main idea of this method is to take full advantage of the Riccati equation which has more new solutions. More new multiple soliton solutions are obtained for the general Burgers-Fisher equation and the Kuramoto-Sivashinsky equation
A new class of nontopological solitons
International Nuclear Information System (INIS)
Li Xinzhou; Ni Zhixiang; Zhang Jianzu
1992-09-01
We construct a new class of nontopological solitons with scalar self-interaction term κφ 4 . Because of the scalar self-interaction, there is a maximum size for these objects. There exists a critical value κ crit for the coupling κ. For κ > κ crit there are no stable nontopological solitons. In thin-walled limit, we show the explicit solutions of NTS with scalar self-interaction and/or gauge interaction. In the case of gauged NTS, soliton becomes a superconductor. (author). 11 refs
Constructing soliton solutions and super-bilinear form of lattice supersymmetric KdV equation
International Nuclear Information System (INIS)
Carstea, A S
2015-01-01
The Hirota bilinear form and multisoliton solution for semidiscrete and fully discrete (difference–difference) versions of the supersymmetric Korteweg–de Vries (KdV) equation found by Xue et al (2013 J. Phys. A: Math. Theor 46 502001) are presented. The solitonic interaction term displays a fermionic dressing factor as in the continuous supersymmetric case. Using bilinear equations it is also shown that a new integrable semidiscrete (and fully discrete) version of supersymmetric KdV can be constructed with a simpler bilinear form but a more complicated interaction dressing. Its continuum limit is also computed. (paper)
International Nuclear Information System (INIS)
Tian Shoufu; Zhang Hongqing
2010-01-01
In this paper, we start from the discrete spectral problem and construct a lattice hierarchy by properly choosing an auxiliary spectral problem V-tilde n (m) , which can reduce to the Volterra hierarchy, the Ablowitz-Ladik hierarchy, positive and negative lattice hierarchies and a new hierarchy. The new hierarchy is integrable in involutory Lax's sense and possesses multi-Hamiltonian structure. In addition, the Darboux transformation of the lattice hierarchy is obtained when the freely adjustable function εn (1) =0 and m=1. Then some soliton solutions are obtained by using Darboux transformation. This method is also suitable for other more general spectral problems in mathematics and physics.
On the stability of soliton solution in NLS-type general field model
International Nuclear Information System (INIS)
Chakrabarti, S.; Nayyar, A.H.
1982-08-01
A model incorporating the nonlinear Schroedinger equation and its generalizations is considered and the stability of its periodic-in-time solutions under the restriction of a fixed charge Q is analysed. It is shown that the necessary condition for the stability is given by the inequality deltaQ/deltaν<0, where ν is the parameter of periodicity of the solution in time. In particular, one specific class of Lagrangians is considered and, in addition, the sufficient conditions for the stability of the soliton solutions are also determined. This study thus examines both the necessary and the sufficient conditions for the stability of the solutions of nonlinear Schroedinger equation and some of its generalizations. (author)
Collisions of Two Spatial Solitons in Inhomogeneous Nonlinear Media
International Nuclear Information System (INIS)
Zhong Weiping; Yi Lin; Yang Zhengping; Xie Ruihua; Milivoj, Belic; Chen Goong
2008-01-01
Collisions of spatial solitons occurring in the nonlinear Schroeinger equation with harmonic potential are studied, using conservation laws and the split-step Fourier method. We find an analytical solution for the separation distance between the spatial solitons in an inhomogeneous nonlinear medium when the light beam is self-trapped in the transverse dimension. In the self-focusing nonlinear media the spatial solitons can be transmitted stably, and the interaction between spatial solitons is enhanced due to the linear focusing effect (and also diminished for the linear defocusing effect). In the self-defocusing nonlinear media, in the absence of self-trapping or in the presence of linear self-defocusing, no transmission of stable spatial solitons is possible. However, in such media the linear focusing effect can be exactly compensated, and the spatial solitons can propagate through
Constraints and Soliton Solutions for KdV Hierarchy and AKNS Hierarchy
International Nuclear Information System (INIS)
Li Nianhua; Li Yuqi
2011-01-01
It is well-known that the finite-gap solutions of the KdV equation can be generated by its recursion operator. We generalize the result to a special form of Lax pair, from which a method to constrain the integrable system to a lower-dimensional or fewer variable integrable system is proposed. A direct result is that the n-soliton solutions of the KdV hierarchy can be completely depicted by a series of ordinary differential equations (ODEs), which may be gotten by a simple but unfamiliar Lax pair. Furthermore the AKNS hierarchy is constrained to a series of univariate integrable hierarchies. The key is a special form of Lax pair for the AKNS hierarchy. It is proved that under the constraints all equations of the AKNS hierarchy are linearizable. (general)
Bright and dark soliton solutions for some nonlinear fractional differential equations
International Nuclear Information System (INIS)
Guner, Ozkan; Bekir, Ahmet
2016-01-01
In this work, we propose a new approach, namely ansatz method, for solving fractional differential equations based on a fractional complex transform and apply it to the nonlinear partial space–time fractional modified Benjamin–Bona–Mahoney (mBBM) equation, the time fractional mKdV equation and the nonlinear fractional Zoomeron equation which gives rise to some new exact solutions. The physical parameters in the soliton solutions: amplitude, inverse width, free parameters and velocity are obtained as functions of the dependent model coefficients. This method is suitable and more powerful for solving other kinds of nonlinear fractional PDEs arising in mathematical physics. Since the fractional derivatives are described in the modified Riemann–Liouville sense. (paper)
Maslov, V. P.; Shafarevich, A. I.
2011-12-01
A description for the asymptotic soliton-like solution of the Kadomtsev-Petviashvili I equation (KPI equation) in terms of the canonical operator is suggested. This solution can smoothly be continued to the vicinity of the focal point.
The soliton solution of BBGKY quantum kinetic equations chain for different type particles system
International Nuclear Information System (INIS)
Rasulova, M.Yu.; Avazov, U.; Hassan, T.
2006-12-01
In the present paper on the basis of BBGKY chain of quantum kinetic equations the chain of equations for correlation matrices is derived, describing the evolution of a system of different types particles, which interact by pair potential. The series, which is the solution of this chain of equations for correlation matrices, is suggested. Using this series the solution of the last chain of equations is reduced to a solution of a set of homogeneous and nonhomogeneous von-Neumann's kinetic equations (analogue of Vlasov equations for quantum case). The first and second equations of this set of equations coincide with the first and second kinetic equations of the set, which is used in plasma physics. For an potential in the form of Dirac delta function, the solution of von-Neumann equation is defined through soliton solution of nonlinear Schrodinger equations. Based on von-Neumann equation one can define all terms of series, which is a solution of a chain of equations for correlation matrices. On the basis of these correlation matrices for a system of different types of particles we can define exact solution of BBGKY chain of quantum kinetic equations
Agalarov, Agalar; Zhulego, Vladimir; Gadzhimuradov, Telman
2015-04-01
The reduction procedure for the general coupled nonlinear Schrödinger (GCNLS) equations with four-wave mixing terms is proposed. It is shown that the GCNLS system is equivalent to the well known integrable families of the Manakov and Makhankov U(n,m)-vector models. This equivalence allows us to construct bright-bright and dark-dark solitons and a quasibreather-dark solution with unconventional dynamics: the density of the first component oscillates in space and time, whereas the density of the second component does not. The collision properties of solitons are also studied.
International Nuclear Information System (INIS)
Zhestkov, S.V.; Romanenko, A.A.
2009-01-01
The problem of existence of soliton-like solutions of (1+1), (2+1), (3+1)-dimensional Schrodinger equations with the third power nonlinearity law is investigated. The numerical-analytical method of constructing solitons is developed. (authors)
Soliton excitations in a class of nonlinear field theory models
International Nuclear Information System (INIS)
Makhan'kov, V.G.; Fedyanin, V.K.
1985-01-01
Investigation results of nonlinear models of the field theory with a lagrangian are described. The theory includes models both with zero stable vacuum epsilon=1 and with condensate epsilon=-1 (of disturbed symmetry). Conditions of existence of particle-like solutions (PLS), stability of these solutions are investigated. Soliton dynamics is studied. PLS formfactors are calculated. Statistical mechanics of solitons is built and their dynamic structure factors are calculated
Comment on "Defocusing complex short-pulse equation and its multi-dark-soliton solution"
Youssoufa, Saliou; Kuetche, Victor K.; Kofane, Timoleon C.
2017-08-01
In their recent paper, Feng et al. [Phys. Rev. E 93, 052227 (2016), 10.1103/PhysRevE.93.052227] proposed a complex short-pulse equation of both focusing and defocusing types. They studied in detail the defocusing case and derived its multi-dark-soliton solutions. Nonetheless, from a physical viewpoint in order to better and deeply understand their genuine implications, we find it useful to provide a real and proper background for the derivation of the previous evolution system while showing that the expression of the nonlinear electric polarization the above authors used in their scheme is not suitable for getting the defocusing complex short-pulse equation.
International Nuclear Information System (INIS)
Yang Pei; Li Zhibin; Chen Yong
2010-01-01
In this paper, the short-wave model equations are investigated, which are associated with the Camassa-Holm (CH) and Degasperis-Procesi (DP) shallow-water wave equations. Firstly, by means of the transformation of the independent variables and the travelling wave transformation, the partial differential equation is reduced to an ordinary differential equation. Secondly, the equation is solved by homotopy analysis method. Lastly, by the transformations back to the original independent variables, the solution of the original partial differential equation is obtained. The two types of solutions of the short-wave models are obtained in parametric form, one is one-cusp soliton for the CH equation while the other one is one-loop soliton for the DP equation. The approximate analytic solutions expressed by a series of exponential functions agree well with the exact solutions. It demonstrates the validity and great potential of homotopy analysis method for complicated nonlinear solitary wave problems. (general)
Hydrodynamic optical soliton tunneling
Sprenger, P.; Hoefer, M. A.; El, G. A.
2018-03-01
A notion of hydrodynamic optical soliton tunneling is introduced in which a dark soliton is incident upon an evolving, broad potential barrier that arises from an appropriate variation of the input signal. The barriers considered include smooth rarefaction waves and highly oscillatory dispersive shock waves. Both the soliton and the barrier satisfy the same one-dimensional defocusing nonlinear Schrödinger (NLS) equation, which admits a convenient dispersive hydrodynamic interpretation. Under the scale separation assumption of nonlinear wave (Whitham) modulation theory, the highly nontrivial nonlinear interaction between the soliton and the evolving hydrodynamic barrier is described in terms of self-similar, simple wave solutions to an asymptotic reduction of the Whitham-NLS partial differential equations. One of the Riemann invariants of the reduced modulation system determines the characteristics of a soliton interacting with a mean flow that results in soliton tunneling or trapping. Another Riemann invariant yields the tunneled soliton's phase shift due to hydrodynamic interaction. Soliton interaction with hydrodynamic barriers gives rise to effects that include reversal of the soliton propagation direction and spontaneous soliton cavitation, which further suggest possible methods of dark soliton control in optical fibers.
Transverse stability of Kawahara solitons
DEFF Research Database (Denmark)
Karpman, V.I.
1993-01-01
The transverse stability of the planar solitons described by the fifth-order Korteweg-de Vries equation (Kawahara solitons) is studied. It is shown that the planar solitons are unstable with respect to bending if the coefficient at the fifth-derivative term is positive and stable if it is negative...
International Nuclear Information System (INIS)
Nishiyama, Seiya; Providencia, Joao da; Komatsu, Takao
2007-01-01
To go beyond perturbative method in terms of variables of collective motion, using infinite-dimensional fermions, we have aimed to construct the self-consistent-field (SCF) theory, i.e., time dependent Hartree-Fock theory on associative affine Kac-Moody algebras along the soliton theory. In this paper, toward such an ultimate goal we will reconstruct a theoretical frame for a υ (external parameter)-dependent SCF method to describe more precisely the dynamics on the infinite-dimensional fermion Fock space. An infinite-dimensional fermion operator is introduced through Laurent expansion of finite-dimensional fermion operators with respect to degrees of freedom of the fermions related to a υ-dependent and a Υ-periodic potential. As an illustration, we derive explicit expressions for the Laurent coefficients of soliton solutions for sl n and for su n on infinite-dimensional Grassmannian. The associative affine Kac-Moody algebras play a crucial role to determine the dynamics on the infinite-dimensional fermion Fock space
International Nuclear Information System (INIS)
Li Juan; Zhang Haiqiang; Xu Tao; Zhang Yaxing; Hu Wei; Tian Bo
2007-01-01
Considering the transverse perturbation and axially non-planar geometry, the cylindrical Kadomtsev-Petviashvili (KP) equation is investigated in this paper, which can describe the propagation of dust-acoustic waves in the dusty plasma with two-temperature ions. Through imposing the decomposition method, such a (2+1)-dimensional equation is decomposed into two variable-coefficient (1+1)-dimensional integrable equations of the same hierarchy. Furthermore, three kinds of Darboux transformations (DTs) for these two (1+1)-dimensional equations are constructed. Via the three DTs obtained, the multi-soliton-like solutions of the cylindrical KP equation are explicitly presented. Especially, the one- and two-parabola-soliton solutions are discussed by several figures and some effects resulting from the physical parameters in the dusty plasma and transverse perturbation are also shown
International Nuclear Information System (INIS)
Li Qi; Duan Qiuyuan; Zhang Jianbing
2012-01-01
The mixed discrete modified Korteweg-de Vries (mKdV) hierarchy and the Lax pair are derived. The hierarchy related to the Ablowitz-Ladik spectral problem is reduced to the isospectral discrete mKdV hierarchy and to the non-isospectral discrete mKdV hierarchy. N-soliton solutions of the hierarchies are obtained through inverse scattering transform.
International Nuclear Information System (INIS)
Liu Chunping; Zhou Ling
2011-01-01
By improving the extended homogeneous balance method, a general method is suggested to derive a new auto-Baecklund transformation (BT) for (3+1)-Dimensional Jimbo-Miwa (JM) equation. The auto-BT obtained by using our method only involves one quadratic homogeneity equation written as a bilinear equation. Based on the auto-BT, two-soliton solution of the (3+1)-Dimensional JM equation is obtained. (general)
International Nuclear Information System (INIS)
Cosgrove, C.M.
1980-01-01
We investigate the precise interrelationships between several recently developed solution-generating techniques capable of generating asymptotically flat gravitational solutions with arbitrary multipole parameters. The transformations we study in detail here are the Lie groups Q and Q of Cosgrove, the Hoenselaers--Kinnersley--Xanthopoulos (HKX) transformations and their SL(2) tensor generalizations, the Neugebauer--Kramer discrete mapping, the Neugebauer Baecklund transformations I 1 and I 2 , the Harrison Baecklund transformation, and the Belinsky--Zakharov (BZ) one- and two-soliton transformations. Two particular results, among many reported here, are that the BZ soliton transformations are essentially equivalent to Harrison transformations and that the generalized HKX transformation may be deduced as a confluent double soliton transformation. Explicit algebraic expressions are given for the transforms of the Kinnersley--Chitre generating functions under all of the above transformations. In less detail, we also study the Kinnersley--Chitre β transformations, the non-null HKX transformations, and the Hilbert problems proposed independently by Belinsky and Zakharov, and Hauser and Ernst. In conclusion, we describe the nature of the exact solutions constructible in a finite number of steps with the available methods
Peng, Wei-Qi; Tian, Shou-Fu; Zou, Li; Zhang, Tian-Tian
2018-01-01
In this paper, the extended nonlinear Schrödinger equation with higher-order odd (third order) and even (fourth order) terms is investigated, whose particular cases are the Hirota equation, the Sasa-Satsuma equation and Lakshmanan-Porsezian-Daniel equation by selecting some specific values on the parameters of higher-order terms. We first study the stability analysis of the equation. Then, using the ansatz method, we derive its bright, dark solitons and some constraint conditions which can guarantee the existence of solitons. Moreover, the Ricatti equation extension method is employed to derive some exact singular solutions. The outstanding characteristics of these solitons are analyzed via several diverting graphics.
Spectral boundary conditions and solitonic solutions in a classical Sellmeier dielectric
Energy Technology Data Exchange (ETDEWEB)
Belgiorno, F. [Politecnico di Milano, Dipartimento di Matematica, Milan (Italy); INdAM-GNFM, Rome (Italy); INFN, Milan (Italy); Cacciatori, S.L. [Universita dell' Insubria, Department of Science and High Technology, Como (Italy); INFN, Milan (Italy); Vigano, A. [Universita degli Studi di Milano, Dipartimento di Fisica, Milan (Italy)
2017-06-15
Electromagnetic field interactions in a dielectric medium represent a longstanding field of investigation, both at the classical level and at the quantum one. We propose a 1+1 dimensional toy-model which consists of an half-line filling dielectric medium, with the aim to set up a simplified situation where technicalities related to gauge invariance and, as a consequence, physics of constrained systems are avoided, and still interesting features appear. In particular, we simulate the electromagnetic field and the polarization field by means of two coupled scalar fields φ, ψ, respectively, in a Hopfield-like model. We find that, in order to obtain a physically meaningful behavior for the model, one has to introduce spectral boundary conditions depending on the particle spectrum one is dealing with. This is the first interesting achievement of our analysis. The second relevant achievement is that, by introducing a nonlinear contribution in the polarization field ψ, with the aim of mimicking a third order nonlinearity in a nonlinear dielectric, we obtain solitonic solutions in the Hopfield model framework, whose classical behavior is analyzed too. (orig.)
Soliton on thin vortex filament
International Nuclear Information System (INIS)
Konno, Kimiaki; Mituhashi, Masahiko; Ichikawa, Y.H.
1990-12-01
Showing that one of the equations found by Wadati, Konno and Ichikawa is equivalent to the equation of motion of a thin vortex filament, we investigate solitons on the vortex filament. N vortex soliton solution is given in terms of the inverse scattering method. We examine two soliton collision processes on the filament. Our analysis provides the theoretical foundation of two soliton collision processes observed numerically by Aref and Flinchem. (author)
Gravitational solitons and the squashed 7-sphere
International Nuclear Information System (INIS)
Bizon, P; Chmaj, T; Gibbons, G W; Pope, C N
2007-01-01
We discuss some aspects of higher-dimensional gravitational solitons and kinks, including in particular their stability. We illustrate our discussion with the examples of (non-BPS) higher-dimensional Taub-NUT solutions as the spatial metrics in (6 + 1) and (8 + 1) dimensions. We find them to be stable against small but non-infinitesimal disturbances, but unstable against large ones, which can lead to black-hole formation. In (8 + 1) dimensions we find a continuous non-BPS family of asymptotically-conical solitons connecting a previously-known kink metric with the supersymmetric A 8 solution which has Spin(7) holonomy. All the solitonic spacetimes we consider are topologically, but not geometrically, trivial. In an appendix we use the techniques developed in the paper to establish the linear stability of five-dimensional Myers-Perry black holes with equal angular momenta against cohomogeneity-2 perturbations
Solitons as Newtonian particles
International Nuclear Information System (INIS)
Eboli, O.J.P.; Marques, G.C.
1982-07-01
The effect of external electromagnetic fields on non relativistic solitons is studied. Although the solitons are distorted by external fields, they still exhibit a Newtonian behavior. Some explicit examples of such a phenomenon are given, presenting solutions which exhibit Newtonian behavior for simple external fields. Furthermore, general results like charge and flux quantization are shown. (Author) [pt
International Nuclear Information System (INIS)
Wang, Pan; Tian, Bo; Jiang, Yan; Wang, Yu-Feng
2013-01-01
For describing the dynamics of alpha helical proteins with internal molecular excitations, nonlinear couplings between lattice vibrations and molecular excitations, and spin excitations in one-dimensional isotropic biquadratic Heisenberg ferromagnetic spin with the octupole–dipole interactions, we consider an inhomogeneous generalized fourth-order nonlinear Schrödinger equation. Based on the Ablowitz–Kaup–Newell–Segur system, infinitely many conservation laws for the equation are derived. Through the auxiliary function, bilinear forms and N-soliton solutions for the equation are obtained. Interactions of solitons are discussed by means of the asymptotic analysis. Effects of linear inhomogeneity on the interactions of solitons are also investigated graphically and analytically. Since the inhomogeneous coefficient of the equation h=α x+β, the soliton takes on the parabolic profile during the evolution. Soliton velocity is related to the parameter α, distance scale coefficient and biquadratic exchange coefficient, but has no relation with the parameter β. Soliton amplitude and width are only related to α. Soliton position is related to β
International Nuclear Information System (INIS)
Yomba, Emmanuel
2008-01-01
With the aid of symbolic computation, we demonstrate that the known method which is based on the new generalized hyperbolic functions and the new kinds of generalized hyperbolic function transformations, generates classes of exact solutions to a system of coupled nonlinear Schroedinger equations. This system includes the modified Hubbard model and the system of coupled nonlinear Schroedinger derived by Lazarides and Tsironis. Four types of solutions for this system are given explicitly, namely: new bright-bright, new dark-dark, new bright-dark and new dark-bright solitons
Accessible solitons of fractional dimension
Energy Technology Data Exchange (ETDEWEB)
Zhong, Wei-Ping, E-mail: zhongwp6@126.com [Department of Electronic and Information Engineering, Shunde Polytechnic, Guangdong Province, Shunde 528300 (China); Texas A& M University at Qatar, P.O. Box 23874, Doha (Qatar); Belić, Milivoj [Texas A& M University at Qatar, P.O. Box 23874, Doha (Qatar); Zhang, Yiqi [Key Laboratory for Physical Electronics and Devices of the Ministry of Education & Shaanxi Key Lab of Information Photonic Technique, Xi’an Jiaotong University, Xi’an 710049 (China)
2016-05-15
We demonstrate that accessible solitons described by an extended Schrödinger equation with the Laplacian of fractional dimension can exist in strongly nonlocal nonlinear media. The soliton solutions of the model are constructed by two special functions, the associated Legendre polynomials and the Laguerre polynomials in the fraction-dimensional space. Our results show that these fractional accessible solitons form a soliton family which includes crescent solitons, and asymmetric single-layer and multi-layer necklace solitons. -- Highlights: •Analytic solutions of a fractional Schrödinger equation are obtained. •The solutions are produced by means of self-similar method applied to the fractional Schrödinger equation with parabolic potential. •The fractional accessible solitons form crescent, asymmetric single-layer and multilayer necklace profiles. •The model applies to the propagation of optical pulses in strongly nonlocal nonlinear media.
International Nuclear Information System (INIS)
Yan Zhenya
2002-01-01
In this paper, an auto-Baecklund transformation is presented for the generalized Burgers equation: u t +u xy + αuu y +αu x ∂ -1 x u y =0 (α is constant) by using an ansatz and symbolic computation. Particularly, this equation is transformed into a (1+2)-dimensional generalized heat equation ω t + ω xy =0 by the Cole-Hopf transformation. This shows that this equation is C-integrable. Abundant types of new soliton-like solutions are obtained by virtue of the obtained transformation. These solutions contain n-soliton-like solutions, shock wave solutions and singular soliton-like solutions, which may be of important significance in explaining some physical phenomena. The approach can also be extended to other types of nonlinear partial differential equations in mathematical physics
International Nuclear Information System (INIS)
Lyu, L.H.; Kan, J.R.
1989-01-01
Nonlinear one-dimensional constant-profile hydromagnetic wave solutions are obtained in finite-temperature two-fluid collisionless plasmas under adiabatic equation of state. The nonlinear wave solutions can be classified according to the wavelength. The long-wavelength solutions are circularly polarized incompressible oblique Alfven wave trains with wavelength greater than hudreds of ion inertial length. The oblique wave train solutions can explain the high degree of alignment between the local average magnetic field and the wave normal direction observed in the solar wind. The short-wavelength solutions include rarefaction fast solitons, compression slow solitons, Alfven solitons and rotational discontinuities, with wavelength of several tens of ion inertial length, provided that the upstream flow speed is less than the fast-mode speed
Energy Technology Data Exchange (ETDEWEB)
Zuo, Da-Wei [Beijing University of Aeronautics and Astronautics, Beijing (China). State Key Laboratory of Software Development Environment; Ministry of Education, Beijing (China). Key Laboratory of Fluid Mechanics; Shijiazhuang Tiedao University (China). Dept. of Mathematics and Physics; Gao, Yi-Tian; Sun, Yu-Hao; Feng, Yu-Jie; Xue, Long [Beijing University of Aeronautics and Astronautics, Beijing (China). State Key Laboratory of Software Development Environment; Ministry of Education, Beijing (China). Key Laboratory of Fluid Mechanics
2014-10-15
The nonlinear Schroedinger (NLS) equation appears in fluid mechanics, plasma physics, etc., while the Hirota equation, a higher-order NLS equation, has been introduced. In this paper, a higher-order Hirota system is investigated, which describes the wave propagation in an erbium-doped nonlinear fiber with higher-order dispersion. By virtue of the Darboux transformation and generalized Darboux transformation, multi-soliton solutions and higher-order rogue-wave solutions are derived, beyond the published first-order consideration. Wave propagation and interaction are analyzed: (i) Bell-shape solitons, bright- and dark-rogue waves are found; (ii) the two-soliton interaction is elastic, i.e., the amplitude and velocity of each soliton remain unchanged after the interaction; (iii) the coefficient in the system affects the direction of the soliton propagation, patterns of the soliton interaction, distance, and direction of the first-order rogue-wave propagation, as well as the range and direction of the second-order rogue-wave interaction.
Spatial solitons in nonlinear photonic crystals
DEFF Research Database (Denmark)
Corney, Joel Frederick; Bang, Ole
2000-01-01
We study solitons in one-dimensional quadratic nonlinear photonic crystals with periodic linear and nonlinear susceptibilities. We show that such crystals support stable bright and dark solitons, even when the effective quadratic nonlinearity is zero.......We study solitons in one-dimensional quadratic nonlinear photonic crystals with periodic linear and nonlinear susceptibilities. We show that such crystals support stable bright and dark solitons, even when the effective quadratic nonlinearity is zero....
International Nuclear Information System (INIS)
Carr, L.D.; Brand, J.
2004-01-01
It is shown that simultaneously changing the scattering length of an elongated, harmonically trapped Bose-Einstein condensate from positive to negative and inverting the axial portion of the trap, so that it becomes expulsive, results in a train of self-coherent solitonic pulses. Each pulse is itself a nondispersive attractive Bose-Einstein condensate that rapidly self-cools. The axial trap functions as a waveguide. The solitons can be made robustly stable with the right choice of trap geometry, number of atoms, and interaction strength. Theoretical and numerical evidence suggests that such a pulsed atomic soliton laser can be made in present experiments
Solutions for the stable roommates problem with payments
Biró, Péter; Bomhoff, M.J.; Golovach, Petr A.; Kern, Walter
2014-01-01
The stable roommates problem with payments has as input a graph G = (V , E ) with an edge weighting w : E → R≥0 and the problem is to find a stable solution. By pinpointing a relationship to the accessibility of the coalition structure core of matching games, we give a constructive proof for showing
Bright Solitons in a PT-Symmetric Chain of Dimers
Directory of Open Access Journals (Sweden)
Omar B. Kirikchi
2016-01-01
Full Text Available We study the existence and stability of fundamental bright discrete solitons in a parity-time- (PT- symmetric coupler composed by a chain of dimers that is modelled by linearly coupled discrete nonlinear Schrödinger equations with gain and loss terms. We use a perturbation theory for small coupling between the lattices to perform the analysis, which is then confirmed by numerical calculations. Such analysis is based on the concept of the so-called anticontinuum limit approach. We consider the fundamental onsite and intersite bright solitons. Each solution has symmetric and antisymmetric configurations between the arms. The stability of the solutions is then determined by solving the corresponding eigenvalue problem. We obtain that both symmetric and antisymmetric onsite mode can be stable for small coupling, in contrast to the reported continuum limit where the antisymmetric solutions are always unstable. The instability is either due to the internal modes crossing the origin or the appearance of a quartet of complex eigenvalues. In general, the gain-loss term can be considered parasitic as it reduces the stability region of the onsite solitons. Additionally, we analyse the dynamic behaviour of the onsite and intersite solitons when unstable, where typically it is either in the form of travelling solitons or soliton blow-ups.
Soliton Resolution for the Derivative Nonlinear Schrödinger Equation
Jenkins, Robert; Liu, Jiaqi; Perry, Peter; Sulem, Catherine
2018-05-01
We study the derivative nonlinear Schrödinger equation for generic initial data in a weighted Sobolev space that can support bright solitons (but exclude spectral singularities). Drawing on previous well-posedness results, we give a full description of the long-time behavior of the solutions in the form of a finite sum of localized solitons and a dispersive component. At leading order and in space-time cones, the solution has the form of a multi-soliton whose parameters are slightly modified from their initial values by soliton-soliton and soliton-radiation interactions. Our analysis provides an explicit expression for the correction dispersive term. We use the nonlinear steepest descent method of Deift and Zhou (Commun Pure Appl Math 56:1029-1077, 2003) revisited by the {\\overline{partial}} -analysis of McLaughlin and Miller (IMRP Int Math Res Pap 48673:1-77, 2006) and Dieng and McLaughlin (Long-time asymptotics for the NLS equation via dbar methods. Preprint, arXiv:0805.2807, 2008), and complemented by the recent work of Borghese et al. (Ann Inst Henri Poincaré Anal Non Linéaire, https://doi.org/10.1016/j.anihpc.2017.08.006, 2017) on soliton resolution for the focusing nonlinear Schrödinger equation. Our results imply that N-soliton solutions of the derivative nonlinear Schrödinger equation are asymptotically stable.
Exact solutions, energy, and charge of stable Q-balls
Energy Technology Data Exchange (ETDEWEB)
Bazeia, D.; Marques, M.A. [Universidade Federal da Paraiba, Departamento de Fisica, Joao Pessoa, PB (Brazil); Menezes, R. [Universidade Federal da Paraiba, Departamento de Ciencias Exatas, Rio Tinto, PB (Brazil); Universidade Federal de Campina Grande, Departamento de Fisica, Campina Grande, PB (Brazil)
2016-05-15
In this work we deal with nontopological solutions of the Q-ball type in two spacetime dimensions. We study models of current interest, described by a Higgs-like and other, similar potentials which unveil the presence of exact solutions. We use the analytic results to investigate how to control the energy and charge to make the Q-balls stable. (orig.)
Real and virtual multidimensional solitons
International Nuclear Information System (INIS)
Boiti, M.; Martina, L.; Pashaev, O.K.; Pempinelli, F.
1993-01-01
Recently it has been shown that in two spatial and one temporal dimensions (2+1) there exist localized solitons. These coherent structures display a richer phenomenology than the one dimensional solitons. Different effects have been reported successively in a series of papers. Some of them are due to the fact that the soliton solution is structurally unstable with respect to special choices of the parameters. Also some quantum-like effects as the non conservation of the number of solitons have been discovered by using direct methods. This report is dedicated to the study of the origin and generality of these new effects in the context of the Spectral Transform (ST) theory. By choosing more general boundaries than those used in previous papers we derive an N 2 -soliton solution, which is parameterized by a point in a space of 4N(N+1) real parameters. Of these parameters 2N(N+2) are determined by the choice of the boundaries and fix the velocity and the possible location of the solitons in the plane at large times, while the remaining 2N govern the dynamics of the solitons during the interaction. The total mass of solitons is conserved but, in general, the mass of the single soliton is not preserved by the interaction. The extreme cases in which the masses of one or more solitons are zero at t = -∞ or/and t = +∞ are also allowed. We call these solitons with asymptotic zero masses and, consequently, with asymptotic zero amplitudes virtual solitons. The total momentum of solitons is not conserved because the boundaries act as external forces. Solitons can simulate inelastic scattering processes of quantum particles including creation and annihilation of particles
Caserta, A.; Kanivetsky, R.; Salusti, E.
2017-11-01
We here analyze a new model of transients of pore pressure p and solute density ρ in geologic porous media. This model is rooted in the nonlinear wave theory, its focus is on advection and effect of large pressure jumps on strain. It takes into account nonlinear and also time-dependent versions of the Hooke law about stress, rate and strain. The model solutions strictly relate p and ρ evolving under the effect of a strong external stress. As a result, the presence of quick and sharp transients in low permeability rocks is unveiled, i.e., the nonlinear "Burgers solitons". We, therefore, show that the actual transport process in porous rocks for large signals is not only the linear diffusion, but also a solitons presence could control the process. A test of a presence of solitons is applied to Pierre shale, Bearpaw shale, Boom clay and Oznam-Mugu silt and clay. An application about the presence of solitons for nuclear waste disposal and salt water intrusions is also discussed. Finally, in a kind of "theoretical experiment" we show that solitons could also be present in higher permeability rocks (Jordan and St. Peter sandstones), thus supporting the idea of a possible occurrence of osmosis also in sandstones.
The q-deformed mKP hierarchy with self-consistent sources, Wronskian solutions and solitons
International Nuclear Information System (INIS)
Lin Runliang; Peng Hua; Manas, Manuel
2010-01-01
Based on the eigenfunction symmetry constraint of the q-deformed modified KP hierarchy, a q-deformed mKP hierarchy with self-consistent sources (q-mKPHSCSs) is constructed. The q-mKPHSCSs contain two types of q-deformed mKP equation with self-consistent sources. By the combination of the dressing method and the method of variation of constants, a generalized dressing approach is proposed to solve the q-deformed KP hierarchy with self-consistent sources (q-KPHSCSs). Using the gauge transformation between the q-KPHSCSs and the q-mKPHSCSs, the q-deformed Wronskian solutions for the q-KPHSCSs and the q-mKPHSCSs are obtained. The one-soliton solutions for the q-deformed KP (mKP) equation with a source are given explicitly.
Impurity solitons with quadratic nonlinearities
DEFF Research Database (Denmark)
Clausen, Carl A. Balslev; Torres, Juan P-; Torner, Lluis
1998-01-01
We fmd families of solitary waves mediated by parametric mixing in quadratic nonlinear media that are localized at point-defect impurities. Solitons localized at attractive impurities are found to be dynamically stable. It is shown that localization at the impurity modifies strongly the soliton...
Helmholtz bright and boundary solitons
Energy Technology Data Exchange (ETDEWEB)
Christian, J M [Joule Physics Laboratory, School of Computing, Science and Engineering, Institute for Materials Research, University of Salford, Salford M5 4WT (United Kingdom); McDonald, G S [Joule Physics Laboratory, School of Computing, Science and Engineering, Institute for Materials Research, University of Salford, Salford M5 4WT (United Kingdom); Chamorro-Posada, P [Departmento de TeorIa de la Senal y Comunicaciones e IngenierIa Telematica, Universidad de Valladolid, ETSI Telecomunicacion, Campus Miguel Delibes s/n, 47011 Valladolid (Spain)
2007-02-16
We report, for the first time, exact analytical boundary solitons of a generalized cubic-quintic nonlinear Helmholtz (NLH) equation. These solutions have a linked-plateau topology that is distinct from conventional dark soliton solutions; their amplitude and intensity distributions are spatially delocalized and connect regions of finite and zero wave-field disturbances (suggesting also the classification as 'edge solitons'). Extensive numerical simulations compare the stability properties of recently derived Helmholtz bright solitons, for this type of polynomial nonlinearity, to those of the new boundary solitons. The latter are found to possess a remarkable stability characteristic, exhibiting robustness against perturbations that would otherwise lead to the destabilizing of their bright-soliton counterparts.
Helmholtz bright and boundary solitons
International Nuclear Information System (INIS)
Christian, J M; McDonald, G S; Chamorro-Posada, P
2007-01-01
We report, for the first time, exact analytical boundary solitons of a generalized cubic-quintic nonlinear Helmholtz (NLH) equation. These solutions have a linked-plateau topology that is distinct from conventional dark soliton solutions; their amplitude and intensity distributions are spatially delocalized and connect regions of finite and zero wave-field disturbances (suggesting also the classification as 'edge solitons'). Extensive numerical simulations compare the stability properties of recently derived Helmholtz bright solitons, for this type of polynomial nonlinearity, to those of the new boundary solitons. The latter are found to possess a remarkable stability characteristic, exhibiting robustness against perturbations that would otherwise lead to the destabilizing of their bright-soliton counterparts
International Nuclear Information System (INIS)
Zheng Yu; Tian Jin-Rong; Dong Zi-Kai; Xu Run-Qin; Li Ke-Xuan; Song Yan-Rong
2017-01-01
A phase-locked bound state soliton with dual-wavelength is observed experimentally in a passively mode-locked Er-doped fiber (EDF) laser with a fiber loop mirror (FLM). The pulse duration of the soliton is 15 ps and the peak-to-peak separation is 125 ps. The repetition rate of the pulse sequence is 3.47 MHz. The output power is 11.8 mW at the pump power of 128 mW, corresponding to the pulse energy of 1.52 nJ. The FLM with a polarization controller can produce a comb spectrum, which acts as a filter. By adjusting the polarization controller or varying the pump power, the central wavelength of the comb spectrum can be tuned. When it combines with the reflective spectrum of the fiber Bragg grating, the total spectrum of the cavity can be cleaved into two parts, then the bound state soliton with dual-wavelength at 1549.7 nm and 1550.4 nm is obtained. (paper)
Vortex solitons at the interface separating square and hexagonal lattices
Energy Technology Data Exchange (ETDEWEB)
Jović Savić, Dragana, E-mail: jovic@ipb.ac.rs; Piper, Aleksandra; Žikić, Radomir; Timotijević, Dejan
2015-06-19
Vortex solitons at the interface separating two different photonic lattices – square and hexagonal – are demonstrated numerically. We consider the conditions for the existence of discrete vortex states at such interfaces and develop a concise picture of different scenarios of the vortex solutions behavior. Various vortices with different size and topological charges are considered, as well as various lattice interfaces. A novel type of discrete vortex surface solitons in a form of five-lobe solution is observed. Besides stable three-lobe and six-lobe discrete surface modes propagating for long distances, we observe various oscillatory vortex surface solitons, as well as dynamical instabilities of different kinds of solutions and study their angular momentum. Dynamical instabilities occur for higher values of the propagation constant, or at higher beam powers. - Highlights: • We demonstrate vortex solitons at the square–hexagonal photonic lattice interface. • A novel type of five-lobe surface vortex solitons is observed. • Different phase structures of surface solutions are studied. • Orbital angular momentum transfer of such solutions is investigated.
Energy Technology Data Exchange (ETDEWEB)
Zhen, Hui-Ling; Tian, Bo, E-mail: tian-bupt@163.com; Wang, Yu-Feng; Sun, Wen-Rong; Liu, Li-Cai [State Key Laboratory of Information Photonics and Optical Communications, and School of Science, Beijing University of Posts and Telecommunications, Beijing 100876 (China)
2014-07-15
The extended Zakharov-Kuznetsov (eZK) equation for the magnetized two-ion-temperature dusty plasma is studied in this paper. With the help of Hirota method, bilinear forms and N-soliton solutions are given, and soliton propagation is graphically analyzed. We find that the soliton amplitude is positively related to the nonlinear coefficient A, while inversely related to the dispersion coefficients B and C. We obtain that the soliton amplitude will increase with the mass of the jth dust grain and the average charge number residing on the dust grain decreased, but the soliton amplitude will increase with the equilibrium number density of the jth dust grain increased. Upon the introduction of the periodic external forcing term, both the weak and developed chaotic motions can occur. Difference between the two chaotic motions roots in the inequality between the nonlinear coefficient l{sub 2} and perturbed term h{sub 1}. The developed chaos can be weakened with B or C decreased and A increased. Periodic motion of the perturbed eZK equation can be observed when there is a balance between l{sub 2} and h{sub 1}.
Tunnelling effects of solitons in optical fibers with higher-order effects
Energy Technology Data Exchange (ETDEWEB)
Dai, Chao-Qing [Zhejiang A and F Univ., Lin' an (China). School of Sciences; Suzhou Univ., Jiangsu (China). School of Physical Science and Technology; Zhu, Hai-Ping [Zhejiang Lishui Univ., Zhejiang (China). School of Science; Zheng, Chun-Long [Shaoguan Univ., Guangdong (China). College of Physics and Electromechanical Engineering
2012-06-15
We construct four types of analytical soliton solutions for the higher-order nonlinear Schroedinger equation with distributed coefficients. These solutions include bright solitons, dark solitons, combined solitons, and M-shaped solitons. Moreover, the explicit functions which describe the evolution of the width, peak, and phase are discussed exactly. We finally discuss the nonlinear soliton tunnelling effect for four types of femtosecond solitons. (orig.)
International Nuclear Information System (INIS)
Mahalingam, A; Porsezian, K; Mani Rajan, M S; Uthayakumar, A
2009-01-01
In this paper, a generalized nonlinear Schroedinger-Maxwell-Bloch model with variable dispersion and nonlinearity management functions, which describes the propagation of optical pulses in an inhomogeneous erbium-doped fiber system under certain restrictive conditions, is under investigation. We derive the Lax pair with a variable spectral parameter and the exact soliton solution is generated from the Baecklund transformation. It is observed that stable solitons are possible only under a very restrictive condition for the spectral parameter and other inhomogeneous functions. For various forms of the inhomogeneous dispersion, nonlinearity and gain/loss functions, construction of different types of solitary waves like classical solitons, breathers, etc is discussed
Stable solutions of nonlocal electron heat transport equations
International Nuclear Information System (INIS)
Prasad, M.K.; Kershaw, D.S.
1991-01-01
Electron heat transport equations with a nonlocal heat flux are in general ill-posed and intrinsically unstable, as proved by the present authors [Phys. Fluids B 1, 2430 (1989)]. A straightforward numerical solution of these equations will therefore lead to absurd results. It is shown here that by imposing a minimal set of constraints on the problem it is possible to arrive at a globally stable, consistent, and energy conserving numerical solution
EL-Kalaawy, O. H.
2018-02-01
We consider the nonlinear propagation of non-planar (cylindrical and spherical) ion-acoustic (IA) envelope solitary waves in an unmagnetized plasma consisting of electron-positron-ion-dust plasma with two-electron temperature distributions in the context of the non-extensive statistics. The basic set of fluid equations is reduced to the modified nonlinear Schrödinger (MNLS) equation in cylindrical and spherical geometry by using the reductive perturbation method (RPM). It is found that the nature of the modulational instabilities would be significantly modified due to the effects of the non-extensive and other plasma parameters as well as cylindrical and spherical geometry. Conservation laws of the MNLS equation are obtained by Lie symmetry and multiplier method. A new exact solution (envelope bright soliton) is obtained by the extended homogeneous balance method. Finally, we study the results of this article.
Geometric solitons of Hamiltonian flows on manifolds
Energy Technology Data Exchange (ETDEWEB)
Song, Chong, E-mail: songchong@xmu.edu.cn [School of Mathematical Sciences, Xiamen University, Xiamen 361005 (China); Sun, Xiaowei, E-mail: sunxw@cufe.edu.cn [School of Applied Mathematics, Central University of Finance and Economics, Beijing 100081 (China); Wang, Youde, E-mail: wyd@math.ac.cn [Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190 (China)
2013-12-15
It is well-known that the LIE (Locally Induction Equation) admit soliton-type solutions and same soliton solutions arise from different and apparently irrelevant physical models. By comparing the solitons of LIE and Killing magnetic geodesics, we observe that these solitons are essentially decided by two families of isometries of the domain and the target space, respectively. With this insight, we propose the new concept of geometric solitons of Hamiltonian flows on manifolds, such as geometric Schrödinger flows and KdV flows for maps. Moreover, we give several examples of geometric solitons of the Schrödinger flow and geometric KdV flow, including magnetic curves as geometric Schrödinger solitons and explicit geometric KdV solitons on surfaces of revolution.
International Nuclear Information System (INIS)
Tasgal, Richard S.; Menabde, G.; Band, Y. B.
2006-01-01
We propose a scheme for making a Bose-Einstein condensate (BEC) of molecules from a BEC of atoms in a strongly confining two-dimensional optical lattice and a weak one-dimensional optical lattice in the third dimension. The stable solutions obtained for the order parameters take the form of a different type of gap soliton, with both atomic and molecular BECs, and also standard gap solitons with only a molecular BEC. The strongly confining dimensions of the lattice stabilize the BEC against inelastic energy transfer in atom-molecule collisions. The solitons with atoms and molecules may be obtained by starting with an atomic BEC, and gradually tuning the resonance by changing the external magnetic-field strength until the desired atom-molecule soliton is obtained. A gap soliton of a BEC of only molecules may be obtained nonadiabatically by starting from an atom-only gap soliton, far from a Feshbach resonance and adjusting the magnetic field to near Feshbach resonance. After a period of time in which the dimer field grows, change the magnetic field such that the detuning is large and negative and Feshbach effects wash out, turn off the optical lattice in phase with the atomic BEC, and turn on an optical lattice in phase with the molecules. The atoms disperse, leaving a gap soliton composed of a molecular BEC. Regarding instabilities in the dimension of the weak optical lattice, the solitons which are comprised of both atoms and molecules are sometimes stable and sometimes unstable--we present numerically obtained results. Gap solitons comprised of only molecules have the same stability properties as the standard gap solitons: stable from frequencies slightly below the middle of the band gap to the top, and unstable below that point. Instabilities are only weakly affected by the soliton velocities, and all instabilities are oscillatory
Evolution of envelope solitons of ionization waves
International Nuclear Information System (INIS)
Ohe, K.; Hashimoto, M.
1985-01-01
The time evolution of a particle-like envelope soliton of ionization waves in plasma was investigated theoretically. The hydrodynamic equations of one spatial dimension were solved and the nonlinear dispersion relation was derived. For the amplitude of the wave the nonlinear Schroedinger equation was derived. Its soliton solution was interpreted as the envelope soliton which was experimentally found. The damping rate of the envelope soliton was estimated. (D.Gy.)
Yin, Hui-Min; Tian, Bo; Zhao, Xin-Chao
2018-06-01
This paper presents an investigation of a (2 + 1)-dimensional variable-coefficient Gross-Pitaevskii equation in the Bose-Einstein condensation. Periodic and complexiton solutions are obtained. Solitons solutions are also gotten through the periodic solutions. Numerical solutions via the split step method are stable. Effects of the weak and strong modulation instability on the solitons are shown: the weak modulation instability permits an observable soliton, and the strong one overwhelms its development.
Solitons in PT-symmetric potential with competing nonlinearity
International Nuclear Information System (INIS)
Khare, Avinash; Al-Marzoug, S.M.; Bahlouli, Hocine
2012-01-01
We investigate the effect of competing nonlinearities on beam dynamics in PT-symmetric potentials. In particular, we consider the stationary nonlinear Schrödinger equation (NLSE) in one dimension with competing cubic and generalized nonlinearity in the presence of a PT-symmetric potential. Closed form solutions for localized states are obtained. These solitons are shown to be stable over a wide range of potential parameters. The transverse power flow associated with these complex solitons is also examined. -- Highlights: ► Effect of competing nonlinearities on beam dynamics in PT-symmetric potentials. ► Closed form solutions for localized states are. ► The transverse power flow associated with these complex solitons is also examined.
International Nuclear Information System (INIS)
Gopakumar, R.
2002-01-01
Though noncommutative field theories have been explored for several years, a resurgence of interest in it was sparked off after it was realised that they arise very naturally as limits of string theory in certain background fields. It became more plausible (at least to string theorists) that these nonlocal deformations of usual quantum field theories are consistent theories in themselves. This led to a detailed exploration of many of their classical and quantum properties. I will elaborate further on the string theory context in the next section. One of the consequences of this exploration was the discovery of novel classical solutions in noncommutative field theories. Since then much work has been done in exploring many of their novel properties. My lectures focussed on some specific aspects of these noncommutative solitons. They primarily reflect the topics that I have worked on and are not intended to be a survey of the large amount of work on this topic. We have tried to give a flavour of the physics that can be captured by the relatively elementary classical solutions of noncommutative field theories. We have seen in different contexts how these solitons are really simple manifestations of D-branes, possessing many of their important features. Though they have been primarily studied in the context of tachyon condensation, we saw that they can also shed some light on the resolution of singularities in spacetime by D-brane probes. In addition to other applications in string theory it is important at this stage to explore their presence in other systems with a strong magnetic field like the quantum hall effect
Energy Technology Data Exchange (ETDEWEB)
Gopakumar, R [Harish-Chandra Research Institute, Jhusi, Allahabad (India)
2002-05-15
Though noncommutative field theories have been explored for several years, a resurgence of interest in it was sparked off after it was realised that they arise very naturally as limits of string theory in certain background fields. It became more plausible (at least to string theorists) that these nonlocal deformations of usual quantum field theories are consistent theories in themselves. This led to a detailed exploration of many of their classical and quantum properties. I will elaborate further on the string theory context in the next section. One of the consequences of this exploration was the discovery of novel classical solutions in noncommutative field theories. Since then much work has been done in exploring many of their novel properties. My lectures focussed on some specific aspects of these noncommutative solitons. They primarily reflect the topics that I have worked on and are not intended to be a survey of the large amount of work on this topic. We have tried to give a flavour of the physics that can be captured by the relatively elementary classical solutions of noncommutative field theories. We have seen in different contexts how these solitons are really simple manifestations of D-branes, possessing many of their important features. Though they have been primarily studied in the context of tachyon condensation, we saw that they can also shed some light on the resolution of singularities in spacetime by D-brane probes. In addition to other applications in string theory it is important at this stage to explore their presence in other systems with a strong magnetic field like the quantum hall effect.
Interaction of solitons with a string of coupled quantum dots
Energy Technology Data Exchange (ETDEWEB)
Kumar, Vijendra, E-mail: vsmedphysics@gmail.com; Swami, O. P., E-mail: omg1789@gmail.com; Nagar, A. K., E-mail: ajaya.nagar@gmail.com [Department of Physics, Govt. Dungar College, Bikaner, Rajasthan 334001 (India); Taneja, S., E-mail: sachintaneja9@gmail.com [Department of Radiotherapy, CHAF Bangalore, Karnataka 560007 (India)
2016-05-06
In this paper, we develop a theory for discrete solitons interaction with a string of coupled quantum dots in view of the local field effects. Discrete nonlinear Schrodinger (DNLS) equations are used to describe the dynamics of the string. Numerical calculations are carried out and results are analyzed with the help of matlab software. With the help of numerical solutions we demonstrate that in the quantum dots string, Rabi oscillations (RO) are self trapped into stable bright Rabi solitons. The Rabi oscillations in different types of nanostructures have potential applications to the elements of quantum logic and quantum memory.
A set of exact two soliton wave solutions to Einstein field equations
International Nuclear Information System (INIS)
Wang Youtang; He Zhixian
1991-09-01
A set of exact solutions of Einstein equations in vacuum is obtained. Taking this set of solutions as seed solutions and making use of the Belinsky-Zakharov generation technique a set of generated solutions is constructed. Both set of exact solutions and a set of generated solutions describe two solition waves, which propagate in opposite directions and collide with each other, and then recover their original shapes. The singularities of the two set of solutions are analyzed. The relationship between our solutions and other solutions is also discussed. (author). 11 refs, 4 figs
Cross-talk dynamics of optical solitons in a broadband Kerr nonlinear system with weak cubic loss
International Nuclear Information System (INIS)
Peleg, Avner; Nguyen, Quan M.; Chung, Yeojin
2010-01-01
We study the dynamics of fast soliton collisions in a Kerr nonlinear optical waveguide with weak cubic loss. We obtain analytic expressions for the amplitude and frequency shifts in a single two-soliton collision and show that the impact of a fast three-soliton collision is given by the sum of the two-soliton interactions. Our analytic predictions are confirmed by numerical simulations with the perturbed nonlinear Schroedinger (NLS) equation. Furthermore, we show that the deterministic collision-induced dynamics of soliton amplitudes in a broadband waveguide system with N frequency channels is described by a Lotka-Volterra model for N competing species. For a two-channel system we find that stable transmission with equal prescribed amplitudes can be achieved by a proper choice of linear amplifier gain. The predictions of the Lotka-Volterra model are confirmed by numerical solution of a perturbed coupled-NLS model.
Stability analysis of cavity solitons governed by the cubic-quintic Ginzburg-Landau equation
International Nuclear Information System (INIS)
Ding, Edwin; Kutz, J Nathan; Luh, Kyle
2011-01-01
A theoretical model is proposed to describe the formation of two-dimensional solitons in a laser cavity, extending the concept of the mode locking of temporal solitons in fibre lasers to spatial mode locking in nonlinear crystals. A linear stability analysis of the governing model based upon radial symmetry is performed to characterize the multi-pulsing instability of the laser as a function of gain. It is found that a stable n-pulse solution of the system bifurcates into a (n + 1)-pulse solution through the development of a periodic solution (Hopf bifurcation), and the results are consistent with simulations of the full model.
International Nuclear Information System (INIS)
Aichelburg, P.C.; Embacher, F.
1987-01-01
In previous work solitons of N = 2 supergravity were described as test particles in an external supergravity field. In the present paper we derive the effective interaction of two solitons by inserting a classical soliton configuration for the background into the Lagrangian and apply a slow-motion and large-distance approximation. We obtain the interaction potential to lowest order that incorporates the effect of the supercharge. The resulting classical system is quantized and, as a final step, an effective quantum field theory is formulated. (Author)
International Nuclear Information System (INIS)
Boya, L.J.; Carinena, J.F.; Mateos, J.
1978-01-01
Starting from classical field theory with a Lagrangian, solitons are identified with solutions of the field equations which satisfy peculiar boundary conditions. The symmetry group which causes the degenerate vacuum is taken generally internal, that is, not operating in space-time. Gauge symmetry plays a dominant role. A precise definition of solitons is given and it is shown how to study some continuous mappings of the ''distant'' parts of space on the set of degenerate vacua. A marvellous instrument, the exact homotopy sequence, is applied to calculate homotopy groups of some higher-dimensional manifolds
Spatiotemporal optical solitons
International Nuclear Information System (INIS)
Malomed, Boris A; Mihalache, Dumitru; Wise, Frank; Torner, Lluis
2005-01-01
In the course of the past several years, a new level of understanding has been achieved about conditions for the existence, stability, and generation of spatiotemporal optical solitons, which are nondiffracting and nondispersing wavepackets propagating in nonlinear optical media. Experimentally, effectively two-dimensional (2D) spatiotemporal solitons that overcome diffraction in one transverse spatial dimension have been created in quadratic nonlinear media. With regard to the theory, fundamentally new features of light pulses that self-trap in one or two transverse spatial dimensions and do not spread out in time, when propagating in various optical media, were thoroughly investigated in models with various nonlinearities. Stable vorticity-carrying spatiotemporal solitons have been predicted too, in media with competing nonlinearities (quadratic-cubic or cubic-quintic). This article offers an up-to-date survey of experimental and theoretical results in this field. Both achievements and outstanding difficulties are reviewed, and open problems are highlighted. Also briefly described are recent predictions for stable 2D and 3D solitons in Bose-Einstein condensates supported by full or low-dimensional optical lattices. (review article)
International Nuclear Information System (INIS)
Anabalón, Andrés; Astefanesei, Dumitru; Choque, David
2016-01-01
We construct exact hairy AdS soliton solutions in Einstein-dilaton gravity theory. We examine their thermodynamic properties and discuss the role of these solutions for the existence of first order phase transitions for hairy black holes. The negative energy density associated to hairy AdS solitons can be interpreted as the Casimir energy that is generated in the dual filed theory when the fermions are antiperiodic on the compact coordinate.
Energy Technology Data Exchange (ETDEWEB)
Anabalón, Andrés, E-mail: andres.anabalon@uai.cl [Departamento de Ciencias, Facultad de Artes Liberales and Facultad de Ingeniería y Ciencias, Universidad Adolfo Ibáñez, Av. Padre Hurtado 750, Viña del Mar (Chile); Astefanesei, Dumitru, E-mail: dumitru.astefanesei@pucv.cl [Instituto de Física, Pontificia Universidad Católica de Valparaíso, Casilla 4059, Valparaíso (Chile); Choque, David, E-mail: brst1010123@gmail.com [Instituto de Física, Pontificia Universidad Católica de Valparaíso, Casilla 4059, Valparaíso (Chile); Universidad Técnica Federico Santa María, Av. España 1680, Valparaíso (Chile)
2016-11-10
We construct exact hairy AdS soliton solutions in Einstein-dilaton gravity theory. We examine their thermodynamic properties and discuss the role of these solutions for the existence of first order phase transitions for hairy black holes. The negative energy density associated to hairy AdS solitons can be interpreted as the Casimir energy that is generated in the dual filed theory when the fermions are antiperiodic on the compact coordinate.
International Nuclear Information System (INIS)
Li Juan; Zhang Haiqiang; Xu Tao; Zhang, Ya-Xing; Tian Bo
2007-01-01
For the long-distance communication and manufacturing problems in optical fibers, the propagation of subpicosecond or femtosecond optical pulses can be governed by the variable-coefficient nonlinear Schroedinger equation with higher order effects, such as the third-order dispersion, self-steepening and self-frequency shift. In this paper, we firstly determine the general conditions for this equation to be integrable by employing the Painleve analysis. Based on the obtained 3 x 3 Lax pair, we construct the Darboux transformation for such a model under the corresponding constraints, and then derive the nth-iterated potential transformation formula by the iterative process of Darboux transformation. Through the one- and two-soliton-like solutions, we graphically discuss the features of femtosecond solitons in inhomogeneous optical fibers
Soliton-soliton effective interaction
International Nuclear Information System (INIS)
Maki, J.N.
1986-01-01
A scheme of semi-phenomenological quantization is proposed for the collision process of two equal size envelopes-solitons provided by nonlinear Schroedinger equation. The time advance due to two envelopes-solitons collision was determined. Considering the solitons as puntual particles and using the description of classical mechanics, the effective envelope soliton-envelope soliton attractive potential, denominated modified Poschl-Teller potential. The obtainment of this potential was possible using the information in from of system memory, done by an analytical expression of time delay. Such system was quantized using this effective potential in Schroeding equation. The S col matrix of two punctual bodies was determined, and it is shown that, in the limit of 1 2 2 /mN 4 it reproduces the exact S 2N matrix obtained from soliton packet wich incurs on another soliton packet. Every ones have the same mass, interacts by contact force between two bodies. These packets have only one bound state, i e, do not have excited states. It was verified that, using the S col matrix, the binding energy of ground state of the system can be obtained, which is coincident with 2N particles in the 1/N approximation. In this scheme infinite spurious bound states are found (M.C.K.) [pt
Exact bright and dark spatial soliton solutions in saturable nonlinear media
International Nuclear Information System (INIS)
Calvo, Gabriel F.; Belmonte-Beitia, Juan; Perez-Garcia, Victor M.
2009-01-01
We present exact analytical bright and dark (black and grey) solitary wave solutions of a nonlinear Schroedinger-type equation describing the propagation of spatial beams in media exhibiting a saturable nonlinearity (such as centrosymmetric photorefractive materials). A qualitative study of the stationary equation is carried out together with a discussion of the stability of the solutions.
Solutions of the lattice sine–Gordon equation and the solitons of its cellular automaton
International Nuclear Information System (INIS)
Willox, R; Ramani, A; Grammaticos, B
2014-01-01
We analyse the solutions of the cellular automaton sine–Gordon equation and link them to solutions of the discrete, lattice, sine–Gordon. We show that while the ultradiscretizable, positive definite, solutions of the latter behave dispersively, certain parts of these dispersive waves nonetheless survive in the ultradiscrete limit, giving rise to the solutions of the cellular automaton. We examine the ultradiscrete solutions in the case of a generalized cellular automaton in which the dependent variable can assume non-integer values and we show that the collision of two solitary waves is inelastic, leading to the creation of a ‘bridge’ of constant height that links two outgoing structures. Based on the ultradiscrete form of the sine–Gordon equation we explain the appearance of this bridging region and we describe its interaction with a solitary wave. (paper)
Generalized sine-Gordon solitons
International Nuclear Information System (INIS)
Santos, C dos; Rubiera-Garcia, D
2011-01-01
In this paper, we construct analytical self-dual soliton solutions in (1+1) dimensions for two families of models which can be seen as generalizations of the sine-Gordon system but where the kinetic term is non-canonical. For that purpose we use a projection method applied to the sine-Gordon soliton. We focus our attention on the wall and lump-like soliton solutions of these k-field models. These solutions and their potentials reduce to those of the Klein-Gordon kink and the standard lump for the case of a canonical kinetic term. As we increase the nonlinearity on the kinetic term the corresponding potentials get modified and the nature of the soliton may change, in particular, undergoing a topology modification. The procedure constructed here is shown to be a sort of generalization of the deformation method for a specific class of k-field models. (paper)
International Nuclear Information System (INIS)
Aichelburg, P.C.; Embacher, F.
1987-01-01
The motion of a soliton in a supergravity background configuration is studied. The dynamics of the soliton is desribed by a trajectory in curved N = 2 superspace. For the proposed Langrangian the moments, the constraints and the generators of local supertranslations are displayed. An additional local gauge symmetry is exhibited. Special emphasis is laid on the classical equations of motion. These turn out to be a supersymmetric generalization of Papapetrou's equation of motion for a spinning particle in a gravitational field. (Author)
International Nuclear Information System (INIS)
Friedberg, R.
1977-01-01
It is pointed out that the study of solitons offers a new departure for the problem of handling bound states in relativistic quantum field theory which has hampered development of a simple conventional model of hadrons. The principle is illustrated by the case of a quantum mechanical particle moving in two dimensions under the centrally symmetric and quasi-harmonic potential. Restriction is made to nontopological solitons. These ideas are applied to a model of hadrons. 10 references
Soliton models in resonant and nonresonant optical fibers
Indian Academy of Sciences (India)
where Γ is the damping (> 0) and gain (< 0) parameter. Using the perturbation method and zeroth approximation, one-soliton solution is constructed and the amplification and damping of soliton is explained in figure 2. In addition, by introducing the initial phase. Figure 1. Two soliton solutions of the NLS equation. Figure 2.
Approximate treatment of two soliton solutions of the sine-Gordon equation
International Nuclear Information System (INIS)
Mihaly, L.
1979-05-01
The so called breather solution of the sine-Gordon equation is phenomenologically described by an appropri.ately choosen potential acting between two particles. For some applications the method proves to be equivalent to other classical and quantum calculations. (author)
Two-soliton interaction as an elementary act of soliton turbulence in integrable systems
Energy Technology Data Exchange (ETDEWEB)
Pelinovsky, E.N. [Department of Information Systems, National Research University – Higher School of Economics, Nizhny Novgorod (Russian Federation); Department of Nonlinear Geophysical Processes, Institute of Applied Physics, Russian Academy of Sciences, Nizhny Novgorod (Russian Federation); Shurgalina, E.G.; Sergeeva, A.V.; Talipova, T.G. [Department of Nonlinear Geophysical Processes, Institute of Applied Physics, Russian Academy of Sciences, Nizhny Novgorod (Russian Federation); Department of Applied Mathematics, Nizhny Novgorod State Technical University, Nizhny Novgorod (Russian Federation); El, G.A., E-mail: g.el@lboro.ac.uk [Department of Mathematical Sciences, Loughborough University (United Kingdom); Grimshaw, R.H.J. [Department of Mathematical Sciences, Loughborough University (United Kingdom)
2013-01-03
Two-soliton interactions play a definitive role in the formation of the structure of soliton turbulence in integrable systems. To quantify the contribution of these interactions to the dynamical and statistical characteristics of the nonlinear wave field of soliton turbulence we study properties of the spatial moments of the two-soliton solution of the Korteweg–de Vries (KdV) equation. While the first two moments are integrals of the KdV evolution, the 3rd and 4th moments undergo significant variations in the dominant interaction region, which could have strong effect on the values of the skewness and kurtosis in soliton turbulence.
Nonlinear density waves in a marginally stable gravitating disk
International Nuclear Information System (INIS)
Korchagin, V.I.
1986-01-01
The evolution of short nonlinear density waves in a disk at the stability limit is studied for arbitrary values of the radial wave number k/sub r/. For waves with wave numbers that do not lie at the minimum of the dispersion curve, the behavior of the amplitude is described by a nonlinear parabolic equation; however, stationary soliton solutions cannot exist in such a system since there is no dispersion spreading of a packet. For wave numbers lying at the minimum of the dispersion curve, soliton structures with determined amplitude are possible. In stable gravitating disks and in a disk at the stability limit, two physically different types of soliton can exist
Gravitational generation of mass in soliton theory
International Nuclear Information System (INIS)
Kozhevnikov, I.R.; Rybakov, Yu.P.
1985-01-01
It is shown that in the framework of a simple scalar field model, that admits soliton solutions, with gravitational field interactions being specially included, one succeeds in ensuring for a scalar field a correct spacial asymptotics that depends on the system mass. Theory, the quantum relation of a corpuscular-wave dualism is fulfilled for soliton solutions in such a model
Bragg solitons in systems with separated nonuniform Bragg grating and nonlinearity
Ahmed, Tanvir; Atai, Javid
2017-09-01
The existence and stability of quiescent Bragg grating solitons are systematically investigated in a dual-core fiber, where one of the cores is uniform and has Kerr nonlinearity while the other one is linear and incorporates a Bragg grating with dispersive reflectivity. Three spectral gaps are identified in the system, in which both lower and upper band gaps overlap with one branch of the continuous spectrum; therefore, these are not genuine band gaps. However, the central band gap is a genuine band gap. Soliton solutions are found in the lower and upper gaps only. It is found that in certain parameter ranges, the solitons develop side lobes. To analyze the side lobes, we have derived exact analytical expressions for the tails of solitons that are in excellent agreement with the numerical solutions. We have analyzed the stability of solitons in the system by means of systematic numerical simulations. We have found vast stable regions in the upper and lower gaps. The effect and interplay of dispersive reflectivity, the group velocity difference, and the grating-induced coupling on the stability of solitons are investigated. A key finding is that a stronger grating-induced coupling coefficient counteracts the stabilization effect of dispersive reflectivity.
The dark soliton on a cnoidal wave background
International Nuclear Information System (INIS)
Shin, H J
2005-01-01
We find a solution of the dark soliton lying on a cnoidal wave background in a defocusing medium. We use the method of Darboux transformation, which is applied to the cnoidal wave solution of the defocusing nonlinear Schroedinger equation. Interesting characteristics of the dark soliton, i.e., the velocity and greyness, are calculated and compared with those of the dark soliton lying on a continuous wave background. We also calculate the shift of the crest of the cnoidal wave along the soliton
Attraction of nonlocal dark optical solitons
DEFF Research Database (Denmark)
Nikolov, Nikola Ivanov; Neshev, Dragomir; Krolikowski, Wieslaw
2004-01-01
We study the formation and interaction of spatial dark optical solitons in materials with a nonlocal nonlinear response. We show that unlike in local materials, where dark solitons typically repel, the nonlocal nonlinearity leads to a long-range attraction and formation of stable bound states...
International Nuclear Information System (INIS)
Darvishi, M.T.; Najafi, M.; Kavitha, L.; Venkatesh, M.
2012-01-01
The multiple exp-function method is a new approach to obtain multiple wave solutions of nonlinear partial differential equations (NLPDEs). By this method one can obtain multi-soliton solutions of NLPDEs. In this paper, using computer algebra systems, we apply the multiple exp-function method to construct the exact multiple wave solutions of a (2+1)-dimensional Boiti—Leon—Manna—Pempinelli equation. Also, we extend the equation to a (3+1)-dimensional case and obtain some exact solutions for the new equation by applying the multiple exp-function method. By these applications, we obtain single-wave, double-wave and multi-wave solutions for these equations.
Hopf solitons in the AFZ model
International Nuclear Information System (INIS)
Gillard, Mike
2011-01-01
The Aratyn–Ferreira–Zimerman (AFZ) model is a conformal field theory in three-dimensional space. It has solutions that are topological solitons classified by an integer-valued Hopf index. There exist infinitely many axial solutions which have been found analytically. Static axial, knot and linked solitons are found numerically using a modified volume preserving flow for Hopf index one to eight, allowing for comparison with other Hopf soliton models. Solutions include a static trefoil knot at Hopf index five. A one-parameter family of conformal Skyrme–Faddeev models, consisting of linear combinations of the Nicole and AFZ models, are also investigated numerically. The transition of solutions for Hopf index four is mapped across these models. A topological change between linked and axial solutions occurs, with fewer models (or a limited range of parameter values) permitting axial solitons than linked solitons at Hopf index four
Averaging for solitons with nonlinearity management
International Nuclear Information System (INIS)
Pelinovsky, D.E.; Kevrekidis, P.G.; Frantzeskakis, D.J.
2003-01-01
We develop an averaging method for solitons of the nonlinear Schroedinger equation with a periodically varying nonlinearity coefficient, which is used to effectively describe solitons in Bose-Einstein condensates, in the context of the recently proposed technique of Feshbach resonance management. Using the derived local averaged equation, we study matter-wave bright and dark solitons and demonstrate a very good agreement between solutions of the averaged and full equations
Intermode Breather Solitons in Optical Microresonators
Guo, Hairun; Lucas, Erwan; Pfeiffer, Martin H. P.; Karpov, Maxim; Anderson, Miles; Liu, Junqiu; Geiselmann, Michael; Jost, John D.; Kippenberg, Tobias J.
2017-10-01
Dissipative solitons can be found in a variety of systems resulting from the double balance between dispersion and nonlinearity, as well as gain and loss. Recently, they have been observed to spontaneously form in Kerr nonlinear microresonators driven by a continuous wave laser, providing a compact source of coherent optical frequency combs. As optical microresonators are commonly multimode, intermode interactions, which give rise to avoided mode crossings, frequently occur and can alter the soliton properties. Recent works have shown that avoided mode crossings cause the soliton to acquire a single-mode dispersive wave, a recoil in the spectrum, or lead to soliton decay. Here, we show that avoided mode crossings can also trigger the formation of breather solitons, solitons that undergo a periodic evolution in their amplitude and duration. This new breather soliton, referred to as an intermode breather soliton, occurs within a laser detuning range where conventionally stationary (i.e., stable) dissipative Kerr solitons are expected. We experimentally demonstrate the phenomenon in two microresonator platforms (crystalline magnesium fluoride and photonic chip-based silicon nitride microresonators) and theoretically describe the dynamics based on a pair of coupled Lugiato-Lefever equations. We show that the breathing is associated with a periodic energy exchange between the soliton and a second optical mode family, a behavior that can be modeled by a response function acting on dissipative solitons described by the Lugiato-Lefever model. The observation of breathing dynamics in the conventionally stable soliton regime is relevant to applications in metrology such as low-noise microwave generation, frequency synthesis, or spectroscopy.
International Nuclear Information System (INIS)
Liu Wenjun; Tian Bo; Xu Tao; Sun Kun; Jiang Yan
2010-01-01
Symbolically investigated in this paper is a nonlinear Schroedinger equation with the varying dispersion and nonlinearity for the propagation of optical pulses in the normal dispersion regime of inhomogeneous optical fibers. With the aid of the Hirota method, analytic one- and two-soliton solutions are obtained. Relevant properties of physical and optical interest are illustrated. Different from the previous results, both the bright and dark solitons are hereby derived in the normal dispersion regime of the inhomogeneous optical fibers. Moreover, different dispersion profiles of the dispersion-decreasing fibers can be used to realize the soliton control. Finally, soliton interaction is discussed with the soliton control confirmed to have no influence on the interaction. The results might be of certain value for the study of the signal generator and soliton control.
International Nuclear Information System (INIS)
Tang, D.Y.; Zhao, L.M.; Zhao, B.; Liu, A.Q.
2005-01-01
We report results of numerical simulations on multiple-soliton generation and soliton energy quantization in a soliton fiber ring laser passively mode locked by using the nonlinear polarization rotation technique. We found numerically that the formation of multiple solitons in the laser is caused by a peak-power-limiting effect of the laser cavity. It is also the same effect that suppresses the soliton pulse collapse, an intrinsic feature of solitons propagating in gain media, and makes the solitons stable in the laser. Furthermore, we show that the soliton energy quantization observed in the lasers is a natural consequence of the gain competition between the multiple solitons. Enlightened by the numerical result we speculate that multisoliton formation and soliton energy quantization observed in other types of soliton fiber lasers could have a similar mechanism
A simple formula for the conserved charges of soliton theories
International Nuclear Information System (INIS)
Ferreira, Luiz Agostinho; Zakrzewski, Wojtek J.
2007-01-01
We present a simple formula for all the conserved charges of soliton theories, evaluated on the solutions belonging to the orbit of the vacuum under the group of dressing transformations. For pedagogical reasons we perform the explicit calculations for the case of the sine-Gordon model, taken as a prototype of soliton theories. We show that the energy and momentum are boundary terms for all the solutions on the orbit of the vacuum. That orbit includes practically all the solutions of physical interest, namely solitons, multi-solitons, breathers, and combinations of solitons and breathers. The example of the mKdV equation is also given explicitly
An(1) Toda solitons and the dressing symmetry
International Nuclear Information System (INIS)
Belich, H.; Paunov, R.
1996-12-01
We present an elementary derivation of the soliton-like solutions in the A n (1) Toda models which is alternative to the previously used Hirota method. The solutions of the underlying linear problem corresponding to the N-solitons are calculated. This enables us to obtain explicit expression for the element which by dressing group action, produces a generic soliton solution. In the particular example of mono solitons we suggest a relation to vertex operator formalism, previously used by olive, Turok and Underwood. Our results can also be considered as generalization of the approach to the sine-Gordon solitons, proposed by Babelon and Bernard. (author)
Collision dynamics of gap solitons in Kerr media
International Nuclear Information System (INIS)
Royston Neill, D.; Atai, Javid
2006-01-01
The collision dynamics of counterpropagating gap solitons in a fiber Bragg grating are investigated. In the case of initially in-phase solitons, it is found that the dynamics are more complex and richer than previously reported. An important finding is that, in general, the outcome of the collisions is dependent upon gap soliton parameters (θ, V) and the initial separation of solitons. However, if the solitons are initially very far apart the dependence on the initial separation is negligible. In the case of π-out-of-phase solitons, we find that they generally bounce off each other with negligible radiation as long as the solitons are stable (i.e., 0 π/1.98) the collision strongly catalyzes the onset of instability and results in the destruction of solitons
International Nuclear Information System (INIS)
Aichelburg, P.C.; Embacher, F.
1987-01-01
The Langrangian for a single free soliton in N = 2 supergravity as proposed in an earlier paper, is studied. We analyze the algebra of constraints and discuss the local gauge symmetry due to the existence of first class constraints. The classical motion as well as a Gupta-Bleuler type quantization are given. (Author)
Tchen, C. M.
1986-01-01
Theoretical and numerical works in atmospheric turbulence have used the Navier-Stokes fluid equations exclusively for describing large-scale motions. Controversy over the existence of an average temperature gradient for the very large eddies in the atmosphere suggested that a new theoretical basis for describing large-scale turbulence was necessary. A new soliton formalism as a fluid analogue that generalizes the Schrodinger equation and the Zakharov equations has been developed. This formalism, processing all the nonlinearities including those from modulation provided by the density fluctuations and from convection due to the emission of finite sound waves by velocity fluctuations, treats large-scale turbulence as coalescing and colliding solitons. The new soliton system describes large-scale instabilities more explicitly than the Navier-Stokes system because it has a nonlinearity of the gradient type, while the Navier-Stokes has a nonlinearity of the non-gradient type. The forced Schrodinger equation for strong fluctuations describes the micro-hydrodynamical state of soliton turbulence and is valid for large-scale turbulence in fluids and plasmas where internal waves can interact with velocity fluctuations.
Seadawy, Aly R.; Kumar, Dipankar; Chakrabarty, Anuz Kumar
2018-05-01
The (2+1)-dimensional hyperbolic and cubic-quintic nonlinear Schrödinger equations describe the propagation of ultra-short pulses in optical fibers of nonlinear media. By using an extended sinh-Gordon equation expansion method, some new complex hyperbolic and trigonometric functions prototype solutions for two nonlinear Schrödinger equations were derived. The acquired new complex hyperbolic and trigonometric solutions are expressed by dark, bright, combined dark-bright, singular and combined singular solitons. The obtained results are more compatible than those of other applied methods. The extended sinh-Gordon equation expansion method is a more powerful and robust mathematical tool for generating new optical solitary wave solutions for many other nonlinear evolution equations arising in the propagation of optical pulses.
International Nuclear Information System (INIS)
Zhang Yufeng; Tam, Honwah; Feng Binlu
2011-01-01
Highlights: → A generalized Zakharov-Shabat equation is obtained. → The generalized AKNS vector fields are established. → The finite-band solution of the g-ZS equation is obtained. → By using a Lie algebra presented in the paper, a new soliton hierarchy with an arbitrary parameter is worked out. - Abstract: In this paper, a generalized Zakharov-Shabat equation (g-ZS equation), which is an isospectral problem, is introduced by using a loop algebra G ∼ . From the stationary zero curvature equation we define the Lenard gradients {g j } and the corresponding generalized AKNS (g-AKNS) vector fields {X j } and X k flows. Employing the nonlinearization method, we obtain the generalized Zhakharov-Shabat Bargmann (g-ZS-B) system and prove that it is Liouville integrable by introducing elliptic coordinates and evolution equations. The explicit relations of the X k flows and the polynomial integrals {H k } are established. Finally, we obtain the finite-band solutions of the g-ZS equation via the Abel-Jacobian coordinates. In addition, a soliton hierarchy and its Hamiltonian structure with an arbitrary parameter k are derived.
SU(2) Yang-Mills solitons in R2 gravity
Perapechka, I.; Shnir, Ya.
2018-05-01
We construct new family of spherically symmetric regular solutions of SU (2) Yang-Mills theory coupled to pure R2 gravity. The particle-like field configurations possess non-integer non-Abelian magnetic charge. A discussion of the main properties of the solutions and their differences from the usual Bartnik-McKinnon solitons in the asymptotically flat case is presented. It is shown that there is continuous family of linearly stable non-trivial solutions in which the gauge field has no nodes.
Hopf solitons in the Nicole model
International Nuclear Information System (INIS)
Gillard, Mike; Sutcliffe, Paul
2010-01-01
The Nicole model is a conformal field theory in a three-dimensional space. It has topological soliton solutions classified by the integer-valued Hopf charge, and all currently known solitons are axially symmetric. A volume-preserving flow is used to construct soliton solutions numerically for all Hopf charges from 1 to 8. It is found that the known axially symmetric solutions are unstable for Hopf charges greater than 2 and new lower energy solutions are obtained that include knots and links. A comparison with the Skyrme-Faddeev model suggests many universal features, though there are some differences in the link types obtained in the two theories.
DEFF Research Database (Denmark)
Esbensen, B.K.; Bache, Morten; Krolikowski, W.
2012-01-01
We employ the formal analogy between quadratic and nonlocal solitons to investigate analytically the properties of solitons and soliton bound states in second-harmonic generation in the regime of negative diffraction or dispersion of the second harmonic. We show that in the nonlocal description...... this regime corresponds to a periodic nonlocal response function. We then use the strongly nonlocal approximation to find analytical solutions of the families of single bright solitons and their bound states in terms of Mathieu functions....
International Nuclear Information System (INIS)
Walliser, Hans
2000-01-01
Chiral Lagrangians as effective field theories of QCD are successfully applied to meson physics in the framework of chiral perturbation theory. Because of their nonlinear structure these Lagrangians allow for static soliton solutions interpreted as baryons. Their semiclassical quantization, which provides the leading order in an 1/N C expansion with N C the number of colors, turned out to be insufficient to obtain satisfactory agreement with empirical baryon observables. However with N C =3, large corrections are expected in the next-to-leading order carried by mesonic fluctuations around the soliton background, which require renormalization to 1-loop. In contrast to chiral perturbation theory, the low-energy Lagrangian proves inapt and terms with an arbitrary number of gradients may in principle contribute. Assumptions about the a priori unknown higher chiral orders are tested by the scale-dependence of the results. For example, in the simple Sine-Gordon model with 1 scalar field in 1+1 dimensions, knowledge of the low-energy behavior together with the mere existence of an underlying 1-loop renormalizable scale-independent solitonic theory is sufficient to regain the full solution. Baryonic observables calculated within that framework generally lead to better agreement with experiment except for the axial quantities. For these quantities the 1/N C expansion does not converge sufficiently fast because the current algebra mixes different N C orders
Lombardi, G.; Van Alphen, W.; Klimin, S. N.; Tempere, J.
2017-09-01
In the present article the snake instability mechanism for dark solitons in superfluid Fermi gases is studied in the context of a recently developed effective field theory [S. N. Klimin et al., Eur. Phys. J. B 88, 122 (2015), 10.1140/epjb/e2015-60213-4]. This theoretical treatment has proven to be suitable to study stable dark solitons in quasi-one-dimensional setups across the BEC-BCS crossover. In this paper the nodal plane of the stable soliton solution is perturbed by adding a transverse modulation. The numerical solution of the system of coupled nonlinear differential equations describing the amplitude of the perturbation leads to an estimate of the growth rate and characteristic length scale of the instability, which are calculated for a wide range of interaction regimes and compared to other theoretical predictions. The behavior of the maximum transverse size that the atomic cloud can have in order to preserve the stability is described across the BEC-BCS crossover. The analysis of the effects of spin imbalance on this critical length reveals a stabilization of the soliton with increasing imbalance and therefore provides the experimental community with a method to achieve the realization of stable solitons in real three-dimensional configurations, without reducing the system dimensionality.
Vector pulsing soliton of self-induced transparency in waveguide
International Nuclear Information System (INIS)
Adamashvili, G.T.
2015-01-01
A theory of an optical resonance vector pulsing soliton in waveguide is developed. A thin transition layer containing semiconductor quantum dots forms the boundary between the waveguide and one of the connected media. Analytical and numerical solutions for the optical vector pulsing soliton in waveguide are obtained. The vector pulsing soliton in the presence of excitonic and bi-excitonic excitations is compared with the soliton for waveguide TM-modes with parameters that can be used in modern optical experiments. It is shown that these nonlinear waves have significantly different parameters and shapes. - Highlights: • An optical vector pulsing soliton in a planar waveguide is presented. • Explicit form of the optical vector pulsing soliton are obtained. • The vector pulsing soliton and the soliton have different parameters and profiles
Energy Technology Data Exchange (ETDEWEB)
Yang, Jin-Wei; Gao, Yi-Tian, E-mail: gaoyt163@163.com; Wang, Qi-Min; Su, Chuan-Qi; Feng, Yu-Jie; Yu, Xin
2016-01-15
In this paper, a fourth-order variable-coefficient nonlinear Schrödinger equation is studied, which might describe a one-dimensional continuum anisotropic Heisenberg ferromagnetic spin chain with the octuple–dipole interaction or an alpha helical protein with higher-order excitations and interactions under continuum approximation. With the aid of auxiliary function, we derive the bilinear forms and corresponding constraints on the variable coefficients. Via the symbolic computation, we obtain the Lax pair, infinitely many conservation laws, one-, two- and three-soliton solutions. We discuss the influence of the variable coefficients on the solitons. With different choices of the variable coefficients, we obtain the parabolic, cubic, and periodic solitons, respectively. We analyse the head-on and overtaking interactions between/among the two and three solitons. Interactions between a bound state and a single soliton are displayed with different choices of variable coefficients. We also derive the quasi-periodic formulae for the three cases of the bound states.
Extension of noncommutative soliton hierarchies
International Nuclear Information System (INIS)
Dimakis, Aristophanes; Mueller-Hoissen, Folkert
2004-01-01
A linear system, which generates a Moyal-deformed two-dimensional soliton equation as an integrability condition, can be extended to a three-dimensional linear system, treating the deformation parameter as an additional coordinate. The supplementary integrability conditions result in a first-order differential equation with respect to the deformation parameter, the flow of which commutes with the flow of the deformed soliton equation. In this way, a deformed soliton hierarchy can be extended to a bigger hierarchy by including the corresponding deformation equations. We prove the extended hierarchy properties for the deformed AKNS hierarchy, and specialize to the cases of deformed NLS, KdV and mKdV hierarchies. Corresponding results are also obtained for the deformed KP hierarchy. A deformation equation determines a kind of Seiberg-Witten map from classical solutions to solutions of the respective 'noncommutative' deformed equation
Solitons in four dimensional gravity
International Nuclear Information System (INIS)
Matos, T.
1990-01-01
An alternative method to solve the Chiral equations with SL (2,R) symmetry is developed. One gets the N-soliton solution using the Neugebauer Ansatz. For N = 1 one obtains the Backlund transformation of the Chiral equations. From the application of this transformation for the flat seed solution one finds the Kerr-NUT solution. This method can be applied to generate solutions of the n-dimensional Einstein equations (Author)
Stable solitary waves in super dense plasmas at external magnetic fields
Ghaani, Azam; Javidan, Kurosh; Sarbishaei, Mohsen
2015-07-01
Propagation of localized waves in a Fermi-Dirac distributed super dense matter at the presence of strong external magnetic fields is studied using the reductive perturbation method. We have shown that stable solitons can be created in such non-relativistic fluids in the presence of an external magnetic field. Such solitary waves are governed by the Zakharov-Kuznetsov (ZK) equation. Properties of solitonic solutions are studied in media with different values of background mass density and strength of magnetic field.
On the solution of high order stable time integration methods
Czech Academy of Sciences Publication Activity Database
Axelsson, Owe; Blaheta, Radim; Sysala, Stanislav; Ahmad, B.
2013-01-01
Roč. 108, č. 1 (2013), s. 1-22 ISSN 1687-2770 Institutional support: RVO:68145535 Keywords : evolution equations * preconditioners for quadratic matrix polynomials * a stiffly stable time integration method Subject RIV: BA - General Mathematics Impact factor: 0.836, year: 2013 http://www.boundaryvalueproblems.com/content/2013/1/108
International Nuclear Information System (INIS)
Goetz, G.
1988-01-01
It is shown that the plane-wave solutions for the equations governing the motion of a self-gravitating isothermal fluid in Newtonian hydrodynamics are generated by a sine-Gordon equation which is solvable by an 'inverse scattering' transformation. A transformation procedure is outlined by means of which one can construct solutions of the gravity system out of a pair of solutions of the sine-Gordon equation, which are interrelated via an auto-Baecklund transformation. In general the solutions to the gravity system are obtained in a parametric representation in terms of characteristic coordinates. All solutions of the gravity system generated by the one-and two-soliton solutions of the sine-Gordon equation can be constructed explicitly. These might provide models for the evolution of flat structures as they are predicted to arise in the process of galaxy formation. (author)
The wrinkle-like N-solitons for the thermophoretic motion equation through graphene sheets
Ma, Yu-Lan; Li, Bang-Qing
2018-03-01
The main work is focused on the thermophoretic motion equation, which was derived from wrinkle wave motions in substrate-supported graphene sheets. Via the bilinear method, a class of wrinkle-like N-soliton solutions is constructed. The one-soliton, two-soliton and three-soliton are observed graphically. The shape, amplitude, open direction and width of the N-solitons are controllable through certain parameters.
Non-topological solitons in field theories with kinetic self-coupling
International Nuclear Information System (INIS)
Diaz-Alonso, Joaquin; Rubiera-Garcia, Diego
2007-01-01
We investigate some fundamental features of a class of non-linear relativistic Lagrangian field theories with kinetic self-coupling. We focus our attention upon theories admitting static, spherically symmetric solutions in three space dimensions which are finite-energy and stable. We determine general conditions for the existence and stability of these non-topological soliton solutions. In particular, we perform a linear stability analysis that goes beyond the usual Derrick-like criteria. On the basis of these considerations we obtain a complete characterization of the soliton-supporting members of the aforementioned class of non-linear field theories. We then classify the family of soliton-supporting theories according to the central and asymptotic behaviors of the soliton field, and provide illustrative explicit examples of models belonging to each of the corresponding sub-families. In the present work we restrict most of our considerations to one and many-components scalar models. We show that in these cases the finite-energy static spherically symmetric solutions are stable against charge-preserving perturbations, provided that the vacuum energy of the model vanishes and the energy density is positive definite. We also discuss briefly the extension of the present approach to models involving other types of fields, but a detailed study of this more general scenario will be addressed in a separate publication
Optical spatial solitons: historical overview and recent advances.
Chen, Zhigang; Segev, Mordechai; Christodoulides, Demetrios N
2012-08-01
Solitons, nonlinear self-trapped wavepackets, have been extensively studied in many and diverse branches of physics such as optics, plasmas, condensed matter physics, fluid mechanics, particle physics and even astrophysics. Interestingly, over the past two decades, the field of solitons and related nonlinear phenomena has been substantially advanced and enriched by research and discoveries in nonlinear optics. While optical solitons have been vigorously investigated in both spatial and temporal domains, it is now fair to say that much soliton research has been mainly driven by the work on optical spatial solitons. This is partly due to the fact that although temporal solitons as realized in fiber optic systems are fundamentally one-dimensional entities, the high dimensionality associated with their spatial counterparts has opened up altogether new scientific possibilities in soliton research. Another reason is related to the response time of the nonlinearity. Unlike temporal optical solitons, spatial solitons have been realized by employing a variety of noninstantaneous nonlinearities, ranging from the nonlinearities in photorefractive materials and liquid crystals to the nonlinearities mediated by the thermal effect, thermophoresis and the gradient force in colloidal suspensions. Such a diversity of nonlinear effects has given rise to numerous soliton phenomena that could otherwise not be envisioned, because for decades scientists were of the mindset that solitons must strictly be the exact solutions of the cubic nonlinear Schrödinger equation as established for ideal Kerr nonlinear media. As such, the discoveries of optical spatial solitons in different systems and associated new phenomena have stimulated broad interest in soliton research. In particular, the study of incoherent solitons and discrete spatial solitons in optical periodic media not only led to advances in our understanding of fundamental processes in nonlinear optics and photonics, but also had a
Ring vortex solitons in nonlocal nonlinear media
DEFF Research Database (Denmark)
Briedis, D.; Petersen, D.E.; Edmundson, D.
2005-01-01
We study the formation and propagation of two-dimensional vortex solitons, i.e. solitons with a phase singularity, in optical materials with a nonlocal focusing nonlinearity. We show that nonlocality stabilizes the dynamics of an otherwise unstable vortex beam. This occurs for either single...... or higher charge fundamental vortices as well as higher order (multiple ring) vortex solitons. Our results pave the way for experimental observation of stable vortex rings in other nonlocal nonlinear systems including Bose-Einstein condensates with pronounced long-range interparticle interaction....
Soliton cellular automata associated with crystal bases
International Nuclear Information System (INIS)
Hatayama, Goro; Kuniba, Atsuo; Takagi, Taichiro
2000-01-01
We introduce a class of cellular automata associated with crystals of irreducible finite dimensional representations of quantum affine algebras U' q (g-circumflex n ). They have solitons labeled by crystals of the smaller algebra U' q (g-circumflex n-1 ). We prove stable propagation of one soliton for g-circumflex n =A (2) 2n-1 ,A (2) 2n ,B (1) n ,C (1) n ,D (1) n and D (2) n+1 . For g-circumflex n =C (1) n , we also prove that the scattering matrices of two solitons coincide with the combinatorial R matrices of U' q (C (1) n-1 )-crystals
Negative mass solitons in gravity
International Nuclear Information System (INIS)
Cebeci, Hakan; Sarioglu, Oezguer; Tekin, Bayram
2006-01-01
We first reconstruct the conserved (Abbott-Deser) charges in the spin-connection formalism of gravity for asymptotically (Anti)-de Sitter spaces, and then compute the masses of the AdS soliton and the recently found Eguchi-Hanson solitons in generic odd dimensions, unlike the previous result obtained for only five dimensions. These solutions have negative masses compared to the global AdS or AdS/Z p spacetimes. As a separate note, we also compute the masses of the recent even dimensional Taub-NUT-Reissner-Nordstroem metrics
Soliton concepts and protein structure
Krokhotin, Andrei; Niemi, Antti J.; Peng, Xubiao
2012-03-01
Structural classification shows that the number of different protein folds is surprisingly small. It also appears that proteins are built in a modular fashion from a relatively small number of components. Here we propose that the modular building blocks are made of the dark soliton solution of a generalized discrete nonlinear Schrödinger equation. We find that practically all protein loops can be obtained simply by scaling the size and by joining together a number of copies of the soliton, one after another. The soliton has only two loop-specific parameters, and we compute their statistical distribution in the Protein Data Bank (PDB). We explicitly construct a collection of 200 sets of parameters, each determining a soliton profile that describes a different short loop. The ensuing profiles cover practically all those proteins in PDB that have a resolution which is better than 2.0 Å, with a precision such that the average root-mean-square distance between the loop and its soliton is less than the experimental B-factor fluctuation distance. We also present two examples that describe how the loop library can be employed both to model and to analyze folded proteins.
Quantum deflation of classical solitons
International Nuclear Information System (INIS)
Sveshnikov, K.; Silaev, P.
1996-01-01
It is shown, that due to nonperturbative effects, in the relativistic QFT the extended particle-like solutions should infinitely long collapse into some discontinuous configurations of the same topology, but vanishing mass. Analytical and numerical results for the dynamics of such a process are given for 1 + 1 dimensional soliton models
About Global Stable of Solutions of Logistic Equation with Delay
Kaschenko, S. A.; Loginov, D. O.
2017-12-01
The article is devoted to the definition of all the arguments for which all positive solutions of logistic equation with delay tend to zero for t → ∞. The authors have proved the acquainted Wright’s conjecture on evaluation of a multitude of such arguments. An approach that enables subsequent refinement of this evaluation has been developed.
International Nuclear Information System (INIS)
Schuur, P.C.
1985-01-01
The author presents a rigorous demonstration of the emergence of solitons from the KdV initial value problem with arbitrary initial function. Studying multisoliton solutions of the KdV in the general case of a nonzero reflection coefficient, he derives a new phase shift formula. He derives an estimate which indicates how well a real potential in the Zakharov-Shabat system is approximated by its reflectionless part. Moreover, the associated inverse scattering formalism is simplified considerably. He presents an asymptotic analysis of the sine-Gordon equation on right half lines almost linearly moving leftward. (Auth.)
International Nuclear Information System (INIS)
Wilets, L.
1988-01-01
Soliton models are well-suited for dynamical calculations, such as hadron-hadron interactions and collisions, since for each variable in the Lagrangian the time derivative of that variable also appears. For such models, constrained (deformed) mean field solutions provide a basis for generator coordinate dynamical calculations. This requires the solution of a large number of coupled, nonlinear, differential equations involving the quark and scalar fields. The Henyey-Wilets method reduces the problem to the solution of a set of coupled, linear, inhomogeneous, differential equations to be iterated. In the chromodielectric model, color confinement is effected by the self and mutual interactios of the quarks through the chromelectric field. This requires the self-consistent calculation of the gluon propagator in a spatially varying dielectric function. This now involves the solution of a set of coupled, nonlinear integro-differential equations, which can be linearized and solved by iterations. The problem is computation intensive. 20 refs
Classical and quantum aspects of topological solitons (using numerical methods)
International Nuclear Information System (INIS)
Weidig, T.
1999-08-01
In Introduction, we review integrable and topological solitons. In Numerical Methods, we describe how to minimise functionals, time-integrate configurations and solve eigenvalue problems. We also present the Simulated Annealing scheme for minimisation in solitonic systems. In Classical Aspects, we analyse the effect of the potential term on the structure of minimal-energy solutions for any topological charge n. The simplest holomorphic baby Skyrme model has no known stable minimal-energy solution for n > 1. The one-vacuum baby Skyrme model possesses non-radially symmetric multi-skyrmions that look like 'skyrmion lattices' formed by skyrmions with n = 2. The two-vacua baby Skyrme model has radially symmetric multi-skyrmions. We implement Simulated Annealing and it works well for higher order terms. We find that the spatial part of the six-derivative term is zero. In Quantum Aspects, we find the first order quantum mass correction for the φ 4 kink using the semi-classical expansion. We derive a trace formula which gives the mass correction by using the eigenmodes and values of the soliton and vacuum perturbations. We show that the zero mode is the most important contribution. We compute the mass correction of φ 4 kink and Sine-Gordon numerically by solving the eigenvalue equations and substituting into the trace formula. (author)
Stable solutions of inflation driven by vector fields
Energy Technology Data Exchange (ETDEWEB)
Emami, Razieh [Institute for Advanced Study, The Hong Kong University of Science and Technology, Clear Water Bay, Kowloon (Hong Kong); Mukohyama, Shinji [Center for Gravitational Physics, Yukawa Institute for Theoretical Physics, Kyoto University, 606-8502, Kyoto (Japan); Namba, Ryo [Department of Physics, McGill University, Montréal, QC, H3A 2T8 (Canada); Zhang, Ying-li, E-mail: iasraziehm@ust.hk, E-mail: shinji.mukohyama@yukawa.kyoto-u.ac.jp, E-mail: namba@physics.mcgill.ca, E-mail: yingli@bao.ac.cn [National Astronomy Observatories, Chinese Academy of Science, Beijing 100012 (China)
2017-03-01
Many models of inflation driven by vector fields alone have been known to be plagued by pathological behaviors, namely ghost and/or gradient instabilities. In this work, we seek a new class of vector-driven inflationary models that evade all of the mentioned instabilities. We build our analysis on the Generalized Proca Theory with an extension to three vector fields to realize isotropic expansion. We obtain the conditions required for quasi de-Sitter solutions to be an attractor analogous to the standard slow-roll one and those for their stability at the level of linearized perturbations. Identifying the remedy to the existing unstable models, we provide a simple example and explicitly show its stability. This significantly broadens our knowledge on vector inflationary scenarios, reviving potential phenomenological interests for this class of models.
Stable solutions of inflation driven by vector fields
International Nuclear Information System (INIS)
Emami, Razieh; Mukohyama, Shinji; Namba, Ryo; Zhang, Ying-li
2017-01-01
Many models of inflation driven by vector fields alone have been known to be plagued by pathological behaviors, namely ghost and/or gradient instabilities. In this work, we seek a new class of vector-driven inflationary models that evade all of the mentioned instabilities. We build our analysis on the Generalized Proca Theory with an extension to three vector fields to realize isotropic expansion. We obtain the conditions required for quasi de-Sitter solutions to be an attractor analogous to the standard slow-roll one and those for their stability at the level of linearized perturbations. Identifying the remedy to the existing unstable models, we provide a simple example and explicitly show its stability. This significantly broadens our knowledge on vector inflationary scenarios, reviving potential phenomenological interests for this class of models.
Nonlinear tunneling of optical soliton in 3 coupled NLS equation with symbolic computation
Energy Technology Data Exchange (ETDEWEB)
Mani Rajan, M.S., E-mail: senthilmanirajanofc@gmail.com [Department of Physics, Anna University, Madurai Region, Ramanathapuram (India); Mahalingam, A. [Department of Physics, Anna University, Chennai - 600 025 (India); Uthayakumar, A. [Department of Physics, Presidency College, Chennai - 600 005 (India)
2014-07-15
We investigated the soliton solution for N coupled nonlinear Schrödinger (CNLS) equations. These equations are coupled due to the cross-phase-modulation (CPM). Lax pair of this system is obtained via the Ablowitz–Kaup–Newell–Segur (AKNS) scheme and the corresponding Darboux transformation is constructed to derive the soliton solution. One and two soliton solutions are generated. Using two soliton solutions of 3 CNLS equation, nonlinear tunneling of soliton for both with and without exponential background has been discussed. Finally cascade compression of optical soliton through multi-nonlinear barrier has been discussed. The obtained results may have promising applications in all-optical devices based on optical solitons, study of soliton propagation in birefringence fiber systems and optical soliton with distributed dispersion and nonlinearity management. -- Highlights: •We consider the nonlinear tunneling of soliton in birefringence fiber. •3-coupled NLS (CNLS) equation with variable coefficients is considered. •Two soliton solutions are obtained via Darboux transformation using constructed Lax pair. •Soliton tunneling through dispersion barrier and well are investigated. •Finally, cascade compression of soliton has been achieved.
Lattice solitons in Bose-Einstein condensates
International Nuclear Information System (INIS)
Efremidis, Nikolaos K.; Christodoulides, Demetrios N.
2003-01-01
We systematically study the properties of lattice solitons in Bose-Einstein condensates with either attractive or repulsive atom interactions. This is done, by exactly solving the mean-field Gross-Pitaevskii equation in the presence of a periodic potential. We find new families of lattice soliton solutions that are characterized by the position of the energy eigenvalue within the associated band structure. These include lattice solitons in condensates with either attractive or repulsive atom interactions that exist in finite or semi-infinite gaps, as well as nonlinear modes that exhibit atomic population cutoffs
Solitons in Gross-Pitaevskii equation
International Nuclear Information System (INIS)
Lopes, E.
1985-01-01
It is observed that, when the potential is integrable and repulsive, the Gross-Pitaevskii Equation, with non-vanishing boundary conditions, describes a family of planar solitons. A method is presented which provides an exact soliton field to the Dirac Delta potential and an approximation solution to any other kind of potential. As an example the method is then applied to the case of a repulsive Yukawa potential. A brief discuss the relation between these solitons and Anderson's superfluidity mechanism, is also presented. (author) [pt
Rational solitons in the parity-time-symmetric nonlocal nonlinear Schrödinger model
International Nuclear Information System (INIS)
Li Min; Xu Tao; Meng Dexin
2016-01-01
In this paper, via the generalized Darboux transformation, rational soliton solutions are derived for the parity-time-symmetric nonlocal nonlinear Schrödinger (NLS) model with the defocusing-type nonlinearity. We find that the first-order solution can exhibit the elastic interactions of rational antidark-antidark, dark-antidark, and antidark-dark soliton pairs on a continuous wave background, but there is no phase shift for the interacting solitons. Also, we discuss the degenerate case in which only one rational dark or antidark soliton survives. Moreover, we reveal that the second-order rational solution displays the interactions between two solitons with combined-peak-valley structures in the near-field regions, but each interacting soliton vanishes or evolves into a rational dark or antidark soliton as |z| → ∞. In addition, we numerically examine the stability of the first- and second-order rational soliton solutions. (author)
Dynamical Instability and Soliton Concept
International Nuclear Information System (INIS)
Kartavenko, V.G.
1994-01-01
The problem of dynamical instability and clustering (stable fragments formation) in a breakup of excited nuclear systems are considered from the points of view of the soliton concept. It is noted that the volume (spinodal) instability can be associated with nonlinear terms, and the surface (Rayleigh-Taylor type) instability, with the dispersion terms in the evolution equations. The spinodal instability and the Rayleigh-Taylor instability may compensate each other and lead to stable quasi-soliton type objects. The simple analytical model is presented to illustrate this physical picture. The time evolution of an initially compressed cold nuclear system is analysed in the framework of the inverse mean-field method. It is demonstrated that the nonlinearity and dispersion terms of the evolution equations can lead to clusterization in the final channel. 8 p
Soliton models for thick branes
International Nuclear Information System (INIS)
Peyravi, Marzieh; Riazi, Nematollah; Lobo, Francisco S.N.
2016-01-01
In this work, we present new soliton solutions for thick branes in 4+1 dimensions. In particular, we consider brane models based on the sine-Gordon (SG), φ 4 and φ 6 scalar fields, which have broken Z 2 symmetry in some cases and are responsible for supporting and stabilizing the thick branes. The origin of the symmetry breaking in these models resides in the fact that the modified scalar field potential may have non-degenerate vacua. These vacua determine the cosmological constant on both sides of the brane. We also study the geodesic equations along the fifth dimension, in order to explore the particle motion in the neighborhood of the brane. Furthermore, we examine the stability of the thick branes, by determining the sign of the w 2 term in the expansion of the potential for the resulting Schroedinger-like equation, where w is the five-dimensional coordinate. It turns out that the φ 4 brane is stable, while there are unstable modes for certain ranges of the model parameters in the SG and φ 6 branes. (orig.)
Soliton models for thick branes
Energy Technology Data Exchange (ETDEWEB)
Peyravi, Marzieh [Ferdowsi University of Mashhad, Department of Physics, School of Sciences, Mashhad (Iran, Islamic Republic of); Riazi, Nematollah [Shahid Beheshti University, Physics Department, Tehran (Iran, Islamic Republic of); Lobo, Francisco S.N. [Faculdade de Ciencias da Universidade de Lisboa, Instituto de Astrofisica e Ciencias do Espaco, Lisbon (Portugal)
2016-05-15
In this work, we present new soliton solutions for thick branes in 4+1 dimensions. In particular, we consider brane models based on the sine-Gordon (SG), φ{sup 4} and φ{sup 6} scalar fields, which have broken Z{sub 2} symmetry in some cases and are responsible for supporting and stabilizing the thick branes. The origin of the symmetry breaking in these models resides in the fact that the modified scalar field potential may have non-degenerate vacua. These vacua determine the cosmological constant on both sides of the brane. We also study the geodesic equations along the fifth dimension, in order to explore the particle motion in the neighborhood of the brane. Furthermore, we examine the stability of the thick branes, by determining the sign of the w{sup 2} term in the expansion of the potential for the resulting Schroedinger-like equation, where w is the five-dimensional coordinate. It turns out that the φ{sup 4} brane is stable, while there are unstable modes for certain ranges of the model parameters in the SG and φ{sup 6} branes. (orig.)
Solitons of scalar field with induced nonlinearity and their stability
International Nuclear Information System (INIS)
Saha, B.
1999-09-01
Exact particle-like static, spherically and/or cylindrically symmetric solutions to the equations of interacting scalar and electromagnetic field system have been obtained. We considered FRW and Goedel universes as external gravitational field with spherical and cylindrical symmetry respectively. Beside the usual solitons some special regular solutions known as droplets, anti-droplets and hats (confined in finite interval and having trivial value beyond it) have been obtained. It has been shown that in FRW space-time equations with different interaction terms may have stable solutions while within the scope of Goedel model only the droplet-like and the hat-like configurations may be stable, providing that they are located in the region where g 00 > 0. (author)
Prinari, Barbara; Demontis, Francesco; Li, Sitai; Horikis, Theodoros P.
2018-04-01
The inverse scattering transform (IST) with non-zero boundary conditions at infinity is developed for an m × m matrix nonlinear Schrödinger-type equation which, in the case m = 2, has been proposed as a model to describe hyperfine spin F = 1 spinor Bose-Einstein condensates with either repulsive interatomic interactions and anti-ferromagnetic spin-exchange interactions (self-defocusing case), or attractive interatomic interactions and ferromagnetic spin-exchange interactions (self-focusing case). The IST for this system was first presented by Ieda et al. (2007) , using a different approach. In our formulation, both the direct and the inverse problems are posed in terms of a suitable uniformization variable which allows to develop the IST on the standard complex plane, instead of a two-sheeted Riemann surface or the cut plane with discontinuities along the cuts. Analyticity of the scattering eigenfunctions and scattering data, symmetries, properties of the discrete spectrum, and asymptotics are derived. The inverse problem is posed as a Riemann-Hilbert problem for the eigenfunctions, and the reconstruction formula of the potential in terms of eigenfunctions and scattering data is provided. In addition, the general behavior of the soliton solutions is analyzed in detail in the 2 × 2 self-focusing case, including some special solutions not previously discussed in the literature.
Noncommutative solitons: moduli spaces, quantization, finite θ effects and stability
Hadasz, Leszek; Rocek, Martin; Lindström, Ulf; von Unge, Rikard
2001-06-01
We find the N-soliton solution at infinite θ, as well as the metric on the moduli space corresponding to spatial displacements of the solitons. We use a perturbative expansion to incorporate the leading θ-1 corrections, and find an effective short range attraction between solitons. We study the stability of various solutions. We discuss the finite θ corrections to scattering, and find metastable orbits. Upon quantization of the two-soliton moduli space, for any finite θ, we find an s-wave bound state.
Helmholtz solitons in power-law optical materials
International Nuclear Information System (INIS)
Christian, J. M.; McDonald, G. S.; Potton, R. J.; Chamorro-Posada, P.
2007-01-01
A nonlinear Helmholtz equation for optical materials with regimes of power-law type of nonlinearity is proposed. This model captures the evolution of broad beams at any angle with respect to the reference direction in a wide range of media, including some semiconductors, doped glasses, and liquid crystals. Exact analytical soliton solutions are presented for a generic nonlinearity, within which known Kerr solitons comprise a subset. Three general conservation laws are also reported. Analysis and numerical simulations examine the stability of the Helmholtz power-law solitons. A propagation feature, associated with spatial solitons in power-law media, constituting a class of oscillatory solution, is identified
Bragg Fibers with Soliton-like Grating Profiles
Directory of Open Access Journals (Sweden)
Bugaychuk S.
2016-01-01
Full Text Available Nonlinear dynamical system corresponding to the optical holography in a nonlocal nonlinear medium with dissipation contains stable localized spatio-temporal states, namely the grid dissipative solitons. These solitons display a non-uniform profile of the grating amplitude, which has the form of the dark soliton in the reflection geometry. The transformation of the grating amplitude gives rise many new atypical effects for the beams diffracted on such grating, and they are very suitable for the fiber Brass gratings. The damped nonlinear Schrodinger equation is derived that describes the properties of the grid dissipative soliton.
One-parameter family of solitons from minimal surfaces
Indian Academy of Sciences (India)
solitons arising from a one parameter family of minimal surfaces. The process enables us to generate a new solution of the B–I equation from a given complex solution of a special type (which are abundant). We illustrate this with many examples. We find that the action or the energy of this family of solitons remains invariant ...
Spinning solitons in cubic-quintic nonlinear media
Indian Academy of Sciences (India)
in contrast to a recently found azimuthal instability of spinning doughnut-shaped solitons in the CQ NLS equation, their GL counterparts may be completely stable. On the other hand, a problem of fundamental interest is the possibility of the formation of fully three-dimensional (3D) optical spatiotemporal solitons, also referred ...
Electromagnetic solitons in degenerate relativistic electron–positron plasma
International Nuclear Information System (INIS)
Berezhiani, V I; Shatashvili, N L; Tsintsadze, N L
2015-01-01
The existence of soliton-like electromagnetic (EM) distributions in a fully degenerate electron–positron plasma is studied applying relativistic hydrodynamic and Maxwell equations. For a circularly polarized wave it is found that the soliton solutions exist both in relativistic as well as nonrelativistic degenerate plasmas. Plasma density in the region of soliton pulse localization is reduced considerably. The possibility of plasma cavitation is also shown. (invited comment)
Three-Dimensional Hermite—Bessel—Gaussian Soliton Clusters in Strongly Nonlocal Media
International Nuclear Information System (INIS)
Jin Hai-Qin; Yi Lin; Liang Jian-Chu; Cai Ze-Bin; Liu Fei
2012-01-01
We analytically and numerically demonstrate the existence of Hermite—Bessel—Gaussian spatial soliton clusters in three-dimensional strongly nonlocal media. It is found that the soliton clusters display the vortex, dipole azimuthon and quadrupole azimuthon in geometry, and the total number of solitons in the necklaces depends on the quantum number n and m of the Hermite functions and generalized Bessel polynomials. The numerical simulation is basically identical to the analytical solution, and white noise does not lead to collapse of the soliton, which confirms the stability of the soliton waves. The theoretical predictions may give new insights into low-energetic spatial soliton transmission with high fidelity
Dark and bright solitons in a quasi-one-dimensional Bose-Einstein condensate
International Nuclear Information System (INIS)
Wang, Shun-Jin; Jia, Cheng-Long; An, Jun-Hong; Zhao, Dun; Luo, Hong-Gang
2003-01-01
The analytical dark and bright soliton solutions of the one-dimensional Gross-Pitaevskii equation with a confining potential are obtained. For the bright soliton, the recent experimental finding is studied, and the particle number of the soliton and the window of the particle numbers for the bright soliton to occur are estimated analytically and in good agreement with the experimental data. The existence of dark soliton for the attractive interaction and bright soliton for the repulsive interaction is predicted under proper conditions
Directory of Open Access Journals (Sweden)
Chen Yue
Full Text Available The propagation of hydrodynamic wave packets and media with negative refractive index is studied in a quintic derivative nonlinear Schrödinger (DNLS equation. The quintic DNLS equation describe the wave propagation on a discrete electrical transmission line. We obtain a Lagrangian and the invariant variational principle for quintic DNLS equation. By using a class of ordinary differential equation, we found four types of exact solutions of the quintic DNLS equation, which are kink-type solitary wave solution, antikink-type solitary wave solution, sinusoidal solitary wave solution, bell-type solitary wave solution. By applying the modulation instability to discuss stability analysis of the obtained solutions. Modulation instabilities of continuous waves and localized solutions on a zero background have been investigated. Keywords: Quintic derivative NLS equation, Solitary wave solutions, Mathematical physics methods, 2000 MR Subject Classification: 35G20, 35Q53, 37K10, 49S05, 76A60
International Nuclear Information System (INIS)
Ochsenfeld, W.; Schmieder, H.
1976-01-01
Fast breeder fuel elements which have been highly burnt-up are reprocessed by extracting uranium and plutonium into an organic solution containing tributyl phosphate. The tributyl phosphate degenerates at least partially into dibutyl phosphate and monobutyl phosphate, which form stable complexes with tetravalent plutonium in the organic solution. This tetravalent plutonium is released from its complexed state and stripped into aqueous phase by contacting the organic solution with an aqueous phase containing tetravalent uranium. 6 claims, 1 drawing figure
International Nuclear Information System (INIS)
Borhanifar, A.; Kabir, M.M.; Maryam Vahdat, L.
2009-01-01
In this paper, the Exp-function method is used to obtain generalized solitonary solutions and periodic solutions of the Generalized Zakharov system and (2 + 1)-dimensional Nizhnik-Novikov-Veselov system. It is shown that the Exp-function method, with the help of symbolic computation, provides a powerful mathematical tool for solving nonlinear evolution equations in mathematical physics.
Quadratic spatial soliton interactions
Jankovic, Ladislav
Quadratic spatial soliton interactions were investigated in this Dissertation. The first part deals with characterizing the principal features of multi-soliton generation and soliton self-reflection. The second deals with two beam processes leading to soliton interactions and collisions. These subjects were investigated both theoretically and experimentally. The experiments were performed by using potassium niobate (KNBO 3) and periodically poled potassium titanyl phosphate (KTP) crystals. These particular crystals were desirable for these experiments because of their large nonlinear coefficients and, more importantly, because the experiments could be performed under non-critical-phase-matching (NCPM) conditions. The single soliton generation measurements, performed on KNBO3 by launching the fundamental component only, showed a broad angular acceptance bandwidth which was important for the soliton collisions performed later. Furthermore, at high input intensities multi-soliton generation was observed for the first time. The influence on the multi-soliton patterns generated of the input intensity and beam symmetry was investigated. The combined experimental and theoretical efforts indicated that spatial and temporal noise on the input laser beam induced multi-soliton patterns. Another research direction pursued was intensity dependent soliton routing by using of a specially engineered quadratically nonlinear interface within a periodically poled KTP sample. This was the first time demonstration of the self-reflection phenomenon in a system with a quadratic nonlinearity. The feature investigated is believed to have a great potential for soliton routing and manipulation by engineered structures. A detailed investigation was conducted on two soliton interaction and collision processes. Birth of an additional soliton resulting from a two soliton collision was observed and characterized for the special case of a non-planar geometry. A small amount of spiraling, up to 30
Solutions of the Strominger System via Stable Bundles on Calabi-Yau Threefolds
DEFF Research Database (Denmark)
Andreas, Björn; Garcia Fernandez, Mario
2012-01-01
We prove that a given Calabi-Yau threefold with a stable holomorphic vector bundle can be perturbed to a solution of the Strominger system provided that the second Chern class of the vector bundle is equal to the second Chern class of the tangent bundle. If the Calabi-Yau threefold has strict SU(......) holonomy then the equations of motion derived from the heterotic string effective action are also satisfied by the solutions we obtain....
Optical analogue of relativistic Dirac solitons in binary waveguide arrays
Energy Technology Data Exchange (ETDEWEB)
Tran, Truong X., E-mail: truong.tran@mpl.mpg.de [Department of Physics, Le Quy Don University, 236 Hoang Quoc Viet str., 10000 Hanoi (Viet Nam); Max Planck Institute for the Science of Light, Günther-Scharowsky str. 1, 91058 Erlangen (Germany); Longhi, Stefano [Department of Physics, Politecnico di Milano and Istituto di Fotonica e Nanotecnologie del Consiglio Nazionale delle Ricerche, Piazza L. da Vinci 32, I-20133 Milano (Italy); Biancalana, Fabio [Max Planck Institute for the Science of Light, Günther-Scharowsky str. 1, 91058 Erlangen (Germany); School of Engineering and Physical Sciences, Heriot-Watt University, EH14 4AS Edinburgh (United Kingdom)
2014-01-15
We study analytically and numerically an optical analogue of Dirac solitons in binary waveguide arrays in the presence of Kerr nonlinearity. Pseudo-relativistic soliton solutions of the coupled-mode equations describing dynamics in the array are analytically derived. We demonstrate that with the found soliton solutions, the coupled mode equations can be converted into the nonlinear relativistic 1D Dirac equation. This paves the way for using binary waveguide arrays as a classical simulator of quantum nonlinear effects arising from the Dirac equation, something that is thought to be impossible to achieve in conventional (i.e. linear) quantum field theory. -- Highlights: •An optical analogue of Dirac solitons in nonlinear binary waveguide arrays is suggested. •Analytical solutions to pseudo-relativistic solitons are presented. •A correspondence of optical coupled-mode equations with the nonlinear relativistic Dirac equation is established.
Potential motion for Thomas-Fermi non-topological solitons
International Nuclear Information System (INIS)
Bahcall, S.
1992-04-01
In the Thomas-Fermi approximation to theories of coupled fermions and scalars, the equations for spherically-symmetric non-topological solitons have the form of potential motion. This gives a straightforward method for proving the existence of non-topological solitons in a given theory and for finding the constant-density, saturating solutions
Soliton excitation in superlattice
International Nuclear Information System (INIS)
Mensah, S.Y.; Allotey, F.K.A.; Mensah, N.G.; Twum, A.K.
1995-10-01
Excitation of soliton in superlattice has been investigated theoretically. It is noted that the soliton velocity u and the length L depend on the amplitude E 0 and that an increase in the amplitude causes soliton width L to approach zero and the velocity u to that of light V in homogeneous medium. The characteristic parameters of soliton u, L and E 0 are related by expression u/L E 0 = ed/2(h/2π) which is constant depending only on the SL period d. It is observed also that the soliton has both energy E = 8V 2 (1 - u 2 /V 2 ) -1/2 and momentum P = u/V 2 E which makes it behave as relativistic free particle with rest energy 8V 2 . Its interaction with electrons can cause the soliton electric effect in SL. (author). 27 refs
Optical solitons and quasisolitons
International Nuclear Information System (INIS)
Zakharov, V.E.; Kuznetsov, E.A.
1998-01-01
Optical solitons and quasisolitons are investigated in reference to Cherenkov radiation. It is shown that both solitons and quasisolitons can exist, if the linear operator specifying their asymptotic behavior at infinity is sign-definite. In particular, the application of this criterion to stationary optical solitons shifts the soliton carrier frequency at which the first derivative of the dielectric constant with respect to the frequency vanishes. At that point the phase and group velocities coincide. Solitons and quasisolitons are absent, if the third-order dispersion is taken into account. The stability of a soliton is proved for fourth order dispersion using the sign-definiteness of the operator and integral estimates of the Sobolev type. This proof is based on the boundedness of the Hamiltonian for a fixed value of the pulse energy
Quark solitons as constituents of hadrons
International Nuclear Information System (INIS)
Ellis, J.; Frishman, Y.; Hanany, A.; Karlinev, M.
1992-01-01
We exhibit static solutions of multi-flavour QCD in two dimensions that have the quantum numbers of baryons and mesons, constructed out of quark and anti-quark solitons. In isolation the latter solitons have infinite energy, corresponding to the presence of a string carrying the non-singlet colour flux off to spatial infinity. When N c solitons of this type are combined, a static, finite-energy, colour singlet solution is formed, corresponding to a baryon. Similarly, static meson solutions are formed out of a soliton and an anti-soliton of different flavours. The stability of the mesons against annihilation is ensured by flavour conservation. The static solutions exist only when the fundamental fields of the bosonized lagrangian belong to U(N c xN f ) rather than to SU(N c )xU(N f ). Discussion of flavour-symmetry breaking requires a careful treatment of the normal-ordering ambiguity. Our results can be viewed as a derivation of the constituent quark model in QCD 2 , allowing a detailed study of constituent mass generation and of the heavy-quark symmetry. (orig.)
Exponentially Stable Stationary Solutions for Stochastic Evolution Equations and Their Perturbation
International Nuclear Information System (INIS)
Caraballo, Tomas; Kloeden, Peter E.; Schmalfuss, Bjoern
2004-01-01
We consider the exponential stability of stochastic evolution equations with Lipschitz continuous non-linearities when zero is not a solution for these equations. We prove the existence of anon-trivial stationary solution which is exponentially stable, where the stationary solution is generated by the composition of a random variable and the Wiener shift. We also construct stationary solutions with the stronger property of attracting bounded sets uniformly. The existence of these stationary solutions follows from the theory of random dynamical systems and their attractors. In addition, we prove some perturbation results and formulate conditions for the existence of stationary solutions for semilinear stochastic partial differential equations with Lipschitz continuous non-linearities
Ring-shaped quasi-soliton solutions to the two-and three-dimensional Sine-Gordon equation
International Nuclear Information System (INIS)
Christiansen, P.L.; Olsen, O.H.
1979-01-01
Ring-shaped solitary wave solutions to the Sine-Gordon equation in two and three spatial dimensions are investigated by numerical computation. Each expanding wave exhibits a return effect. The reflection of the shrinking wave at the singularity at the center of the wave is investigated in a particular case. Collision experiments in numero for expanding and shrinking concentric ring waves show that the solutions possess quasisoliton properties. A Baecklund transformation for the non-symmetric three-dimensional case is given. (Auth.)
International Nuclear Information System (INIS)
Manciu, M.; Sen, S.; Hurd, A.J.
1999-01-01
The authors consider a chain of elastic (Hertzian) grains that repel upon contact according to the potential V = adelta u , u > 2, where delta is the overlap between the grains. They present numerical and analytical results to show that an impulse initiated at an end of a chain of Hertzian grains in contact eventually propagates as a soliton for all n > 2 and that no solitons are possible for n le 2. Unlike continuous, they find that colliding solitons in discrete media initiative multiple weak solitons at the point of crossing
International Nuclear Information System (INIS)
Rajasekaran, G.
1978-01-01
Recent developments in the theory of solitons and related objects in the fields of high energy physics and nuclear physics are reviewed. The aim is to concentrate on the physical aspects and explain why these objects have awakened the interest of physicists. The physics of solitons is discussed with the help of a simple one-dimensional soliton. Then the physically more interesting monopole-soliton is considered and its connection with the original Dirac monopole is pointed out. The ''revolutionary'' possibility of making fermions as composites of bosons is indicated. Both the one-dimensional solitons and the monopole-soliton are examples of ''topological solitons'' and the role of topology in the physics of solitons is explained. The possible importance of topological quantum numbers in providing a fundamental understanding of the basic conservation laws of physics is pointed out. Two examples of non-topological solitons namely, the nucleon as a bag of almost-massless quarks and the abnormal nucleons as a bag of almost massless nucleons is discussed. (auth.)
Polarization-dependent solitons in the strong coupling regime of semiconductor microcavities
International Nuclear Information System (INIS)
Fu, Y.; Zhang, W.L.; Wu, X.M.
2015-01-01
This paper studies the influence of polarization on formation of vectorial polariton soliton in semiconductor microcavities through numerical simulations. It is found that the polariton solution greatly depends on the polarization of both the pump and exciting fields. By properly choosing the pump and exciting field polarization, bright–bright or bright–dark vectorial polariton solitons can be formed. Especially, when the input conditions of pump or exciting field of the two opposite polarizations are slightly asymmetric, an interesting phenomenon that the dark solitons transform into bright solitons occurs in the branch of soliton solutions.
Dynamical formation of a hairy black hole in a cavity from the decay of unstable solitons
International Nuclear Information System (INIS)
Sanchis-Gual, Nicolas; Font, José A; Carlos Degollado, Juan; Herdeiro, Carlos; Radu, Eugen
2017-01-01
Recent numerical relativity simulations within the Einstein–Maxwell–(charged-)Klein–Gordon (EMcKG) system have shown that the non-linear evolution of a superradiantly unstable Reissner–Nordström black hole (BH) enclosed in a cavity, leads to the formation of a BH with scalar hair. Perturbative evidence for the stability of such hairy BHs has been independently established, confirming they are the true endpoints of superradiant instability. The same EMcKG system admits also charged scalar soliton-type solutions, which can be either stable or unstable. Using numerical relativity techniques, we provide evidence that the time evolution of some of these unstable solitons leads, again, to the formation of a hairy BH. In some other cases, unstable solitons evolve into a (bald) Reissner–Nordström BH. These results establish that the system admits two distinct channels to form hairy BHs at the threshold of superradiance: growing hair from an unstable (bald) BH, or growing a horizon from an unstable (horizonless) soliton. Some parallelism with the case of asymptotically flat boson stars and Kerr BHs with scalar hair is drawn. (paper)
Dynamical formation of a hairy black hole in a cavity from the decay of unstable solitons
Sanchis-Gual, Nicolas; Degollado, Juan Carlos; Font, José A.; Herdeiro, Carlos; Radu, Eugen
2017-08-01
Recent numerical relativity simulations within the Einstein-Maxwell-(charged-)Klein-Gordon (EMcKG) system have shown that the non-linear evolution of a superradiantly unstable Reissner-Nordström black hole (BH) enclosed in a cavity, leads to the formation of a BH with scalar hair. Perturbative evidence for the stability of such hairy BHs has been independently established, confirming they are the true endpoints of superradiant instability. The same EMcKG system admits also charged scalar soliton-type solutions, which can be either stable or unstable. Using numerical relativity techniques, we provide evidence that the time evolution of some of these unstable solitons leads, again, to the formation of a hairy BH. In some other cases, unstable solitons evolve into a (bald) Reissner-Nordström BH. These results establish that the system admits two distinct channels to form hairy BHs at the threshold of superradiance: growing hair from an unstable (bald) BH, or growing a horizon from an unstable (horizonless) soliton. Some parallelism with the case of asymptotically flat boson stars and Kerr BHs with scalar hair is drawn.
Energy Technology Data Exchange (ETDEWEB)
Mancas, Stefan C. [Department of Mathematics, University of Central Florida, Orlando, FL 32816-1364 (United States)], E-mail: smancas@mail.ucf.edu; Roy Choudhury, S. [Department of Mathematics, University of Central Florida, Orlando, FL 32816-1364 (United States)], E-mail: choudhur@longwood.cs.ucf.edu
2009-04-15
Comprehensive numerical simulations (reviewed in Dissipative Solitons, Akhmediev and Ankiewicz (Eds.), Springer, Berlin, 2005) of pulse solutions of the cubic-quintic Ginzburg-Landau Equation (CGLE), a canonical equation governing the weakly nonlinear behavior of dissipative systems in a wide variety of disciplines, reveal various intriguing and entirely novel classes of solutions. In particular, there are five new classes of pulse or solitary waves solutions, viz. pulsating, creeping, snake, erupting, and chaotic solitons. In contrast to the regular solitary waves investigated in numerous integrable and non-integrable systems over the last three decades, these dissipative solitons are not stationary in time. Rather, they are spatially confined pulse-type structures whose envelopes exhibit complicated temporal dynamics. The numerical simulations also reveal very interesting bifurcations sequences of these pulses as the parameters of the CGLE are varied. In this paper, we address the issues of central interest in the area, i.e., the conditions for the occurrence of the five categories of dissipative solitons, as well the dependence of both their shape and their stability on the various parameters of the CGLE, viz. the nonlinearity, dispersion, linear and nonlinear gain, loss and spectral filtering parameters. Our predictions on the variation of the soliton amplitudes, widths and periods with the CGLE parameters agree with simulation results. First, we elucidate the Hopf bifurcation mechanism responsible for the various pulsating solitary waves, as well as its absence in Hamiltonian and integrable systems where such structures are absent. Next, we develop and discuss a variational formalism within which to explore the various classes of dissipative solitons. Given the complex dynamics of the various dissipative solutions, this formulation is, of necessity, significantly generalized over all earlier approaches in several crucial ways. Firstly, the starting formulation
International Nuclear Information System (INIS)
Li Biao; Chen Yong
2007-01-01
In this paper, the inhomogeneous nonlinear Schroedinger equation with the loss/gain and the frequency chirping is investigated. With the help of symbolic computation, three families of exact analytical solutions are presented by employing the extended projective Riccati equation method. From our results, many previous known results of nonlinear Schroedinger equation obtained by some authors can be recovered by means of some suitable selections of the arbitrary functions and arbitrary constants. Of optical and physical interests, soliton propagation and soliton interaction are discussed and simulated by computer, which include snake-soliton propagation and snake-solitons interaction, boomerang-like soliton propagation and boomerang-like solitons interaction, dispersion managed (DM) bright (dark) soliton propagation and DM solitons interaction
Coupling effects of grey-grey separate spatial screening soliton pairs
International Nuclear Information System (INIS)
Jiang Qichang; Su Yanli; Ji Xuanmang
2012-01-01
The existence and coupling effects of grey-grey separate spatial soliton pairs in a biased series non-photovoltaic photorefractive crystal circuit are investigated in this paper. The numerical solution of grey-grey soliton pairs is derived. The coupling effects between two grey solitons resulting from the input optical intensity and crystal temperature are analyzed numerically. The results show that when the input optical intensity of one crystal changes, two grey solitons in a soliton pair will all change; that is, two grey solitons can affect each other by the light-induced current that flows from one crystal to another. When the temperature of one crystal increases, the intensity width of the grey soliton in this crystal first decreases and then increases. Simultaneously, the intensity width of another grey soliton increases monotonically.
Soliton on a cnoidal wave background in the coupled nonlinear Schroedinger equation
International Nuclear Information System (INIS)
Shin, H J
2004-01-01
An application of the Darboux transformation on a cnoidal wave background in the coupled nonlinear Schroedinger equation gives a new solution which describes a soliton moving on a cnoidal wave. This is a generalized version of the previously known soliton solutions of dark-bright pair. Here a dark soliton resides on a cnoidal wave instead of on a constant background. It also exhibits a new type of soliton solution in a self-focusing medium, which describes a breakup of a generalized dark-bright pair into another generalized dark-bright pair and an 'oscillating' soliton. We calculate the shift of the crest of the cnoidal wave along a soliton and the moving direction of the soliton on a cnoidal wave
Phononless soliton waves as early forerunners of crystalline material fracture
International Nuclear Information System (INIS)
Dubovskij, O.A.; Orlov, A.V.
2007-01-01
Phononless soliton waves of compression are shown to generate at a critical tension of crystals featuring real Lennard-Jones potential of interatomic interaction just before their fracture. A new method of nonlinear micro dynamics was applied to define the initial atomic displacements at high excitation energies. A solution is found that corresponds to a soliton wave running before the front of fracture. In a bounded crystal, the soliton being reflected from the crystal boundary passes the front of fracture and deforms while moving in the opposite direction. The amplitude and spectral characteristics of that type of soliton waves in crystals with a modified Lennard-Jones potential have been investigated. An approximate analytical solution was found for the soliton waves [ru
Solitons on H bonds in proteins
DEFF Research Database (Denmark)
d'Ovidio, F.; Bohr, H.G.; Lindgård, Per-Anker
2003-01-01
system shows that the solitons are spontaneously created and are stable and moving along the helix axis. A perturbation on one of the three H-bond lines forms solitons on the other H bonds as well. The robust solitary wave may explain very long-lived modes in the frequency range of 100 cm(-1) which...... are found in recent x-ray laser experiments. The dynamics parameters of the Toda lattice are in accordance with the usual Lennard-Jones parameters used for realistic H-bond potentials in proteins....
Introduction to solitons and their applications in physics and biology
International Nuclear Information System (INIS)
Peyrard, M.
1995-01-01
The response of most of the physical systems to combined excitations is not a simple superposition of their response to individual stimuli. This is particularly true for biological systems in which the nonlinear effects are often the dominant ones. The intrinsic treatment of nonlinearities in mathematical models and physical systems has led to the emergence of the chaos and solitons concepts. The concept of soliton, relevant for systems with many degrees of freedom, provides a new tool in the studies of biomolecules because it has no equivalent in the world of linear excitations. The aim of this lecture is to present the main ideas that underline the soliton concept and to discuss some applications. Solitons are solitary waves, that propagate at constant speed without changing their shape. They are extremely stable to perturbations, in particular to collisions with small amplitude linear waves and with other solitons. Conditions to have solitons and equations of solitons propagation are analysed. Solitons can be divided into two main classes: topological and non-topological solitons which can be found at all scales and in various domains of physics and chemistry. Using simple examples, this paper shows how linear expansions can miss completely essential physical properties of a system. This is particularly characteristic for the pendulum chain example. Soliton theory offers alternative methods. Multiple scale approximations, or expansion on a soliton basis, can be very useful to provide a description of some physical phenomena. Nonlinear energy localization is also a very important concept valid for a large variety of systems. These concepts are probably even more relevant for biological molecules than for solid state physics, because these molecules are very deformable objects where large amplitude nonlinear motions or conformational changes are crucial for function. (J.S.). 14 refs., 9 figs
Novel loop-like solitons for the generalized Vakhnenko equation
International Nuclear Information System (INIS)
Zhang Min; Ma Yu-Lan; Li Bang-Qing
2013-01-01
A non-traveling wave solution of a generalized Vakhnenko equation arising from the high-frequent wave motion in a relaxing medium is derived via the extended Riccati mapping method. The solution includes an arbitrary function of an independent variable. Based on the solution, two hyperbolic functions are chosen to construct new solitons. Novel single-loop-like and double-loop-like solitons are found for the equation
Indian Academy of Sciences (India)
The history leading to the discovery of soliton is interesting and impressive. The first documented observation of the solitary wave was made in 1834 by the .... Through the inverse scattering method, we are in a position to define the soliton in a rigorous manner. A transformation from the field variables to the scattering data is ...
Wakeless triple soliton accelerator
International Nuclear Information System (INIS)
Mima, K.; Ohsuga, T.; Takabe, H.; Nishihara, K.; Tajima, T.; Zaidman, E.; Horton, W.
1986-09-01
We introduce and analyze the concept of a wakeless triple soliton accelerator in a plasma fiber. Under appropriate conditions the triple soliton with two electromagnetic and one electrostatic waves in the beat-wave resonance propagates with velocity c leaving no plasma wake behind, while the phase velocity of the electrostatic wave is made also c in the fiber
Directory of Open Access Journals (Sweden)
Arnaldo Simal do Nascimento
1997-12-01
Full Text Available We use $Gamma$--convergence to prove existence of stable multiple--layer stationary solutions (stable patterns to the reaction--diffusion equation. $$ eqalign{ {partial v_varepsilon over partial t} =& varepsilon^2, hbox{div}, (k_1(xabla v_varepsilon + k_2(x(v_varepsilon -alpha(Beta-v_varepsilon (v_varepsilon -gamma_varepsilon(x,,hbox{ in }Omegaimes{Bbb R}^+ cr &v_varepsilon(x,0 = v_0 quad {partial v_varepsilon over partial widehat{n}} = 0,, quadhbox{ for } xin partialOmega,, t >0,.} $$ Given nested simple closed curves in ${Bbb R}^2$, we give sufficient conditions on their curvature so that the reaction--diffusion problem possesses a family of stable patterns. In particular, we extend to two-dimensional domains and to a spatially inhomogeneous source term, a previous result by Yanagida and Miyata.
Multi-hump bright solitons in a Schrödinger-mKdV system
Cisneros-Ake, Luis A.; Parra Prado, Hugo; López Villatoro, Diego Joselito; Carretero-González, R.
2018-03-01
We consider the problem of energy transport in a Davydov model along an anharmonic crystal medium obeying quartic longitudinal interactions corresponding to rigid interacting particles. The Zabusky and Kruskal unidirectional continuum limit of the original discrete equations reduces, in the long wave approximation, to a coupled system between the linear Schrödinger (LS) equation and the modified Korteweg-de Vries (mKdV) equation. Single- and two-hump bright soliton solutions for this LS-mKdV system are predicted to exist by variational means and numerically confirmed. The one-hump bright solitons are found to be the anharmonic supersonic analogue of the Davydov's solitons while the two-hump (in both components) bright solitons are found to be a novel type of soliton consisting of a two-soliton solution of mKdV trapped by the wave function associated to the LS equation. This two-hump soliton solution, as a two component solution, represents a new class of polaron solution to be contrasted with the two-soliton interaction phenomena from soliton theory, as revealed by a variational approach and direct numerical results for the two-soliton solution.
Topological solitons of the Nambu-Jona-Lasinio model
International Nuclear Information System (INIS)
Reinhardt, H.; Wuensch, R.
1989-06-01
The baryon number one soliton solution of the Nambu-Jona-Lasinio model are found numerically in the mean-field approximation with full inclusion of the Dirac sea using the proper-time regularization for the underlying fermion determinant (quark loop). Explicit breaking of chiral symmetry is included by bare (current) quark masses. The obtained lowest-energy chiral soliton solutions with baryon number one carry winding number one. Fitting the parameters of the model from low-energy pion data the classical energies of these solitons are of the order of the nucleon mass. (orig.)
Bistable Helmholtz solitons in cubic-quintic materials
International Nuclear Information System (INIS)
Christian, J. M.; McDonald, G. S.; Chamorro-Posada, P.
2007-01-01
We propose a nonlinear Helmholtz equation for modeling the evolution of broad optical beams in media with a cubic-quintic intensity-dependent refractive index. This type of nonlinearity is appropriate for some semiconductor materials, glasses, and polymers. Exact analytical soliton solutions are presented that describe self-trapped nonparaxial beams propagating at any angle with respect to the reference direction. These spatially symmetric solutions are, to the best of our knowledge, the first bistable Helmholtz solitons to be derived. Accompanying conservation laws (both integral and particular forms) are also reported. Numerical simulations investigate the stability of the solitons, which appear to be remarkably robust against perturbations
Travelling Solitons in the Damped Driven Nonlinear Schroedinger Equation
Barashenkov, I V
2003-01-01
The well-known effect of the linear damping on the moving nonlinear Schrodinger soliton (even when there is energy supply via the spatially homogeneous driving) is to quench its momentum to zero. Surprisingly, the zero momentum does not necessarily mean zero velocity. We show that two or more parametrically driven damped solitons can form a complex travelling with zero momentum at a nonzero constant speed. All travelling complexes we have found so far, turned out to be unstable. Thus, the parametric driving is capable of sustaining the uniform motion of damped solitons, but some additional agent is required to make this motion stable.
Soliton interaction in quadratic and cubic bulk media
DEFF Research Database (Denmark)
Johansen, Steffen Kjær; Bang, Ole
2000-01-01
Summary form only given. The understanding of how and to what extend the cubic nonlinearity affects beam propagation and spatial soliton formation in quadratic media is of vital importance in fundamental and applied nonlinear physics. We consider beam propagation under type-I SHG conditions...... in lossless bulk second order nonlinear optical materials with a nonvanishing third order nonlinearity. It is known that in pure second order systems a single soliton can never collapse whereas in systems with both nonlinearities and that stable single soliton propagation can only in some circumstances...
Travelling solitons in the damped driven nonlinear Schroedinger equation
International Nuclear Information System (INIS)
Barashenkov, I.V.; Zemlyanaya, E.V.
2003-01-01
The well known effect of the linear damping on the moving nonlinear Schroedinger soliton (even when there is energy supply via the spatially homogeneous driving) is to quench its momentum to zero. Surprisingly, the zero momentum does not necessarily mean zero velocity. We show that two or more parametrically driven damped solitons can form a complex travelling with zero momentum at a nonzero constant speed. All travelling complexes we have found so far, turned out to be unstable. Thus, the parametric driving is capable of sustaining the uniform motion of damped solitons, but some additional agent is required to make this motion stable
Two-dimensional discrete solitons in dipolar Bose-Einstein condensates
International Nuclear Information System (INIS)
Gligoric, Goran; Stepic, Milutin; Hadzievski, Ljupco; Maluckov, Aleksandra; Malomed, Boris A.
2010-01-01
We analyze the formation and dynamics of bright unstaggered solitons in the disk-shaped dipolar Bose-Einstein condensate, which features the interplay of contact (collisional) and long-range dipole-dipole (DD) interactions between atoms. The condensate is assumed to be trapped in a strong optical-lattice potential in the disk's plane, hence it may be approximated by a two-dimensional (2D) discrete model, which includes the on-site nonlinearity and cubic long-range (DD) interactions between sites of the lattice. We consider two such models, which differ by the form of the on-site nonlinearity, represented by the usual cubic term, or more accurate nonpolynomial one, derived from the underlying three-dimensional Gross-Pitaevskii equation. Similar results are obtained for both models. The analysis is focused on the effects of the DD interaction on fundamental localized modes in the lattice (2D discrete solitons). The repulsive isotropic DD nonlinearity extends the existence and stability regions of the fundamental solitons. New families of on-site, inter-site, and hybrid solitons, built on top of a finite background, are found as a result of the interplay of the isotropic repulsive DD interaction and attractive contact nonlinearity. By themselves, these solutions are unstable, but they evolve into robust breathers which exist on an oscillating background. In the presence of the repulsive contact interactions, fundamental localized modes exist if the DD interaction (attractive isotropic or anisotropic) is strong enough. They are stable in narrow regions close to the anticontinuum limit, while unstable solitons evolve into breathers. In the latter case, the presence of the background is immaterial.
Soliton interaction in the coupled mixed derivative nonlinear Schroedinger equations
International Nuclear Information System (INIS)
Zhang Haiqiang; Tian Bo; Lue Xing; Li He; Meng Xianghua
2009-01-01
The bright one- and two-soliton solutions of the coupled mixed derivative nonlinear Schroedinger equations in birefringent optical fibers are obtained by using the Hirota's bilinear method. The investigation on the collision dynamics of the bright vector solitons shows that there exists complete or partial energy switching in this coupled model. Such parametric energy exchanges can be effectively controlled and quantificationally measured by analyzing the collision dynamics of the bright vector solitons. The influence of two types of nonlinear coefficient parameters on the energy of each vector soliton, is also discussed. Based on the significant energy transfer between the two components of each vector soliton, it is feasible to exploit the future applications in the design of logical gates, fiber directional couplers and quantum information processors.
Energy Technology Data Exchange (ETDEWEB)
Christian, J M; McDonald, G S [Joule Physics Laboratory, School of Computing, Science and Engineering, Materials and Physics Research Centre, University of Salford, Salford M5 4WT (United Kingdom); Chamorro-Posada, P, E-mail: j.christian@salford.ac.u [Departamento de Teoria de la Senal y Comunicaciones e Ingenieria Telematica, Universidad de Valladolid, ETSI Telecomunicacion, Campus Miguel Delibes s/n, 47011 Valladolid (Spain)
2010-02-26
We report, to the best of our knowledge, the first exact analytical algebraic solitons of a generalized cubic-quintic Helmholtz equation. This class of governing equation plays a key role in photonics modelling, allowing a full description of the propagation and interaction of broad scalar beams. New conservation laws are presented, and the recovery of paraxial results is discussed in detail. The stability properties of the new solitons are investigated by combining semi-analytical methods and computer simulations. In particular, new general stability regimes are reported for algebraic bright solitons.
International Nuclear Information System (INIS)
Christian, J M; McDonald, G S; Chamorro-Posada, P
2010-01-01
We report, to the best of our knowledge, the first exact analytical algebraic solitons of a generalized cubic-quintic Helmholtz equation. This class of governing equation plays a key role in photonics modelling, allowing a full description of the propagation and interaction of broad scalar beams. New conservation laws are presented, and the recovery of paraxial results is discussed in detail. The stability properties of the new solitons are investigated by combining semi-analytical methods and computer simulations. In particular, new general stability regimes are reported for algebraic bright solitons.
Air-stable, solution-processed oxide p-n heterojunction ultraviolet photodetector.
Kim, Do Young; Ryu, Jiho; Manders, Jesse; Lee, Jaewoong; So, Franky
2014-02-12
Air-stable solution processed all-inorganic p-n heterojunction ultraviolet photodetector is fabricated with a high gain (EQE, 25 300%). Solution-processed NiO and ZnO films are used as p-type and n-type ultraviolet sensitizing materials, respectively. The high gain in the detector is due to the interfacial trap-induced charge injection that occurs at the ITO/NiO interface by photogenerated holes trapped in the NiO film. The gain of the detector is controlled by the post-annealing temperature of the solution-processed NiO films, which are studied by X-ray photoelectron spectroscopy (XPS).
Large amplitude ion-acoustic solitons in dusty plasmas
International Nuclear Information System (INIS)
Tiwari, R. S.; Jain, S. L.; Mishra, M. K.
2011-01-01
Characteristics of ion-acoustic soliton in dusty plasma, including the dynamics of heavily charged massive dust grains, are investigated following the Sagdeev Potential formalism. Retaining fourth order nonlinearities of electric potential in the expansion of the Sagdeev Potential in the energy equation for a pseudo particle and integrating the resulting energy equation, large amplitude soliton solution is determined. Variation of amplitude (A), half width (W) at half maxima and the product P = AW 2 of the Korteweg-deVries (KdV), dressed and large amplitude soliton as a function of wide range of dust concentration are numerically studied for recently observed parameters of dusty plasmas. We have also presented the region of existence of large amplitude ion-acoustic soliton in the dusty plasma by analyzing the structure of the pseudo potential. It is found that in the presence of positively charged dust grains, system supports only compressive solitons, on the other hand, in the presence of negatively charged dust grains, the system supports compressive solitons up to certain critical concentration of dust grains and above this critical concentration, the system can support rarefactive solitons also. The effects of dust concentration, charge, and mass of the dust grains, on the characteristics of KdV, dressed and large amplitude the soliton, i.e., amplitude (A), half width at half maxima (W), and product of amplitude (A) and half width at half maxima (P = AW 2 ), are discussed in detail
Quantization of bag-like solitons
International Nuclear Information System (INIS)
Breit, J.D.
1982-01-01
The method of collective coordinates is used to quantize bag-like solitons formed by scalar and spinor fields. This method leads to approximate wave functions for quarks in the bag that are orthogonal to the translational modes. Solutions are given for the MIT bag limit of the fields. (orig.)
Classification of stable solutions for non-homogeneous higher-order elliptic PDEs
Directory of Open Access Journals (Sweden)
Abdellaziz Harrabi
2017-04-01
Full Text Available Abstract Under some assumptions on the nonlinearity f, we will study the nonexistence of nontrivial stable solutions or solutions which are stable outside a compact set of R n $\\mathbb {R}^{n}$ for the following semilinear higher-order problem: ( − Δ k u = f ( u in R n , $$\\begin{aligned} (-\\Delta^{k} u= f(u \\quad \\mbox{in }\\mathbb {R}^{n}, \\end{aligned}$$ with k = 1 , 2 , 3 , 4 $k=1,2,3,4$ . The main methods used are the integral estimates and the Pohozaev identity. Many classes of nonlinearity will be considered; even the sign-changing nonlinearity, which has an adequate subcritical growth at zero as for example f ( u = − m u + λ | u | θ − 1 u − μ | u | p − 1 u $f(u= -m u +\\lambda|u|^{\\theta-1}u-\\mu |u|^{p-1}u$ , where m ≥ 0 $m\\geq0$ , λ > 0 $\\lambda>0$ , μ > 0 $\\mu>0$ , p , θ > 1 $p, \\theta>1$ . More precisely, we shall revise the nonexistence theorem of Berestycki and Lions (Arch. Ration. Mech. Anal. 82:313-345, 1983 in the class of smooth finite Morse index solutions as the well known work of Bahri and Lions (Commun. Pure Appl. Math. 45:1205-1215, 1992. Also, the case when f ( u u $f(uu$ is a nonnegative function will be studied under a large subcritical growth assumption at zero, for example f ( u = | u | θ − 1 u ( 1 + | u | q $f(u=|u|^{\\theta-1}u(1 + |u|^{q}$ or f ( u = | u | θ − 1 u e | u | q $f(u= |u|^{\\theta-1}u e^{|u|^{q}}$ , θ > 1 $\\theta>1$ and q > 0 $q>0$ . Extensions to solutions which are merely stable are discussed in the case of supercritical growth with k = 1 $k=1$ .
Slunyaev, Alexey; Klein, Marco; Clauss, Günther F.
2016-04-01
Envelope soliton solutions are key elements governing the nonlinear wave dynamics within a simplified theory for unidirectional weakly modulated weakly nonlinear wave groups on the water surface. Within integrable models the solitons preserve their structure in collisions with other waves; they do not disperse and can carry energy infinitively long. Steep and short soliton-like wave groups have been shown to exist in laboratory tests [1] and, even earlier, in numerical simulations [2, 3]. Thus, long-living wave groups may play important role in the dynamics of intense sea waves and wave-structure interactions. The solitary wave groups may change the wave statistics and can be taken into account when developing approaches for the deterministic forecasting of dangerous waves, including so-called rogue waves. An experimental campaign has been conducted in the wave basin of the Technical University of Berlin on simulations of intense solitary wave groups. The first successful experimental observation of intense envelope solitons took place in this facility [1]. The new experiments aimed at following main goals: 1) to reproduce intense envelope solitons with different carrier wave lengths; 2) to estimate the rate of envelope soliton dissipation; 3) to consider the reflection of envelope solitons on a vertical wall; 4) to consider head-on collisions of envelope solitons, and 5) to consider overtaking interactions of envelope solitons. Up to 9 wave gauges were used in each experimental run, which enabled registration of the surface movement at different distances from the wavemaker, at different locations across the wave flume and near the wall. Besides surface displacements, the group envelope shapes were directly recorded, with use of phase shifts applied to the modulated waves generated by the wavemaker. [1] A. Slunyaev, G.F. Clauss, M. Klein, M. Onorato, Simulations and experiments of short intense envelope solitons of surface water waves. Phys. Fluids 25, 067105
Domain wall networks on solitons
International Nuclear Information System (INIS)
Sutcliffe, Paul
2003-01-01
Domain wall networks on the surface of a soliton are studied in a simple theory. It consists of two complex scalar fields, in 3+1 dimensions, with a global U(1)xZ n symmetry, where n>2. Solutions are computed numerically in which one of the fields forms a Q ball and the other field forms a network of domain walls localized on the surface of the Q ball. Examples are presented in which the domain walls lie along the edges of a spherical polyhedron, forming junctions at its vertices. It is explained why only a small restricted class of polyhedra can arise as domain wall networks
Sakkaravarthi, K; Kanna, T; Vijayajayanthi, M; Lakshmanan, M
2014-11-01
We consider a general multicomponent (2+1)-dimensional long-wave-short-wave resonance interaction (LSRI) system with arbitrary nonlinearity coefficients, which describes the nonlinear resonance interaction of multiple short waves with a long wave in two spatial dimensions. The general multicomponent LSRI system is shown to be integrable by performing the Painlevé analysis. Then we construct the exact bright multisoliton solutions by applying the Hirota's bilinearization method and study the propagation and collision dynamics of bright solitons in detail. Particularly, we investigate the head-on and overtaking collisions of bright solitons and explore two types of energy-sharing collisions as well as standard elastic collision. We have also corroborated the obtained analytical one-soliton solution by direct numerical simulation. Also, we discuss the formation and dynamics of resonant solitons. Interestingly, we demonstrate the formation of resonant solitons admitting breather-like (localized periodic pulse train) structure and also large amplitude localized structures akin to rogue waves coexisting with solitons. For completeness, we have also obtained dark one- and two-soliton solutions and studied their dynamics briefly.
International Nuclear Information System (INIS)
Swieca, J.A.
1976-01-01
Some aspects of two recent developments in quantum field theory are discussed. First, related with 'extended particles' such as soliton, kink and the 't Hooft monopole. Second, with confinement of particles which are realized in the Schwinger model [pt
The Baryon Number Two System in the Chiral Soliton Model
International Nuclear Information System (INIS)
Mantovani-Sarti, V.; Drago, A.; Vento, V.; Park, B.-Y.
2013-01-01
We study the interaction between two B = 1 states in a chiral soliton model where baryons are described as non-topological solitons. By using the hedgehog solution for the B = 1 states we construct three possible B = 2 configurations to analyze the role of the relative orientation of the hedgehog quills in the dynamics. The strong dependence of the inter soliton interaction on these relative orientations reveals that studies of dense hadronic matter using this model should take into account their implications. (author)
Unusual black-holes: about some stable (non-evaporating) extremal solutions of Einstein equations
International Nuclear Information System (INIS)
Tonin-Zanchin, V.; Recami, E.
1990-01-01
Within a purely classical formulation of ''strong gravity'', we associated hadron constituents (and even hadrons themselves) with suitable stationary, axisymmetric solutions of certain new Einsten-type equations supposed to describe the strong field inside hadrons. As a consequence, the cosmological constant Λ and the masses M result in theory to be scaled up, and transformed into a ''hadronic constant'' and into ''strong masses'', respectively. Due to the unusual range of Λ and M values considered, we met a series of solutions of the Kerr-Newman-de Sitter (KNdS) type with so uncommon horizon properties (e.g., completely impermeable horizons), that it is worth studing them also in the case of ordinary gravity. This is the aim of the present work. The requirement that those solutions be stable, i.e., that their temperature (or surface gravity) be vanishingly small, implies the coincidence of at least two of their (in general, three) horizons. In the case of ordinary Einstein equations and for stable black holes of the KNdS type, we get Regge-like relations among mass M, angular momentum J, charge q and cosmological constant Λ. For instance, with the standard definitions Q 2 ≡ Gq 2 / (4Π ε 0 c 4 )); a ≡ J/(Mc); m ≡ GM/c 2 , in the case Λ = 0 in which m 2 = a 2 + Q 2 and q is negligible we find M 2 = J, where c = G = 1. When considering, for simplicity, Λ > 0 and J = 0 (and q still negligible), then we obtain m 2 = 1/(9Λ). In the most general case, the condition, for instance, of ''triple coincidence'' among the three horizons yields for |Λa 2 / 2 = 2/(9Λ) ; m 2 = 8(a 2 + Q 2 )/9. One of the interesting points is that - with few exceptions - all such relations (among M, J, q, Λ) lead to solutions that can be regarded as (stable) cosmological models. Worth of notice are those representing isolated worlds, bounded by a two-way impermeable horizon. (author) [pt
Directory of Open Access Journals (Sweden)
Mohamed Abdalla Darwish
2014-01-01
Full Text Available We study a generalized fractional quadratic functional-integral equation of Erdélyi-Kober type in the Banach space BC(ℝ+. We show that this equation has at least one asymptotically stable solution.
Bifurcations and chaos of DNA solitonic dynamics
International Nuclear Information System (INIS)
Gonzalez, J.A.; Martin-Landrove, M.; Carbo, J.R.; Chacon, M.
1994-09-01
We investigated the nonlinear DNA torsional equations proposed by Yakushevich in the presence of damping and external torques. Analytical expressions for some solutions are obtained in the case of the isolated chain. Special attention is paid to the stability of the solutions and the range of soliton interaction in the general case. The bifurcation analysis is performed and prediction of chaos is obtained for some set of parameters. Some biological implications are suggested. (author). 11 refs, 13 figs
Bistable dark solitons of a cubic-quintic Helmholtz equation
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Christian, J. M.; McDonald, G. S.; Chamorro-Posada, P.
2010-01-01
We provide a report on exact analytical bistable dark spatial solitons of a nonlinear Helmholtz equation with a cubic-quintic refractive-index model. Our analysis begins with an investigation of the modulational instability characteristics of Helmholtz plane waves. We then derive a dark soliton by mapping the desired asymptotic form onto a uniform background field and obtain a more general solution by deploying rotational invariance laws in the laboratory frame. The geometry of the new soliton is explored in detail, and a range of new physical predictions is uncovered. Particular attention is paid to the unified phenomena of arbitrary-angle off-axis propagation and nondegenerate bistability. Crucially, the corresponding solution of paraxial theory emerges in a simultaneous multiple limit. We conclude with a set of computer simulations that examine the role of Helmholtz dark solitons as robust attractors.
International Nuclear Information System (INIS)
Adam, C.; Haberichter, M.; Wereszczynski, A.
2016-01-01
There exists, in general, no unique definition of the size (volume, area, etc., depending on dimension) of a soliton. Here we demonstrate that the geometric volume (area etc.) of a soliton is singled out in the sense that it exactly coincides with the thermodynamical or continuum-mechanical volume. In addition, this volume may be defined uniquely for rather arbitrary solitons in arbitrary dimensions.
Energy Technology Data Exchange (ETDEWEB)
Adam, C., E-mail: adam@fpaxp1.usc.es [Departamento de Física de Partículas, Universidad de Santiago de Compostela and Instituto Galego de Física de Altas Enerxias (IGFAE), E-15782 Santiago de Compostela (Spain); Haberichter, M. [School of Mathematics, Statistics and Actuarial Science, University of Kent, Canterbury, CT2 7NF (United Kingdom); Wereszczynski, A. [Institute of Physics, Jagiellonian University, Lojasiewicza 11, Kraków (Poland)
2016-03-10
There exists, in general, no unique definition of the size (volume, area, etc., depending on dimension) of a soliton. Here we demonstrate that the geometric volume (area etc.) of a soliton is singled out in the sense that it exactly coincides with the thermodynamical or continuum-mechanical volume. In addition, this volume may be defined uniquely for rather arbitrary solitons in arbitrary dimensions.
International Nuclear Information System (INIS)
Adhikari, Sadhan K.
2005-01-01
We demonstrate the formation of bright solitons in coupled self-defocusing nonlinear Schroedinger (NLS) equation supported by attractive coupling. As an application we use a time-dependent dynamical mean-field model to study the formation of stable bright solitons in two-component repulsive Bose-Einstein condensates (BECs) supported by interspecies attraction in a quasi one-dimensional geometry. When all interactions are repulsive, there cannot be bright solitons. However, bright solitons can be formed in two-component repulsive BECs for a sufficiently attractive interspecies interaction, which induces an attractive effective interaction among bosons of same type
International Nuclear Information System (INIS)
Kono, M.; Kawakita, M.
1990-01-01
A nonlinear equation describing the development of the Buneman instability has been derived and solved with the aid of Hirota's bilinear transform [J. Math. Phys. 14, 810 (1973)] to give a variety of stationary solutions, such as pulsating solitons, temporally localized and spatially periodic solutions, as well as ordinary solitons
Multiple atomic dark solitons in cigar-shaped Bose-Einstein condensates
International Nuclear Information System (INIS)
Theocharis, G.; Kevrekidis, P. G.; Weller, A.; Ronzheimer, J. P.; Gross, C.; Oberthaler, M. K.; Frantzeskakis, D. J.
2010-01-01
We consider the stability and dynamics of multiple dark solitons in cigar-shaped Bose-Einstein condensates. Our study is motivated by the fact that multiple matter-wave dark solitons may naturally form in such settings as per our recent work [Phys. Rev. Lett. 101, 130401 (2008)]. First, we study the dark soliton interactions and show that the dynamics of well-separated solitons (i.e., ones that undergo a collision with relatively low velocities) can be analyzed by means of particle-like equations of motion. The latter take into regard the repulsion between solitons (via an effective repulsive potential) and the confinement and dimensionality of the system (via an effective parabolic trap for each soliton). Next, based on the fact that stationary, well-separated dark multisoliton states emerge as a nonlinear continuation of the appropriate excited eigenstates of the quantum harmonic oscillator, we use a Bogoliubov-de Gennes analysis to systematically study the stability of such structures. We find that for a sufficiently large number of atoms, multiple soliton states are dynamically stable, while for a small number of atoms, we predict a dynamical instability emerging from resonance effects between the eigenfrequencies of the soliton modes and the intrinsic excitation frequencies of the condensate. Finally, we present experimental realizations of multisoliton states including a three-soliton state consisting of two solitons oscillating around a stationary one and compare the relevant results to the predictions of the theoretical mean-field model.
Surface-wave solitons between linear media and nonlocal nonlinear media
International Nuclear Information System (INIS)
Shi Zhiwei; Li Huagang; Guo Qi
2011-01-01
We address surface solitons at the interface between linear media and nonlocal nonlinear media in the presence of a discontinuity in refractive index at the surface of these two materials. We investigated the influence of the degree of nonlocality on the stability, energy flow, and full width at half-maximum of the surface wave solitons. It is shown that surface solitons will be stable only if the degree of nonlocality exceeds a critical value. We find that the refractive index difference can affect the power distribution of the surface solitons in the two media. Also, different boundary values at the interface can lead to different relative peak positions of the surface solitons. However, neither the refractive index nor the boundary conditions can affect the stability of the solitons, for a given degree of nonlocality.
Stabilization of matter wave solitons in weakly coupled atomic condensates
International Nuclear Information System (INIS)
Radha, R.; Vinayagam, P.S.
2012-01-01
We investigate the dynamics of a weakly coupled two component Bose–Einstein condensate and generate bright soliton solutions. We observe that when the bright solitons evolve in time, the density of the condensates shoots up suddenly by virtue of weak coupling indicating the onset of instability in the dynamical system. However, this instability can be overcome either through Feshbach resonance by tuning the temporal scattering length or by suitably changing the time dependent coupling coefficient, thereby extending the lifetime of the condensates.
Multiple soliton production and the Korteweg-de Vries equation.
Hershkowitz, N.; Romesser, T.; Montgomery, D.
1972-01-01
Compressive square-wave pulses are launched in a double-plasma device. Their evolution is interpreted according to the Korteweg-de Vries description of Washimi and Taniuti. Square-wave pulses are an excitation for which an explicit solution of the Schrodinger equation permits an analytical prediction of the number and amplitude of emergent solitons. Bursts of energetic particles (pseudowaves) appear above excitation voltages greater than an electron thermal energy, and may be mistaken for solitons.
Intensity limits for stationary and interacting multi-soliton complexes
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Sukhorukov, Andrey A.; Akhmediev, Nail N.
2002-01-01
We obtain an accurate estimate for the peak intensities of multi-soliton complexes for a Kerr-type nonlinearity in the (1+1) dimension problem. Using exact analytical solutions of the integrable set of nonlinear Schroedinger equations, we establish a rigorous relationship between the eigenvalues of incoherently-coupled fundamental solitons and the range of admissible intensities. A clear geometrical interpretation of this effect is given
The propagation property of ion-acoustic soliton in an inhomogeneous plasma
International Nuclear Information System (INIS)
Zhu Jiazhen; Wang Gengguo.
1990-01-01
The propagation property of ion-acoustic soliton in a weakly inhomogeneous plamsa caused by ionization is studied. Finite ion temperature and ion-neutral collisions are considered the self consistent stationary distribution N(x), v(x) and the corresponding soliton solution are obtained, numerical results of soliton amplitude, speed and width dependent on position are given, which are reasonable and consistent with experiments
On the reflection of solitons of the cubic nonlinear Schrödinger equation
Katsaounis, Theodoros
2016-07-05
In this paper, we perform a numerical study on the interesting phenomenon of soliton reflection of solid walls. We consider the 2D cubic nonlinear Schrödinger equation as the underlying mathematical model, and we use an implicit-explicit type Crank-Nicolson finite element scheme for its numerical solution. After verifying the perfect reflection of the solitons on a vertical wall, we present the imperfect reflection of a dark soliton on a diagonal wall.
Direct method for the periodic amplification of a soliton in an optical fibre link with loss
International Nuclear Information System (INIS)
Li Lu; Xue Wenrui; Xu Zhiyong; Li Zhonghao; Zhou Guosheng
2003-01-01
A direct approach is applied to the periodic amplification of a soliton in an optical fibre link with loss. In a single soliton case, the adiabatic solution and first-order correction are given for the system. The apparent advantage of this direct approach is that it not only presents the slow evolution of soliton parameters, but also the perturbation-induced radiation, and can be easily used to investigate the system of dispersion management with periodically varying dispersion and other fields
Bose gas with two- and three-particle interaction: evolution of soliton-like bubbles
International Nuclear Information System (INIS)
Barashenkov, I.V.; Kholmurodov, Kh.T.
1988-01-01
Solutions of the non-linear Schroedinger equation (NSE) for the Bose gas with two- and three-particle interaction are considered. Problems of soliton-like bubble existence, stability and evolution of the moving soliton are studied. It is shown that at D=2.3 for low-amplitude waves propagating at the transonic velocity the NSE is reduced to a two- and three-dimensional Kadomtsev-Petviashvili (KP) equation and the NSE bubble soliton transfers to the KP one
On the classification of the spectrally stable standing waves of the Hartree problem
Georgiev, Vladimir; Stefanov, Atanas
2018-05-01
We consider the fractional Hartree model, with general power non-linearity and arbitrary spatial dimension. We construct variationally the "normalized" solutions for the corresponding Choquard-Pekar model-in particular a number of key properties, like smoothness and bell-shapedness are established. As a consequence of the construction, we show that these solitons are spectrally stable as solutions to the time-dependent Hartree model. In addition, we analyze the spectral stability of the Moroz-Van Schaftingen solitons of the classical Hartree problem, in any dimensions and power non-linearity. A full classification is obtained, the main conclusion of which is that only and exactly the "normalized" solutions (which exist only in a portion of the range) are spectrally stable.
International Nuclear Information System (INIS)
Brand, Joachim; Reinhardt, William P.
2002-01-01
The connection between quantized vortices and dark solitons in a waveguidelike trap geometry is explored in the framework of the nonlinear Schroedinger equation. Variation of the transverse confinement leads from the quasi-one-dimensional (1D) regime, where solitons are stable, to 2D (or 3D) confinement, where soliton stripes are subject to a transverse modulational instability known as the 'snake instability'. We present numerical evidence of a regime of intermediate confinement where solitons decay into single, deformed vortices with solitonic properties rather than vortex pairs as associated with the 'snake' metaphor. Further relaxing the transverse confinement leads to the production of two and then three vortices, which correlates perfectly with a Bogoliubov stability analysis. The decay of a stationary dark soliton (or, planar node) into a single solitonic vortex is predicted to be experimentally observable in a 3D harmonically confined dilute-gas Bose-Einstein condensate
Ricci solitons, Ricci flow and strongly coupled CFT in the Schwarzschild Unruh or Boulware vacua
International Nuclear Information System (INIS)
Figueras, Pau; Lucietti, James; Wiseman, Toby
2011-01-01
The elliptic Einstein-DeTurck equation may be used to numerically find Einstein metrics on Riemannian manifolds. Static Lorentzian Einstein metrics are considered by analytically continuing to Euclidean time. The Ricci-DeTurck flow is a constructive algorithm to solve this equation, and is simple to implement when the solution is a stable fixed point, the only complication being that Ricci solitons may exist which are not Einstein. Here we extend previous work to consider the Einstein-DeTurck equation for Riemannian manifolds with boundaries, and those that continue to static Lorentzian spacetimes which are asymptotically flat, Kaluza-Klein, locally AdS or have extremal horizons. Using a maximum principle, we prove that Ricci solitons do not exist in these cases and so any solution is Einstein. We also argue that the Ricci-DeTurck flow preserves these classes of manifolds. As an example, we simulate the Ricci-DeTurck flow for a manifold with asymptotics relevant for AdS 5 /CFT 4 . Our maximum principle dictates that there are no soliton solutions, and we give strong numerical evidence that there exists a stable fixed point of the flow which continues to a smooth static Lorentzian Einstein metric. Our asymptotics are such that this describes the classical gravity dual relevant for the CFT on a Schwarzschild background in either the Unruh or Boulware vacua. It determines the leading O(N 2 c ) part of the CFT stress tensor, which interestingly is regular on both the future and past Schwarzschild horizons. (paper)
Solitons and nonlinear waves in space plasmas
International Nuclear Information System (INIS)
Stasiewicz, K.
2005-01-01
Recent measurements made on the ESA/NASA Cluster mission to the Earth's magnetosphere have provided first detailed measurements of magnetosonic solitons in space. The solitons represent localized enhancements of the magnetic field by a factor of 2-10, or depressions down to 10% of the ambient field. The magnetic field signatures are associated with density depressions/enhancements A two-fluid model of nonlinear electron and ion inertial waves in anisotropic plasmas explains the main properties of these structures. It is shown that warm plasmas support four types of nonlinear waves, which correspond to four linear modes: Alfvenic, magnetosonic, sound, and electron inertial waves. Each of these nonlinear modes has slow and fast versions. It is shown by direct integration that the exponential growth rate of nonlinear modes is balanced by the ion and electron dispersion leading to solutions in the form of trains of solitons or cnoidal waves. By using a novel technique of phase portraits it is shown how the dispersive properties of electron and ion inertial waves change at the transition between warm and hot plasmas, and how trains of solitons ('' mirror modes '') are produced in a hot, anisotropic plasma. The applicability of the model is illustrated with data from Cluster spacecraft. (author)
Decay of solitons in an isotropic collisionless quasineutral plasma with isothermal pressure
International Nuclear Information System (INIS)
Bakholdin, I.B.; Zharkov, A.A.; Il'ichev, A.T.
2000-01-01
Soliton-type solutions of the complete unreduced system of transport equations describing the plane-parallel motions of an isotropic collisionless quasineutral plasma in a magnetic field with constant ion and electron temperatures are studied. The regions of the physical parameters for fast and slow magnetosonic branches, where solitons and generalized solitary waves - nonlocal soliton structures in the form of a soliton 'core' with asymptotic behavior at infinity in the form of a periodic low-amplitude wave - exist, are determined. In the range of parameters where solitons are replaced by generalized solitary waves, soliton-like disturbances are subjected to decay whose mechanisms are qualitatively different for slow and fast magnetosonic waves. A specific feature of the decay of such disturbances for fast magnetosonic waves is that the energy of the disturbance decreases primarily as a result of the quasistationary emission of a resonant periodic wave of the same nature. Similar disturbances in the form of a soliton core of a slow magnetosonic generalized solitary wave essentially do not emit resonant modes on the Alfven branch but they lose energy quite rapidly because of continuous emission of a slow magnetosonic wave. Possible types of shocks which are formed by two types of existing soliton solutions (solitons and generalized solitary waves) are examined in the context of such solutions
Xie, Xi-Yang; Tian, Bo; Liu, Lei; Guan, Yue-Yang; Jiang, Yan
2017-06-01
In this paper, we investigate a generalized nonautonomous nonlinear equation, which describes the ultrashort optical pulse propagating in a nonlinear inhomogeneous fiber. Under certain integrable constraints, bilinear forms, bright one- and two-soliton solutions are obtained. Via certain transformation, we investigate the properties of the solitons with the first-order dispersion parameter σ1(x, t), second-order dispersion parameter σ2(x, t), third-order dispersion parameter σ3(x, t), phase modulation and gain (loss) v(x, t). Soliton propagation and collision are graphically presented and analyzed: One soliton is shown to maintain its amplitude and width during the propagation. When we choose σ1(x, t), σ2(x, t) and σ3(x, t) differently, travelling direction of the soliton is found to alter. v(x, t) is observed to affect the amplitude of the soliton. Head-on collision between the two solitons is presented with σ1(x, t), σ2(x, t), σ3(x, t) and v(x, t) as the constants, and solitons' amplitudes are the same before and after the collision. When σ1(x, t), σ2(x, t) and σ3(x, t) are chosen as certain functions, the solitons' traveling directions change during the collision. v(x, t) can influence the amplitudes of the two solitons.
Application of stable, nitroxide free radicals in solution to low magnetic fields measurements
International Nuclear Information System (INIS)
Besson, Rene
1973-01-01
The first attempts to use the Overhauser-Abragam effect for measuring low magnetic fields date back to 1956. However, the instability of the free radical used, PREMY'S Salt, as well as its virtual insolubility in solvents other than water, hampered the development of the nuclear magnetic resonance magnetometer realized in accordance to this principle: dynamic polarization of protons. New free radicals stable and soluble in many solvents, will enhanced the interest in the device. In particular, the use of 2,2,6,6, tetramethyl- piperidine-4-one-1-oxide (TANO or TANONE) leads to a high sensitivity, low field magnetometer. The methods of measurements, the required apparatus and sample preparation are first described. Next the results of measurements made both in high and low magnetic fields with various free radicals in different solvents are presented in tabular and graphical form. These measurements have determined which radical-solvent couple will yield a high dynamic polarization coefficient. In addition, the improvement obtained by complete deuteration of the free radical has been demonstrated. Problems connected with the application of such radicals in solution to the 'double effect probe' of the magnetometer built by LETI at CEN Grenoble and the solutions reached are discussed. (author) [fr
Stable, metastable and unstable solutions of a spin-1 Ising system based on the free energy surfaces
Keskİin, Mustafa; Özgan, Şükrü
1990-04-01
Stable, metastable and unstable solutions of a spin-1 Ising model with bilinear and biquadratic interactions are found by using the free energy surfaces. The free energy expression is obtained in the lowest approximation of the cluster variation method. All these solutions are shown in the two-dimensional phase space, especially the unstable solutions which in some cases are difficult to illustrate in the two-dimensional phase space, found by Keskin et al. recently.
International Nuclear Information System (INIS)
Shi, Zhiwei; Li, Huagang; Guo, Qi
2012-01-01
We address multipole surface solitons occurring at the interface between a linear medium and a nonlocal nonlinear medium. We show the impact of nonlocality, the propagation constant, and the linear index difference of two media on the properties of the surface solitons. We find that there exist a threshold value of the degree of the nonlocality at the same linear index difference of two media, only when the degree of the nonlocality goes beyond the value, the multipole surface solitons can be stable. -- Highlights: ► We show the impact of nonlocality and the linear index difference of two media on the properties of the surface solitons. ► For the surface solitons, only when the degree of the nonlocality goes beyond a threshold value, they can be stable. ► The number of poles and the index difference of two media can all influence the threshold value.
The nontopological soliton model
International Nuclear Information System (INIS)
Wilets, L.
1988-01-01
The nontopological soliton model introduced by Friedberg and Lee, and variations of it, provide a method for modeling QCD which can effectively include the dynamics of hadronic collisions as well as spectra. Absolute color confinement is effected by the assumed dielectric properties of the medium. A recently proposed version of the model is chirally invariant. 32 refs., 5 figs., 1 tab
International Nuclear Information System (INIS)
Wilets, L.; Bickeboeller, M.; Birse, M.C.
1985-01-01
A summary of recent and current research on the Soliton Bag Model is presented. The unique feature of the model, namely dynamics, is emphasized, since this permits calculation of reactions within the framework of a covariant effective Lagrangian. One gluon exchange effects are included. 17 refs., 3 figs
Statistical mechanics of solitons
International Nuclear Information System (INIS)
Bishop, A.
1980-01-01
The status of statistical mechanics theory (classical and quantum, statics and dynamics) is reviewed for 1-D soliton or solitary-wave-bearing systems. Primary attention is given to (i) perspective for existing results with evaluation and representative literature guide; (ii) motivation and status report for remaining problems; (iii) discussion of connections with other 1-D topics
Solitons as candidates for energy carriers in Fermi-Pasta-Ulam lattices
Ming, Yi; Ye, Liu; Chen, Han-Shuang; Mao, Shi-Feng; Li, Hui-Min; Ding, Ze-Jun
2018-01-01
Currently, effective phonons (renormalized or interacting phonons) rather than solitary waves (for short, solitons) are regarded as the energy carriers in nonlinear lattices. In this work, by using the approximate soliton solutions of the corresponding equations of motion and adopting the Boltzmann distribution for these solitons, the average velocities of solitons are obtained and are compared with the sound velocities of energy transfer. Excellent agreements with the numerical results and the predictions of other existing theories are shown in both the symmetric Fermi-Pasta-Ulam-β lattices and the asymmetric Fermi-Pasta-Ulam-α β lattices. These clearly indicate that solitons are suitable candidates for energy carriers in Fermi-Pasta-Ulam lattices. In addition, the root-mean-square velocity of solitons can be obtained from the effective phonons theory.
Soliton wave-speed management: Slowing, stopping, or reversing a solitary wave
Baines, Luke W. S.; Van Gorder, Robert A.
2018-06-01
While dispersion management is a well-known tool to control soliton properties such as shape or amplitude, far less effort has been directed toward the theoretical control of the soliton wave speed. However, recent experiments concerning the stopping or slowing of light demonstrate that the control of the soliton wave speed is of experimental interest. Motivated by these and other studies, we propose a management approach for modifying the wave speed of a soliton (or of other nonlinear wave solutions, such as periodic cnoidal waves) under the nonlinear Schrödinger equation. Making use of this approach, we are able to slow, stop, or even reverse a solitary wave, and we give several examples to bright solitons, dark solitons, and periodic wave trains, to demonstrate the method. An extension of the approach to spatially heterogeneous media, for which the wave may propagate differently at different spatial locations, is also discussed.
Interactions of Soliton Waves for a Generalized Discrete KdV Equation
International Nuclear Information System (INIS)
Zhou Tong; Zhu Zuo-Nong
2017-01-01
It is well known that soliton interactions in discrete integrable systems often possess new properties which are different from the continuous integrable systems, e.g., we found that there are such discrete solitons in a semidiscrete integrable system (the time variable is continuous and the space one is discrete) that the shorter solitary waves travel faster than the taller ones. Very recently, this kind of soliton was also observed in a full discrete generalized KdV system (the both of time and space variables are discrete) introduced by Kanki et al. In this paper, for the generalized discrete KdV (gdKdV) equation, we describe its richer structures of one-soliton solutions. The interactions of two-soliton waves to the gdKdV equation are studied. Some new features of the soliton interactions are proposed by rigorous theoretical analysis. (paper)
Stability of line solitons for the KP-II equation in R2
Mizumachi, Tetsu
2015-01-01
The author proves nonlinear stability of line soliton solutions of the KP-II equation with respect to transverse perturbations that are exponentially localized as x\\to\\infty. He finds that the amplitude of the line soliton converges to that of the line soliton at initial time whereas jumps of the local phase shift of the crest propagate in a finite speed toward y=\\pm\\infty. The local amplitude and the phase shift of the crest of the line solitons are described by a system of 1D wave equations with diffraction terms.
Waves and solitons in the continuum limit of the Calogero-Sutherland model
Polychronakos, A P
1995-01-01
We examine a collection of classical particles interacting with inverse-square two-body potentials in the thermodynamic limit of finite particle density. We find explicit large-amplitude density waves and soliton solutions for the motion of the system. Waves can be constructed as coherent states of either solitons or phonons (small-amplitude waves). Therefore, either solitons or phonons can be considered as the fundamental excitations. The generic wave is shown to correspond to a two-band state in the quantum description of the system, while the limiting cases of solitons and phonons correspond to particle and hole excitations.
Nonlinear de Broglie waves and the relation between relativistic and nonrelativistic solitons
International Nuclear Information System (INIS)
Barut, A.O.; Baby, B.V.
1988-07-01
It is shown that the well-known envelope soliton and kink solutions of the nonlinear Schroedinger equation are the nonrelativistic limit of the corresponding solutions of the nonlinear Klein-Gordon equation. 34 refs
Stability of the static solitons in a pure spinor theory with fractional power nonlinearities
International Nuclear Information System (INIS)
Akdeniz, K.G.; Tezgor, G.; Barut, A.O.; Kalayci, J.; Okan, S.E.
1988-08-01
Soliton solutions are obtained in a pure fermionic model with fractional power nonlinear self-interactions. The stability properties of the minimum solutions have also been investigated within the framework of the Shatah-Strauss formalism. (author). 10 refs
On-Demand Dark Soliton Train Manipulation in a Spinor Polariton Condensate
Pinsker, F.; Flayac, H.
2014-01-01
or electrically to provide a stable and efficient output signal modulation. Taking the polarization of the condensate into account, we elucidate the possibility of forming on-demand half-soliton trains. © 2014 American Physical Society.
Soliton analysis in complex molecular systems: A zig-zag chain
International Nuclear Information System (INIS)
Christiansen, P.L.; Savin, A.V.; Zolotaryuk, A.V.
1997-01-01
A simple numerical method for seeking solitary wave solutions of a permanent profile in molecular systems of big complexity is presented. The method is essentially based on the minimization of a finite-dimensional function which is chosen under an appropriate discretization of time derivatives in equations of motion. In the present paper, it is applied to a zig-zag chain backbone of coupled particles, each of which has two degrees of freedom (longitudinal and transverse). Both topological and nontopological soliton solutions are treated for this chain when it is (i) subjected to a two-dimensional periodic substrate potential or (ii) considered as an isolated object, respectively. In the first case, which may be considered as a zig-zag generalization of the Frenkel-Kontorova chain model, two types of kink solutions with different topological charges, describing vacancies of one or two atoms (I- or II-kinks) and defects with excess one or two atoms in the chain (I- or II-antikinks), have been found. The second case (isolated chain) is a generalization of the well-known Fermi-Pasta-Ulam chain model, which takes into account transverse degrees of freedom of the chain molecules. Two types of stable nontopological soliton solutions which describe either (i) a supersonic solitary wave of longitudinal stretching accompanied by transverse slandering or supersonic pulses of longitudinal compression propagating together with localized transverse thickening (bulge) have been obtained. 32 refs., 11 figs
Pfaffian Solutions and Resonant Interaction Properties of a Coupled BKP Lattice
International Nuclear Information System (INIS)
Zhao Hai-Qiong; Yu Guo-Fu
2014-01-01
In this paper, we give a coupled lattice equation with the help of Hirota operators, which comes from a special BKP lattice. Two-soliton and three-soliton solutions to the coupled system are constructed. Furthermore, resonant interaction of the two-soliton solution is analyzed in detail. Under some special resonant condition, it is shown that low soliton can propagate faster than high one. Finally, the N-soliton solution is presented in the Pfaffian form. (general)
Aspects of solitons in noncommutative field theories. The modified Ward model
International Nuclear Information System (INIS)
Petersen, S.
2006-01-01
In this thesis several aspects of solutions to the equations of motions to noncommutative field theories are investigated in detail. The main focus of the analysis is on the integrable chiral or modified unitary sigma model with U(n)-valued fields as introduced by Ward and its noncommutative extension where the above mentioned new solutions arise. Of particular interest in this context are to us the question of stability of static solitons and the applicability of the so-called adiabatic approach to as a means to approximate time-dependent solutions by geodesic motion in the moduli space of static solutions. After some introductory remarks we proceed to present the Ward model together with its noncommutative extension and give a unified exposition of its known static solutions. This model, as the prime example of an almost Lorentz-invariant field theory in 1+2 dimensions, has several virtues which make its analysis worthwhile. First of all it is integrable thus allowing for powerful, well developed, techniques to generate soliton solutions. At the same time these feature interaction among them. Furthermore, the commutative counterpart of the Ward model has been investigated in great detail such that many results are available for comparison. Next, the question of stability for the present static solutions is considered. This stability is governed by the quadratic form of the fluctuations, which, upon concentrating on the case of diagonal U(1) solutions, is explicitly computed. We show that the considered solutions are stable within a certain subsector of possible configurations, namely the grassmannian ones, and become unstable upon embedding them into the full unitary sigma model. Finally, we remark on some possible generalization of these results. This subject is followed, after a brief review of time-dependent Ward model solutions, by the application of the adiabatic approach, as proposed by Manton, to the static solutions. (orig.)
Solitons and cnoidal waves of the Klein–Gordon–Zakharov equation ...
Indian Academy of Sciences (India)
In (3), κ represents the wave number of the soliton while ω represents ... integration constant to be zero, since the search is for soliton solutions only, gives ..... and also using relations (3)–(5) gives the following rational travelling wave ... In future, the plan is to study the numerical simulations for this equation along with.
Properties of bright solitons in averaged and unaveraged models for SDG fibres
Kumar, Ajit; Kumar, Atul
1996-04-01
Using the slowly varying envelope approximation and averaging over the fibre cross-section the evolution equation for optical pulses in semiconductor-doped glass (SDG) fibres is derived from the nonlinear wave equation. Bright soliton solutions of this equation are obtained numerically and their properties are studied and compared with those of the bright solitons in the unaveraged model.
Static solitons in more than one dimension
International Nuclear Information System (INIS)
O'Raifeartaigh, L.
1978-01-01
The most important development of the last decade in particle physics and field theory has undoubtedly been the advent of hidden-symmetric gauge theories. One of the more interesting by-products of this development has been the discovery that hidden-symmetric gauge theories admit static solutions to the field equations which are regular everywhere and for which the energy is finite. Such solutions will be called solitons. The hidden-symmetric gauge solutions exist for n space dimensions, where 1 [de
Singular solitons of generalized Camassa-Holm models
International Nuclear Information System (INIS)
Tian Lixin; Sun Lu
2007-01-01
Two generalizations of the Camassa-Holm system associated with the singular analysis are proposed for Painleve integrability properties and the extensions of already known analytic solitons. A remarkable feature of the physical model is that it has peakon solution which has peak form. An alternative WTC test which allowed the identifying of such models directly if formulated in terms of inserting a formed ansatz into these models. For the two models have Painleve property, Painleve-Baecklund systems can be constructed through the expansion of solitons about the singularity manifold. By the implementations of Maple, plentiful new type solitonic structures and some kink waves, which are affected by the variation of energy, are explored. If the energy is infinite in finite time, there will be a collapse in soliton systems by direct numerical simulations. Particularly, there are two collapses coexisting in our regular solitons, which occurred around its central regions. Simulation shows that in the bottom of periodic waves arises the non-zero parts of compactons and anti-compactons. We also get floating solitary waves whose amplitude is infinite. In contrary to which a finite-amplitude blow-up soliton is obtained. Periodic blow-ups are found too. Special kinks which have periodic cuspons are derived
Ion-acoustic dressed solitons in a dusty plasma
International Nuclear Information System (INIS)
Tiwari, R.S.; Mishra, M.K.
2006-01-01
Using the reductive perturbation method, equations for ion-acoustic waves governing the evolution of first- and second-order potentials in a dusty plasma including the dynamics of charged dust grains have been derived. The renormalization procedure of Kodama and Taniuti is used to obtain a steady state nonsecular solution of these equations. The variation of velocity and width of the Korteweg-de Vries (KdV) as well as dressed solitons with amplitude have been studied for different concentrations and charge multiplicity of dust grains. The higher-order perturbation corrections to the KdV soliton description significantly affect the characteristics of the solitons in dusty plasma. It is found that in the presence of positively charged dust grains the system supports only compressive solitons. However, the plasma with negatively charged dust grains can support compressive solitons only up to a certain concentration of dust. Above this critical concentration of negative charge, the dusty plasma can support rarefactive solitons. An expression for the critical concentration of negatively charged dust in terms of charge and mass ratio of dust grains with plasma ions is also derived
Stability of matter-wave solitons in optical lattices
Ali, Sk. Golam; Roy, S. K.; Talukdar, B.
2010-08-01
We consider localized states of both single- and two-component Bose-Einstein condensates (BECs) confined in a potential resulting from the superposition of linear and nonlinear optical lattices and make use of Vakhitov-Kolokolov criterion to investigate the effect of nonlinear lattice on the stability of the soliton solutions in the linear optical lattice (LOL). For the single-component case we show that a weak nonlinear lattice has very little effect on the stability of such solitons while sufficiently strong nonlinear optical lattice (NOL) squeezes them to produce narrow bound states. For two-component condensates we find that when the strength of the NOL (γ1) is less than that of the LOL (V0) a relatively weak intra-atomic interaction (IAI) has little effect on the stability of the component solitons. This is true for both attractive and repulsive IAI. A strong attractive IAI, however, squeezes the BEC solitons while a similar repulsive IAI makes the component solitons wider. For γ1 > V0, only a strong attractive IAI squeezes the BEC solitons but the squeezing effect is less prominent than that found for γ1 < V0. We make useful checks on the results of our semianalytical stability analysis by solving the appropriate Gross-Pitaevskii equations numerically.
Traveling solitons in Lorentz and CPT breaking systems
International Nuclear Information System (INIS)
Souza Dutra, A. de; Correa, R. A. C.
2011-01-01
In this work we present a class of traveling solitons in Lorentz and CPT breaking systems. In the case of Lorentz violating scenarios, as far as we know, only static solitonic configurations were analyzed up to now in the literature. Here it is shown that it is possible to construct some traveling solitons which cannot be mapped into static configurations by means of Lorentz boosts due to explicit breaking. In fact, the traveling solutions cannot be reached from the static ones by using something similar to a Lorentz boost in those cases. Furthermore, in the model studied, a complete set of exact solutions is obtained. The solutions present a critical behavior controlled by the choice of an arbitrary integration constant.
Musammil, N. M.; Porsezian, K.; Nithyanandan, K.; Subha, P. A.; Tchofo Dinda, P.
2017-09-01
We present the study of the dark soliton dynamics in an inhomogeneous fiber by means of a variable coefficient modified nonlinear Schrödinger equation (Vc-MNLSE) with distributed dispersion, self-phase modulation, self-steepening and linear gain/loss. The ultrashort dark soliton pulse evolution and interaction is studied by using the Hirota bilinear (HB) method. In particular, we give much insight into the effect of self-steepening (SS) on the dark soliton dynamics. The study reveals a shock wave formation, as a major effect of SS. Numerically, we study the dark soliton propagation in the continuous wave background, and the stability of the soliton solution is tested in the presence of photon noise. The elastic collision behaviors of the dark solitons are discussed by the asymptotic analysis. On the other hand, considering the nonlinear tunneling of dark soliton through barrier/well, we find that the tunneling of the dark soliton depends on the height of the barrier and the amplitude of the soliton. The intensity of the tunneling soliton either forms a peak or valley and retains its shape after the tunneling. For the case of exponential background, the soliton tends to compress after tunneling through the barrier/well.
Soliton microcomb range measurement
Suh, Myoung-Gyun; Vahala, Kerry J.
2018-02-01
Laser-based range measurement systems are important in many application areas, including autonomous vehicles, robotics, manufacturing, formation flying of satellites, and basic science. Coherent laser ranging systems using dual-frequency combs provide an unprecedented combination of long range, high precision, and fast update rate. We report dual-comb distance measurement using chip-based soliton microcombs. A single pump laser was used to generate dual-frequency combs within a single microresonator as counterpropagating solitons. We demonstrated time-of-flight measurement with 200-nanometer precision at an averaging time of 500 milliseconds within a range ambiguity of 16 millimeters. Measurements at distances up to 25 meters with much lower precision were also performed. Our chip-based source is an important step toward miniature dual-comb laser ranging systems that are suitable for photonic integration.
Non-topological soliton bag model
International Nuclear Information System (INIS)
Wilets, L.
1986-01-01
The Friedberg-Lee soliton model, which effects confinement by a quantal scalar field, is discussed. The Lagrangian for the non-topological soliton model is the usual QCD Lagrangian supplemented by a non-linear scalar sigma field term. Static solutions to the field equations are considered in the mean field approximation. Small amplitude oscillations are discussed. Quantum alternatives to the mean field approximation are also considered. Methods of momentum projection and Lorentz boost are described, and the generator coordinate method is discussed. Calculations of the N-N interaction are reviewed briefly. Also discussed is one-gluon exchange, as well as the pion and dressing of the baryons. The hadron states are summarized. One loop quantum corrections are discussed briefly. Work in progress is mentioned in the areas of N-anti N annihilation, the many bag problem, and a Pauli equation for the nucleon. 31 refs
Chiral solitons in spinor polariton rings
Zezyulin, D. A.; Gulevich, D. R.; Skryabin, D. V.; Shelykh, I. A.
2018-04-01
We consider theoretically one-dimensional polariton ring accounting for both longitudinal-transverse (TE-TM) and Zeeman splittings of spinor polariton states and spin-dependent polariton-polariton interactions. We present a class of solutions in the form of the localized defects rotating with constant angular velocity and analyze their properties for realistic values of the parameters of the system. We show that the effects of the geometric phase arising from the interplay between the external magnetic field and the TE-TM splitting introduce chirality in the system and make solitons propagating in clockwise and anticlockwise directions nonequivalent. This can be interpreted as a solitonic analog of the Aharonov-Bohm effect.
Soliton Analysis in Complex Molecular Systems: A Zig-Zag Chain
Christiansen, P. L.; Savin, A. V.; Zolotaryuk, A. V.
1997-06-01
A simple numerical method for seeking solitary wavesolutions of a permanent profile in molecular systems of big complexity is presented. The method is essentially based on the minimization of a finite-dimensional function which is chosen under an appropriate discretization of time derivatives in equations of motion. In the present paper, it is applied to a zig-zag chain backbone of coupled particles, each of which has twodegrees of freedom (longitudinal and transverse). Both topological and nontopological soliton solutions are treated for this chain when it is (i) subjected to a two-dimensional periodic substrate potential or (ii) considered as an isolated object, respectively. In the first case, which may be considered as a zig-zag generalization of the Frenkel-Kontorova chain model, two types of kink solutions with different topological charges, describing vacancies of one or two atoms (I- or II-kinks) and defects with excess one or two atoms in the chain (I- or II-antikinks), have been found. The second case (isolated chain) is a generalization of the well-known Fermi-Pasta-Ulam chain model, which takes into account transverse degrees of freedom of the chain molecules. Two types of stable nontopological soliton solutions which describe either (i) a supersonic solitary wave of longitudinal stretching accompanied by transverse slendering or (ii) supersonic pulses of longitudinal compression propagating together with localized transverse thickening (bulge) have been obtained.
Rao, Jiguang; Porsezian, Kuppuswamy; He, Jingsong; Kanna, Thambithurai
2018-01-01
General semi-rational solutions of an integrable multi-component (2+1)-dimensional long-wave-short-wave resonance interaction system comprising multiple short waves and a single long wave are obtained by employing the bilinear method. These solutions describe the interactions between various types of solutions, including line rogue waves, lumps, breathers and dark solitons. We only focus on the dynamical behaviours of the interactions between lumps and dark solitons in this paper. Our detailed study reveals two different types of excitation phenomena: fusion and fission. It is shown that the fundamental (simplest) semi-rational solutions can exhibit fission of a dark soliton into a lump and a dark soliton or fusion of one lump and one dark soliton into a dark soliton. The non-fundamental semi-rational solutions are further classified into three subclasses: higher-order, multi- and mixed-type semi-rational solutions. The higher-order semi-rational solutions show the process of annihilation (production) of two or more lumps into (from) one dark soliton. The multi-semi-rational solutions describe N(N≥2) lumps annihilating into or producing from N-dark solitons. The mixed-type semi-rational solutions are a hybrid of higher-order semi-rational solutions and multi-semi-rational solutions. For the mixed-type semi-rational solutions, we demonstrate an interesting dynamical behaviour that is characterized by partial suppression or creation of lumps from the dark solitons.
Rao, Jiguang; Porsezian, Kuppuswamy; He, Jingsong; Kanna, Thambithurai
2018-01-01
General semi-rational solutions of an integrable multi-component (2+1)-dimensional long-wave-short-wave resonance interaction system comprising multiple short waves and a single long wave are obtained by employing the bilinear method. These solutions describe the interactions between various types of solutions, including line rogue waves, lumps, breathers and dark solitons. We only focus on the dynamical behaviours of the interactions between lumps and dark solitons in this paper. Our detailed study reveals two different types of excitation phenomena: fusion and fission. It is shown that the fundamental (simplest) semi-rational solutions can exhibit fission of a dark soliton into a lump and a dark soliton or fusion of one lump and one dark soliton into a dark soliton. The non-fundamental semi-rational solutions are further classified into three subclasses: higher-order, multi- and mixed-type semi-rational solutions. The higher-order semi-rational solutions show the process of annihilation (production) of two or more lumps into (from) one dark soliton. The multi-semi-rational solutions describe N ( N ≥2) lumps annihilating into or producing from N -dark solitons. The mixed-type semi-rational solutions are a hybrid of higher-order semi-rational solutions and multi-semi-rational solutions. For the mixed-type semi-rational solutions, we demonstrate an interesting dynamical behaviour that is characterized by partial suppression or creation of lumps from the dark solitons.
International Nuclear Information System (INIS)
Pelinovsky, Dmitry E.; Yang Jianke
2005-01-01
We study the generalized third-order nonlinear Schroedinger (NLS) equation which admits a one-parameter family of single-hump embedded solitons. Analyzing the spectrum of the linearization operator near the embedded soliton, we show that there exists a resonance pole in the left half-plane of the spectral parameter, which explains linear stability, rather than nonlinear semistability, of embedded solitons. Using exponentially weighted spaces, we approximate the resonance pole both analytically and numerically. We confirm in a near-integrable asymptotic limit that the resonance pole gives precisely the linear decay rate of parameters of the embedded soliton. Using conserved quantities, we qualitatively characterize the stable dynamics of embedded solitons
Soliton motion in a parametrically ac-driven damped Toda lattice
International Nuclear Information System (INIS)
Rasmussen, K.O.; Malomed, B.A.; Bishop, A.R.; Groenbech-Jensen, N.
1998-01-01
We demonstrate that a staggered parametric ac driving term can support stable progressive motion of a soliton in a Toda lattice with friction, while an unstaggered driving force cannot. A physical context of the model is that of a chain of anharmonically coupled particles adsorbed on a solid surface of a finite size. The ac driving force is generated by a standing acoustic wave excited on the surface. Simulations demonstrate that the state left behind the moving soliton, with the particles shifted from their equilibrium positions, gradually relaxes back to the equilibrium state that existed before the passage of the soliton. The perturbation theory predicts that the ac-driven soliton exists if the amplitude of the drive exceeds a certain threshold. The analytical prediction for the threshold is in reasonable agreement with that found numerically. Collisions between two counterpropagating solitons is also simulated, demonstrating that the collisions are, effectively, fully elastic. copyright 1998 The American Physical Society
Effect of scalar field mass on gravitating charged scalar solitons and black holes in a cavity
Energy Technology Data Exchange (ETDEWEB)
Ponglertsakul, Supakchai, E-mail: supakchai.p@gmail.com; Winstanley, Elizabeth, E-mail: E.Winstanley@sheffield.ac.uk
2017-01-10
We study soliton and black hole solutions of Einstein charged scalar field theory in cavity. We examine the effect of introducing a scalar field mass on static, spherically symmetric solutions of the field equations. We focus particularly on the spaces of soliton and black hole solutions, as well as studying their stability under linear, spherically symmetric perturbations of the metric, electromagnetic field, and scalar field.
International Nuclear Information System (INIS)
Ichikawa, Y.H.
1990-09-01
Plasma exhibits a full of variety of nonlinear phenomena. Active research in nonlinear plasma physics contributed to explore the concepts of soliton and chaos. Structure of soliton equations and dynamics of low dimensional Hamiltonian systems are discussed to emphasize the universality of these novel concepts in the wide branch of science and engineering. (author) 52 refs
Oscillating solitons in nonlinear optics
Indian Academy of Sciences (India)
... are derived, and the relevant properties and features of oscillating solitons are illustrated. Oscillating solitons are controlled by the reciprocal of the group velocity and Kerr nonlinearity. Results of this paper will be valuable to the study of dispersion-managed optical communication system and mode-locked fibre lasers.
Integrable Abelian vortex-like solitons
Energy Technology Data Exchange (ETDEWEB)
Contatto, Felipe, E-mail: felipe.contatto@damtp.cam.ac.uk [Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA (United Kingdom); CAPES Foundation, Ministry of Education of Brazil, Brasília, DF 70040-020 (Brazil)
2017-05-10
We propose a modified version of the Ginzburg–Landau energy functional admitting static solitons and determine all the Painlevé-integrable cases of its Bogomolny equations of a given class of models. Explicit solutions are determined in terms of the third Painlevé transcendents, allowing us to calculate physical quantities such as the vortex number and the vortex strength. These solutions can be interpreted as the usual Abelian-Higgs vortices on surfaces of non-constant curvature with conical singularity.
Integrable Abelian vortex-like solitons
Directory of Open Access Journals (Sweden)
Felipe Contatto
2017-05-01
Full Text Available We propose a modified version of the Ginzburg–Landau energy functional admitting static solitons and determine all the Painlevé-integrable cases of its Bogomolny equations of a given class of models. Explicit solutions are determined in terms of the third Painlevé transcendents, allowing us to calculate physical quantities such as the vortex number and the vortex strength. These solutions can be interpreted as the usual Abelian-Higgs vortices on surfaces of non-constant curvature with conical singularity.
International Nuclear Information System (INIS)
Karavaeva, E.N.; Molchanova, I.V.
1976-01-01
The results of experiments performed to study the behaviour of radioactive and stable isotopes of Ca in soil - solution - plant system at different soil moistening are given. The experiments have been conducted in culture pans with two soils: soddy-meadow and soddy-podzolic differing in a number of physico-chemical properties. The solution of radioactive Ca( 45 CaCl 2 ) has been applied to soddy-meadow soil at the rate of 0.2 μcurie/kg, and to soddy-podzolic soil - at the rate of 0.1 μcurie/kg. The distribution and accumulation coefficients are estimated by the ratio to the total content of stable Ca and 45 Ca in soil. A direct relationship between distribution coefficients and the rate of soil moistening is observed. It has been established that 45 Ca and the natural stable isotopes of Ca applied to the soil differ in the type of distribution in soil - soil solution system and in accumulation by plants. However, a great similarity has been observed in behaviour of radioactive and stable isotopes of Ca depending on soil moistening
Two-component vector solitons in defocusing Kerr-type media with spatially modulated nonlinearity
Energy Technology Data Exchange (ETDEWEB)
Zhong, Wei-Ping, E-mail: zhongwp6@126.com [Department of Electronic and Information Engineering, Shunde Polytechnic, Guangdong Province, Shunde 528300 (China); Texas A and M University at Qatar, P.O. Box 23874 Doha (Qatar); Belić, Milivoj [Texas A and M University at Qatar, P.O. Box 23874 Doha (Qatar); Institute of Physics, University of Belgrade, P.O. Box 57, 11001 Belgrade (Serbia)
2014-12-15
We present a class of exact solutions to the coupled (2+1)-dimensional nonlinear Schrödinger equation with spatially modulated nonlinearity and a special external potential, which describe the evolution of two-component vector solitons in defocusing Kerr-type media. We find a robust soliton solution, constructed with the help of Whittaker functions. For specific choices of the topological charge, the radial mode number and the modulation depth, the solitons may exist in various forms, such as the half-moon, necklace-ring, and sawtooth vortex-ring patterns. Our results show that the profile of such solitons can be effectively controlled by the topological charge, the radial mode number, and the modulation depth. - Highlights: • Two-component vector soliton clusters in defocusing Kerr-type media are reported. • These soliton clusters are constructed with the help of Whittaker functions. • The half-moon, necklace-ring and vortex-ring patterns are found. • The profile of these solitons can be effectively controlled by three soliton parameters.
Zhong, Rong-Xuan; Huang, Nan; Li, Huang-Wu; He, He-Xiang; Lü, Jian-Tao; Huang, Chun-Qing; Chen, Zhao-Pin
2018-04-01
We numerically and analytically investigate the formations and features of two-dimensional discrete Bose-Einstein condensate solitons, which are constructed by quadrupole-quadrupole interactional particles trapped in the tunable anisotropic discrete optical lattices. The square optical lattices in the model can be formed by two pairs of interfering plane waves with different intensities. Two hopping rates of the particles in the orthogonal directions are different, which gives rise to a linear anisotropic system. We find that if all of the pairs of dipole and anti-dipole are perpendicular to the lattice panel and the line connecting the dipole and anti-dipole which compose the quadrupole is parallel to horizontal direction, both the linear anisotropy and the nonlocal nonlinear one can strongly influence the formations of the solitons. There exist three patterns of stable solitons, namely horizontal elongation quasi-one-dimensional discrete solitons, disk-shape isotropic pattern solitons and vertical elongation quasi-continuous solitons. We systematically demonstrate the relationships of chemical potential, size and shape of the soliton with its total norm and vertical hopping rate and analytically reveal the linear dispersion relation for quasi-one-dimensional discrete solitons.
Generation and dynamics of quadratic birefringent spatial gap solitons
International Nuclear Information System (INIS)
Anghel-Vasilescu, P.; Dorignac, J.; Geniet, F.; Leon, J.; Taki, A.
2011-01-01
A method is proposed to generate and study the dynamics of spatial light solitons in a birefringent medium with quadratic nonlinearity. Although no analytical expression for propagating solitons has been obtained, our numerical simulations show the existence of stable localized spatial solitons in the frequency forbidden band gap of the medium. The dynamics of these objects is quite rich and manifests for instance elastic reflections, or inelastic collisions where two solitons merge and propagate as a single solitary wave. We derive the dynamics of the slowly varying envelopes of the three fields (second harmonic pump and two-component signal) and study this new system theoretically. We show that it does present a threshold for nonlinear supratransmission that can be calculated from a series expansion approach with a very high accuracy. Specific physical implications of our theoretical predictions are illustrated on LiGaTe 2 (LGT) crystals. Once irradiated by a cw laser beam of 10 μm wavelength, at an incidence beyond the extinction angle, such crystals will transmit light, in the form of spatial solitons generated in the nonlinear regime above the nonlinear supratransmission threshold.
Cubic-quintic solitons in the checkerboard potential
International Nuclear Information System (INIS)
Driben, Rodislav; Zyss, Joseph; Malomed, Boris A.; Gubeskys, Arthur
2007-01-01
We introduce a two-dimensional (2D) model which combines a checkerboard potential, alias the Kronig-Penney (KP) lattice, with the self-focusing cubic and self-defocusing quintic nonlinear terms. The beam-splitting mechanism and soliton multistability are explored in this setting, following the recently considered 1D version of the model. Families of single- and multi-peak solitons (in particular, five- and nine-peak species naturally emerge in the 2D setting) are found in the semi-infinite gap, with both branches of bistable families being robust against perturbations. For single-peak solitons, the variational approximation (VA) is developed, providing for a qualitatively correct description of the transition from monostability to the bistability. 2D solitons found in finite band gaps are unstable. Also constructed are two different species of stable vortex solitons, arranged as four-peak patterns ('oblique' and 'straight' ones). Unlike them, compact 'crater-shaped' vortices are unstable, transforming themselves into randomly walking fundamental beams
The use of stable isotopes for Cr(VI) determination in silty-clay soil solution.
Zuliani, Tea; Sčančar, Janez; Milačič, Radmila
2013-09-01
In assessing the environmental hazard of Cr(VI) present in soil, exchangeable Cr(VI) is important, since it can be easily washed out from the upper part of the soil into subsurface soil, surface and ground water, and taken up by plants. The aim of this study was to evaluate the degree of species interconversion that may occur during the extraction of exchangeable Cr(VI) from silty-clay soil with phosphate buffer in order to establish an extraction method that would be effective, accurate and with minimal or no species interconversions. The Cr(VI) concentration in soil extracts was determined by speciated isotope dilution inductively coupled plasma mass spectrometry (SID-ICP-MS). The study was performed on soil samples from a field treated with tannery waste for 17 years. Samples were spiked by enriched stable isotopic solutions of (50)Cr(VI) and (53)Cr(III) that were added to phosphate buffers (0.1 M KH2PO4-K2HPO4 (pH 7.2) and/or 0.1 M K2HPO4 (pH 8)). To optimize extraction, mechanical shaking and/or ultrasound-assisted extraction were compared. The separation and detection of Cr species was performed by high-performance liquid chromatography (HPLC) ICP-MS. When mechanical shaking was applied, 90 % reduction of Cr(VI) was induced by extraction with 0.1 M KH2PO4-K2HPO4, while with 0.1 M K2HPO4 reduction was around 40 %. To shorten the extraction time and the possibility of species interconversions, ultrasound-assisted extraction was further applied only with 0.1 M K2HPO4. For total extraction of exchangeable Cr(VI) with a maximum 10 % reduction of Cr(VI), five consecutive ultrasound-assisted extractions were needed.
Directory of Open Access Journals (Sweden)
Kilic Bulent
2016-01-01
Full Text Available This paper integrates dispersive optical solitons in special optical metamaterials with a time dependent coefficient. We obtained some optical solitons of the aforementioned equation. It is shown that the examined dependent coefficients are affected by the velocity of the wave. The first integral method (FIM and ansatz method are applied to reach the optical soliton solutions of the one-dimensional nonlinear Schrödinger’s equation (NLSE with time dependent coefficients.
Crosta, M.
2011-12-05
We characterize the full family of soliton solutions sitting over a background plane wave and ruled by the cubic-quintic nonlinear Schrödinger equation in the regime where a quintic focusing term represents a saturation of the cubic defocusing nonlinearity. We discuss the existence and properties of solitons in terms of catastrophe theory and fully characterize bistability and instabilities of the dark-antidark pairs, revealing mechanisms of decay of antidark solitons into dispersive shock waves.
Crosta, M.; Fratalocchi, Andrea; Trillo, S.
2011-01-01
We characterize the full family of soliton solutions sitting over a background plane wave and ruled by the cubic-quintic nonlinear Schrödinger equation in the regime where a quintic focusing term represents a saturation of the cubic defocusing nonlinearity. We discuss the existence and properties of solitons in terms of catastrophe theory and fully characterize bistability and instabilities of the dark-antidark pairs, revealing mechanisms of decay of antidark solitons into dispersive shock waves.
Solitons in quadratic nonlinear photonic crystals
DEFF Research Database (Denmark)
Corney, Joel Frederick; Bang, Ole
2001-01-01
We study solitons in one-dimensional quadratic nonlinear photonic crystals with modulation of both the linear and nonlinear susceptibilities. We derive averaged equations that include induced cubic nonlinearities, which can be defocusing, and we numerically find previously unknown soliton families....... Because of these induced cubic terms, solitons still exist even when the effective quadratic nonlinearity vanishes and conventional theory predicts that there can be no soliton. We demonstrate that both bright and dark forms of these solitons can propagate stably....
International Nuclear Information System (INIS)
Sun, Zhi-Yuan; Gao, Yi-Tian; Yu, Xin; Liu, Ying
2013-01-01
We respectively investigate breakup and switching of the Manakov-typed bound vector solitons (BVSs) induced by two types of stochastic perturbations: the homogenous and nonhomogenous. Symmetry-recovering is discovered for the asymmetrical homogenous case, while soliton switching is found to relate with the perturbation amplitude and soliton coherence. Simulations show that soliton switching in the circularly-polarized light system is much weaker than that in the Manakov and linearly-polarized systems. In addition, the homogenous perturbations can enhance the soliton switching in both of the Manakov and non-integrable (linearly- and circularly-polarized) systems. Our results might be helpful in interpreting dynamics of the BVSs with stochastic noises in nonlinear optics or with stochastic quantum fluctuations in Bose–Einstein condensates.
Periodic modulations controlling Kuznetsov–Ma soliton formation in nonlinear Schrödinger equations
Energy Technology Data Exchange (ETDEWEB)
Tiofack, C.G.L., E-mail: glatchio@yahoo.fr [Univ. Lille, CNRS, UMR 8523 – PhLAM – Physique des Lasers Atomes et Molécules, F-59000 Lille (France); Coulibaly, S.; Taki, M. [Univ. Lille, CNRS, UMR 8523 – PhLAM – Physique des Lasers Atomes et Molécules, F-59000 Lille (France); De Bièvre, S.; Dujardin, G. [Univ. Lille, CNRS, UMR 8524 – Laboratoire Paul Painlevé, F-59000 Lille (France); Équipe-Projet Mephysto, INRIA Lille-Nord Europe (France)
2017-06-28
We analyze the exact Kuznetsov–Ma soliton solution of the one-dimensional nonlinear Schrödinger equation in the presence of periodic modulations satisfying an integrability condition. We show that, in contrast to the case without modulation, the Kuznetsov–Ma soliton develops multiple compression points whose number, shape and position are controlled both by the intensity of the modulation and by its frequency. In addition, when this modulation frequency is a rational multiple of the natural frequency of the Kuznetsov–Ma soliton, a scenario similar to a nonlinear resonance is obtained: in this case the spatial oscillations of the Kuznetsov–Ma soliton's intensity are periodic. When the ratio of the two frequencies is irrational, the soliton's intensity is a quasiperiodic function. A striking and important result of our analysis is the possibility to suppress any component of the output spectrum of the Kuznetsov–Ma soliton by a judicious choice of the amplitude and frequency of the modulation. - Highlights: • Exact Kuznetsov–Ma soliton solution in presence of periodic coefficients is obtained. • The multiple compression points of the solution are studied. • The quasi-periodicity of the solution is discussed. • The possibility to suppress any component of the spectrum is analyzed.
Facão, M.; Carvalho, M. I.
2017-10-01
In this work, we present parameter regions for the existence of stable plain solitons of the cubic complex Ginzburg-Landau equation (CGLE) with higher-order terms associated with a fourth-order expansion. Using a perturbation approach around the nonlinear Schrödinger equation soliton and a full numerical analysis that solves an ordinary differential equation for the soliton profiles and using the Evans method in the search for unstable eigenvalues, we have found that the minimum equation allowing these stable solitons is the cubic CGLE plus a term known in optics as Raman-delayed response, which is responsible for the redshift of the spectrum. The other favorable term for the occurrence of stable solitons is a term that represents the increase of nonlinear gain with higher frequencies. At the stability boundary, a bifurcation occurs giving rise to stable oscillatory solitons for higher values of the nonlinear gain. These oscillations can have very high amplitudes, with the pulse energy changing more than two orders of magnitude in a period, and they can even exhibit more complex dynamics such as period-doubling.
Exact optical solitons in (n + 1)-dimensions with anti-cubic nonlinearity
Younis, Muhammad; Shahid, Iram; Anbreen, Sumaira; Rizvi, Syed Tahir Raza
2018-02-01
The paper studies the propagation of optical solitons in (n + 1)-dimensions under anti-cubic law of nonlinearity. The bright, dark and singular optical solitons are extracted using the extended trial equation method. The constraint conditions, for the existence of these solitons, are also listed. Additionally, a couple of other solutions known as singular periodic and Jacobi elliptic solutions, fall out as a by-product of this scheme. The obtained results are new and reported first time in (n + 1)-dimensions with anti-cubic law of nonlinearity.
Time dependent solitons of noncommutative Chern-Simons theory coupled to scalar fields
Hadasz, Leszek; Lindström, Ulf; Roček, Martin; von Unge, Rikard
2004-05-01
We study one- and two-soliton solutions of noncommutative Chern-Simons theory coupled to a nonrelativistic or a relativistic scalar field. In the nonrelativistic case, we find a tower of new stationary time-dependent solutions, all with the same charge density, but with increasing energies. The dynamics of these solitons cannot be studied using traditional moduli space techniques, but we do find a nontrivial symplectic form on the phase space indicating that the moduli space is not flat. In the relativistic case we find the metric on the two soliton moduli space.
Time dependent solitons of noncommutative Chern-Simons theory coupled to scalar fields
International Nuclear Information System (INIS)
Hadasz, Leszek; Lindstroem, Ulf; Rocek, Martin; Unge, Rikard von
2004-01-01
We study one- and two-soliton solutions of noncommutative Chern-Simons theory coupled to a nonrelativistic or a relativistic scalar field. In the nonrelativistic case, we find a tower of new stationary time-dependent solutions, all with the same charge density, but with increasing energies. The dynamics of these solitons cannot be studied using traditional moduli space techniques, but we do find a nontrivial symplectic form on the phase space indicating that the moduli space is not flat. In the relativistic case we find the metric on the two soliton moduli space
Stability of Modified K-dV soliton in plasma with negative ion
International Nuclear Information System (INIS)
Matsukawa, Michiaki; Watanabe, Shinsuke
1988-01-01
The K-P and Modified K-P equations for ion acoustic wave are derived from the fluid equations for plasma with negative ion. At the critical density of the negative ion where the nonlinearity of the K-P equation vanishes, the ion acoustic soliton is described by the Modified K-P equation. The stability of Modified K-dV soliton against bending are investigated by using the Modified K-P equation. It is found that the soliton is stable, independent of the sign of amplitude. (author)
Existence of Torsional Solitons in a Beam Model of Suspension Bridge
Benci, Vieri; Fortunato, Donato; Gazzola, Filippo
2017-11-01
This paper studies the existence of solitons, namely stable solitary waves, in an idealized suspension bridge. The bridge is modeled as an unbounded degenerate plate, that is, a central beam with cross sections, and displays two degrees of freedom: the vertical displacement of the beam and the torsional angles of the cross sections. Under fairly general assumptions, we prove the existence of solitons. Under the additional assumption of large tension in the sustaining cables, we prove that these solitons have a nontrivial torsional component. This appears relevant for security since several suspension bridges collapsed due to torsional oscillations.
Soliton dynamical properties of Bose—Einstein condensates trapped in a double square well potential
International Nuclear Information System (INIS)
Li Jin-Hui; Li Zhi-Jian
2011-01-01
We first present an analytical solution of the single and double solitions of Bose—Einstein condensates trapped in a double square well potential using the multiple-scale method. Then, we show by numerical calculation that a dark soliton can be transmitted through the square well potential. With increasing depth of the square well potential, the amplitude of the dark soliton becomes larger, and the soliton propagates faster. In particular, we treat the collision behaviour of the condensates trapped in either equal or different depths of the double square well potential. If we regard the double square well potential as the output source of the solitons, the collision locations (position and time) between two dark solitons can be controlled by its depth. (general)
The nonlinear Fourier analysis of internal solitons in the Andaman sea
International Nuclear Information System (INIS)
Osborne, A.R.; Provenzale, A.; Bergamasco, L.
1983-01-01
A preliminary spectral analysis of large-amplitude internal solitons in the Andaman Sea was conducted, employing method based upon the spectral (or scattering) transform solution of the Korteweg-de Vries equation
A soliton perturbation scheme for 3x3 inverse scattering transform
International Nuclear Information System (INIS)
Roy Chowdhury, A.; Banerjee, R.S.; Roy, T.
1979-01-01
A perturbation method for the soliton solutions of nonlinear equations tractable using 3x3 matrix IST formalism is discussed in detait. The corresponding changes in conservation laws are also considered. (author)
Energy Technology Data Exchange (ETDEWEB)
Bi, Xiaoman; Zuo, Weiwei; Liu, Yingliang, E-mail: liuylxn@sohu.com; Zhang, Zhenru; Zeng, Cen; Xu, Shengang; Cao, Shaokui, E-mail: caoshaokui@zzu.edu.cn
2015-10-15
Highlights: • The D–A–D electroluminescent molecular glasses are synthesized. • Non-doped red electroluminescent film is fabricated by spin-coating. • Red OLED shows stable wavelength, luminous efficiency and chromaticity. • CIE1931 coordinate is in accord with standard red light in PAL system. - Abstract: Organic light-emitting molecular glasses (OEMGs) are synthesized through the introduction of nonplanar donor and branched aliphatic chain into electroluminescent emitters. The target OEMGs are characterized by {sup 1}H NMR, {sup 13}C NMR, IR, UV–vis and fluorescent spectra as well as elemental analysis, TG and DSC. The results indicated that the optical, electrochemical and electroluminescent properties of OEMGs are adjusted successfully by the replacement of electron-donating group. The non-doped OLED device with a standard red electroluminescent emission is achieved by spin-coating the THF solution of OEMG with a triphenylamine moiety. This non-doped red OLED device takes on an electrically stable electroluminescent performance, including the stable maximum electroluminescent wavelength of 640 nm, the stable luminous efficiency of 2.4 cd/A and the stable CIE1931 coordinate of (x, y) = (0.64, 0.35), which is basically in accord with the CIE1931 coordinate (x, y) = (0.64, 0.33) of standard red light in PAL system.
Basic methods of soliton theory
Cherednik, I
1996-01-01
In the 25 years of its existence Soliton Theory has drastically expanded our understanding of "integrability" and contributed a lot to the reunification of Mathematics and Physics in the range from deep algebraic geometry and modern representation theory to quantum field theory and optical transmission lines.The book is a systematic introduction to the Soliton Theory with an emphasis on its background and algebraic aspects. It is the first one devoted to the general matrix soliton equations, which are of great importance for the foundations and the applications.Differential algebra (local cons
Solitons in relativistic cosmologies
International Nuclear Information System (INIS)
Pullin, J.
1988-08-01
The application to the construction of solitonic cosmologies in General Relativity of the Inverse Scattering Technique of Belinskii an Zakharov is analyzed. Three improvements to the mentioned technique are proposed: the inclusion of higher order poles in the scattering matrix, a new renormalization technique for diagonal metrics and the extension of the technique to include backgrounds with material content by means of a Kaluza-Klein formalism. As a consequence of these improvements, three new aspects can be analyzed: a) The construction of anisotropic and inhomogeneous cosmological models which can mimic the formation of halos and voids, due to the presence of a material content. The new renormalization technique allows to construct an exact perturbation theory. b) The analysis of the dynamics of models with cosmological constant (inflationary models) and their perturbations. c) The study of interaction of gravitational solitonic waves on material backgrounds. Moreover, some additional works, connected with the existance of 'Crack of doom' type singularities in Kaluza-Klein cosmologies, stochastic perturbations in inflationary universes and inflationary phase transitions in rotating universes are described. (Author) [es
Ion- and electron-acoustic solitons in two-electron temperature space plasmas
International Nuclear Information System (INIS)
Lakhina, G. S.; Kakad, A. P.; Singh, S. V.; Verheest, F.
2008-01-01
Properties of ion- and electron-acoustic solitons are investigated in an unmagnetized multicomponent plasma system consisting of cold and hot electrons and hot ions using the Sagdeev pseudopotential technique. The analysis is based on fluid equations and the Poisson equation. Solitary wave solutions are found when the Mach numbers exceed some critical values. The critical Mach numbers for the ion-acoustic solitons are found to be smaller than those for electron-acoustic solitons for a given set of plasma parameters. The critical Mach numbers of ion-acoustic solitons increase with the increase of hot electron temperature and the decrease of cold electron density. On the other hand, the critical Mach numbers of electron-acoustic solitons increase with the increase of the cold electron density as well as the hot electron temperature. The ion-acoustic solitons have positive potentials for the parameters considered. However, the electron-acoustic solitons have positive or negative potentials depending whether the fractional cold electron density with respect to the ion density is greater or less than a certain critical value. Further, the amplitudes of both the ion- and electron-acoustic solitons increase with the increase of the hot electron temperature. Possible application of this model to electrostatic solitary waves observed on the auroral field lines by the Viking spacecraft is discussed
Solitons in a relativistic plasma with negative ions--
International Nuclear Information System (INIS)
Das, G.C.; Karmakar, B.; Ibohanbi Singh, KH.
1990-01-01
The interaction of the nonlinearity and the dispersiveness causing the solitary waves are studied in a relativistic plasma with negative ions through the derivation of a nonlinear partial differential equation known as the Korteweg-Devries (K-DV) equation. The negative ions play a salient feature on the existence and behavior of the solitons and could be of interest in laboratory plasmas. First, the observations are made in a nonisothermal plasma, and later the reduction to the nonisothermality of the plasma shows entirely different characteristics as compared to the solitons in the isothermal plasmas. A comparison with the various solutions has been emphasized
Solitons, Bose-Einstein condensation and superfluidity in He II
International Nuclear Information System (INIS)
Chela-Flores, J.; Ghassib, H.B.
1985-09-01
The analytic form of a wave propagating with a constant velocity and a permanent profile is inferred for a weakly interacting Bose gas, using an exact (rather than asymptotic) solution of the field equation of the self-consistent Hartree model. The significance of this approach is indicated, especially when realistic interatomic potentials are used. In addition, the general relation between solitons and Bose-Einstein condensation is underlined by invoking the profound insight recently acquired in studies of the quantum liquids involved in the living state. It is concluded that solitons may occur in He II, and may play a significant role in the phenomena of superfluidity. (author)
Soliton formation at critical density in laser-irradiated plasmas
International Nuclear Information System (INIS)
Anderson, D.; Bondeson, A.; Lisak, M.
1979-01-01
The generation of Langmuir solitons at the resonance layer in a plasma irradiated by a strong high-frequency pump is investigated. The process is modelled by the nonlinear Schrodinger equation including an external pump, a density gradient and linear damping. The evolution equation is reformulated as an exact variational principle and the one-soliton generation process is studied by substituting various trial solutions. The applicability conditions for the nonlinear Schrodinger equation are re-examined and found to be more restrictive than previously stated. (author)
A fluid dynamic approach to the dust-acoustic soliton
International Nuclear Information System (INIS)
McKenzie, J.F.; Doyle, T.B.
2002-01-01
The properties of dust-acoustic solitons are derived from a fluid dynamic viewpoint in which conservation of total momentum, combined with the Bernoulli-like energy equations for each species, yields the structure equation for the heavy (or dust) speed in the stationary wave. This fully nonlinear approach reveals the crucial role played by the heavy sonic point in limiting the collective dust-acoustic Mach number, above which solitons cannot exist. An exact solution illustrates that the cold heavy species is compressed and this implies concomitant contraints on the potential and on the flow speed of the electrons and protons in the wave
A Fluid Dynamic Approach to the Dust-Acoustic Soliton
McKenzie, J. F.; Doyle, T. B.
2002-12-01
The properties of dust-acoustic solitons are derived from a fluid dynamic viewpoint in which conservation of total momentum, combined with the Bernoulli-like energy equations for each species, yields the structure equation for the heavy (or dust) speed in the stationary wave. This fully nonlinear approach reveals the crucial role played by the heavy sonic point in limiting the collective dust-acoustic Mach number, above which solitons cannot exist. An exact solution illustrates that the cold heavy species is compressed and this implies concomitant contraints on the potential and on the flow speed of the electrons and protons in the wave.
Stable preparations of tyrosine hydroxylase provide the solution structure of the full-length enzyme
Bezem, Maria T.; Baumann, Anne; Skjærven, Lars; Meyer, Romain; Kursula, Petri; Martinez, Aurora; Flydal, Marte I.
2016-01-01
Tyrosine hydroxylase (TH) catalyzes the rate-limiting step in the biosynthesis of catecholamine neurotransmitters. TH is a highly complex enzyme at mechanistic, structural, and regulatory levels, and the preparation of kinetically and conformationally stable enzyme for structural characterization has been challenging. Here, we report on improved protocols for purification of recombinant human TH isoform 1 (TH1), which provide large amounts of pure, stable, active TH1 with an intact N-terminus. TH1 purified through fusion with a His-tagged maltose-binding protein on amylose resin was representative of the iron-bound functional enzyme, showing high activity and stabilization by the natural feedback inhibitor dopamine. TH1 purified through fusion with a His-tagged ZZ domain on TALON is remarkably stable, as it was partially inhibited by resin-derived cobalt. This more stable enzyme preparation provided high-quality small-angle X-ray scattering (SAXS) data and reliable structural models of full-length tetrameric TH1. The SAXS-derived model reveals an elongated conformation (Dmax = 20 nm) for TH1, different arrangement of the catalytic domains compared with the crystal structure of truncated forms, and an N-terminal region with an unstructured tail that hosts the phosphorylation sites and a separated Ala-rich helical motif that may have a role in regulation of TH by interacting with binding partners. PMID:27462005
Trofimov, Vyacheslav A.; Lysak, Tatiana M.
2018-04-01
We investigate both numerically and analytically the spectrum evolution of a novel type soliton - nonlinear chirped accelerating or decelerating soliton - at a femtosecond pulse propagation in a medium containing noble nanoparticles. In our consideration, we take into account one- or two-photon absorption of laser radiation by nanorods, and time-dependent nanorod aspect ratio changing due to their melting or reshaping because of laser energy absorption. The chirped solitons are formed due to the trapping of laser radiation by the nanorods reshaping fronts, if a positive or negative phase-amplitude grating is induced by laser radiation. Accelerating or slowing down chirped soliton formation is accompanied by the soliton spectrum blue or red shift. To prove our numerical results, we derived the approximate analytical law for the spectrum maximum intensity evolution along the propagation coordinate, based on earlier developed approximate analytical solutions for accelerating and decelerating solitons.
Protocol of networks using energy sharing collisions of bright solitons
Indian Academy of Sciences (India)
Equations (13a) and (13b) can be satisfied by choosing αk as .... (right) configurations of the two-soliton solution in the Manakov-type system on PSG. .... receivers of messages, the present phase change can be used as protocols of network.
Quadratic soliton self-reflection at a quadratically nonlinear interface
Jankovic, Ladislav; Kim, Hongki; Stegeman, George; Carrasco, Silvia; Torner, Lluis; Katz, Mordechai
2003-11-01
The reflection of bulk quadratic solutions incident onto a quadratically nonlinear interface in periodically poled potassium titanyl phosphate was observed. The interface consisted of the boundary between two quasi-phase-matched regions displaced from each other by a half-period. At high intensities and small angles of incidence the soliton is reflected.
Gap solitons in periodic Schrodinger lattice system with nonlinear hopping
Directory of Open Access Journals (Sweden)
Ming Cheng
2016-10-01
Full Text Available This article concerns the periodic discrete Schrodinger equation with nonlinear hopping on the infinite integer lattice. We obtain the existence of gap solitons by the linking theorem and concentration compactness method together with a periodic approximation technique. In addition, the behavior of such solutions is studied as $\\alpha\\to 0$. Notice that the nonlinear hopping can be sign changing.
Dynamics of solitons and quasisolitons of the cubic third-order nonlinear Schrödinger equation
DEFF Research Database (Denmark)
Karpman, V.I.; Juul Rasmussen, J.; Shagalov, A.G.
2001-01-01
The dynamics of soliton and quasisoliton solutions of the cubic third-order nonlinear Schrodinger equation is studied. Regular solitons exist due to a balance between the nonlinear terms and (linear) third-order dispersion; they are not important at small alpha (3) (alpha (3) is the coefficient...... in the third derivative term) and vanish at alpha3 -->0. The most essential, at small alpha (3), is a quasisoliton emitting resonant radiation (resonantly radiating soliton). Its relationship with the other (steady) quasisoliton, called embedded soliton, is studied analytically and also in numerical...
International Nuclear Information System (INIS)
Belmonte-Beitia, Juan; Perez-Garcia, Victor M.; Vekslerchik, Vadym
2007-01-01
In this paper, we study a system of coupled nonlinear Schroedinger equations modelling a quantum degenerate mixture of bosons and fermions. We analyze the stability of plane waves, give precise conditions for the existence of solitons and write explicit solutions in the form of periodic waves. We also check that the solitons observed previously in numerical simulations of the model correspond exactly to our explicit solutions and see how plane waves destabilize to form periodic waves
On-Demand Dark Soliton Train Manipulation in a Spinor Polariton Condensate
Pinsker, F.
2014-04-10
We theoretically demonstrate the generation of dark soliton trains in a one-dimensional exciton-polariton condensate within experimentally accessible schemes. In particular, we show that the frequency of the train can be finely tuned fully optically or electrically to provide a stable and efficient output signal modulation. Taking the polarization of the condensate into account, we elucidate the possibility of forming on-demand half-soliton trains. © 2014 American Physical Society.
All-fiber nonlinearity- and dispersion-managed dissipative soliton nanotube mode-locked laser
Energy Technology Data Exchange (ETDEWEB)
Zhang, Z. [Department of Physics, Bilkent University, 06800 Ankara (Turkey); Nanjing University of Posts and Communications, Nanjing 210003 (China); Popa, D., E-mail: dp387@cam.ac.uk; Wittwer, V. J.; Milana, S.; Hasan, T.; Jiang, Z.; Ferrari, A. C. [Cambridge Graphene Centre, University of Cambridge, Cambridge CB3 0FA (United Kingdom); Ilday, F. Ö. [Department of Physics, Bilkent University, 06800 Ankara (Turkey); Department of Electrical and Electronics Engineering, Bilkent University, 06800 Ankara (Turkey)
2015-12-14
We report dissipative soliton generation from an Yb-doped all-fiber nonlinearity- and dispersion-managed nanotube mode-locked laser. A simple all-fiber ring cavity exploits a photonic crystal fiber for both nonlinearity enhancement and dispersion compensation. The laser generates stable dissipative solitons with large linear chirp in the net normal dispersion regime. Pulses that are 8.7 ps long are externally compressed to 118 fs, outperforming current nanotube-based Yb-doped fiber laser designs.
Soliton scatterings by impurities in a short-length sine-Gordon chain
International Nuclear Information System (INIS)
Dikande, A.M.; Kofane, T.C.
1995-07-01
The scattering of soliton by impurities at the frontiers of a finite-length region of an infinite sine-Gordon chain is analyzed. The impurities consist of two isotopic inhomogeneities installed at the boundaries of the finite-length region. The soliton solution in the region is found in term of snoidal sine-Gordon soliton which properly takes into account the effects of the boundaries. By contrast, the soliton solutions in the neighboring sides of the region are obtained in terms of the so-called large-amplitude, localized kinks with limiting spatial extensions at x → ± ∞, which is equal ±π. Using the continuity of these soliton solutions at the frontiers as well as appropriate boundary conditions, it is shown that the soliton may be either i) reflected by the incident impurity; ii) trapped (with oscillating motions) between the two impurities (i.e. inside the infinite region); or iii) transmitted by the second impurity into the third, infinitely extended region. The threshold velocities for the reflection and transmission into different regions are found and shown to vary exponentially as a function of the length of the bounded region. The frequency of soliton oscillations between the impurities has also been calculated in some acceptable limit. (author). 28 refs, 1 fig
Collective states of externally driven, damped nonlinear Schroedinger solitons
International Nuclear Information System (INIS)
Barashenkov, I.V.; Smirnov, Yu.S.
1997-01-01
We study bifurcations of localized stationary solitons of the externally driven, damped nonlinear Schroedinger equation iΨ t + Ψ xx + 2|Ψ| 2 Ψ=-iγΨ-h e iΩt , in the region of large γ (γ>1/2). For each pair of h and γ, there are two coexisting solitons, Ψ + and Ψ - . As the driver's strength h increases for the fixed γ, the Ψ + soliton merges with the flat background while the Ψ - forms a stationary collective state with two 'psi-pluses': Ψ - → Ψ (+ - +) . We obtain other stationary solutions and identify them as multisoliton complexes Ψ (++) , Ψ (--) , Ψ (-+) , Ψ (---) , Ψ (-+- ) etc. The corresponding intersoliton separations are compared to predictions of a variational approximation
Solitonic Integrable Perturbations of Parafermionic Theories
Fernández-Pousa, C R; Hollowood, Timothy J; Miramontes, J L
1997-01-01
The quantum integrability of a class of massive perturbations of the parafermionic conformal field theories associated to compact Lie groups is established by showing that they have quantum conserved densities of scale dimension 2 and 3. These theories are integrable for any value of a continuous vector coupling constant, and they generalize the perturbation of the minimal parafermionic models by their first thermal operator. The classical equations-of-motion of these perturbed theories are the non-abelian affine Toda equations which admit (charged) soliton solutions whose semi-classical quantization is expected to permit the identification of the exact S-matrix of the theory.
Detection of Moving Targets Using Soliton Resonance Effect
Kulikov, Igor K.; Zak, Michail
2013-01-01
The objective of this research was to develop a fundamentally new method for detecting hidden moving targets within noisy and cluttered data-streams using a novel "soliton resonance" effect in nonlinear dynamical systems. The technique uses an inhomogeneous Korteweg de Vries (KdV) equation containing moving-target information. Solution of the KdV equation will describe a soliton propagating with the same kinematic characteristics as the target. The approach uses the time-dependent data stream obtained with a sensor in form of the "forcing function," which is incorporated in an inhomogeneous KdV equation. When a hidden moving target (which in many ways resembles a soliton) encounters the natural "probe" soliton solution of the KdV equation, a strong resonance phenomenon results that makes the location and motion of the target apparent. Soliton resonance method will amplify the moving target signal, suppressing the noise. The method will be a very effective tool for locating and identifying diverse, highly dynamic targets with ill-defined characteristics in a noisy environment. The soliton resonance method for the detection of moving targets was developed in one and two dimensions. Computer simulations proved that the method could be used for detection of singe point-like targets moving with constant velocities and accelerations in 1D and along straight lines or curved trajectories in 2D. The method also allows estimation of the kinematic characteristics of moving targets, and reconstruction of target trajectories in 2D. The method could be very effective for target detection in the presence of clutter and for the case of target obscurations.
Solitons supported by localized nonlinearities in periodic media
International Nuclear Information System (INIS)
Dror, Nir; Malomed, Boris A.
2011-01-01
Nonlinear periodic systems, such as photonic crystals and Bose-Einstein condensates (BEC's) loaded into optical lattices, are often described by the nonlinear Schroedinger or Gross-Pitaevskii equation with a sinusoidal potential. Here, we consider a model based on such a periodic potential, with the nonlinearity (attractive or repulsive) concentrated either at a single point or at a symmetric set of two points, which are represented, respectively, by a single δ function or a combination of two δ functions. With the attractive or repulsive sign of the nonlinearity, this model gives rise to ordinary solitons or gap solitons (GS's), which reside, respectively, in the semi-infinite or finite gaps of the system's linear spectrum, being pinned to the δ functions. Physical realizations of these systems are possible in optics and BEC's, using diverse variants of the nonlinearity management. First, we demonstrate that the single δ function multiplying the nonlinear term supports families of stableregular solitons in the self-attractive case, while a family of solitons supported by the attractive δ function in the absence of the periodic potential is completely unstable. In addition, we show that the δ function can support stable GS's in the first finite band gap in both the self-attractive and repulsive models. The stability analysis for the GS's in the second finite band gap is reported too, for both signs of the nonlinearity. Alongside the numerical analysis, analytical approximations are developed for the solitons in the semi-infinite and first two finite gaps, with the single δ function positioned at a minimum or maximum of the periodic potential. In the model with the symmetric set of two δ functions, we study the effect of the spontaneous symmetry breaking of the pinned solitons. Two configurations are considered, with the δ functions set symmetrically with respect to the minimum or maximum of the underlying potential.
International Nuclear Information System (INIS)
Brekke, L.; Imbo, T.D.
1992-01-01
The authors study the inequivalent quantizations of (1 + 1)-dimensional nonlinear sigma models with space manifold S 1 and target manifold X. If x is multiply connected, these models possess topological solitons. After providing a definition of spin and statistics for these solitons and demonstrating a spin-statistics correlation, we give various examples where the solitons can have exotic statistics. In some of these models, the solitons may obey a generalized version of fractional statistics called ambistatistics. In this paper the relevance of these 2d models to the statistics of vortices in (2 + 1)-dimensional spontaneously broken gauge theories is discussed. The authors close with a discussion concerning the extension of our results to higher dimensions
Zhang, Jie-Fang; Li, Yi-Shen; Meng, Jianping; Wu, Lei; Malomed, Boris A.
2010-09-01
We investigate solitons and nonlinear Bloch waves in Bose-Einstein condensates trapped in optical lattices (OLs). By introducing specially designed localized profiles of the spatial modulation of the attractive nonlinearity, we construct an infinite set of exact soliton solutions in terms of Mathieu and elliptic functions, with the chemical potential belonging to the semi-infinite gap of the OL-induced spectrum. Starting from the particular exact solutions, we employ the relaxation method to construct generic families of soliton solutions in a numerical form. The stability of the solitons is investigated through the computation of the eigenvalues for small perturbations, and also by direct simulations. Finally, we demonstrate a virtually exact (in the numerical sense) composition relation between nonlinear Bloch waves and solitons.
International Nuclear Information System (INIS)
Zhang Jiefang; Meng Jianping; Wu Lei; Li Yishen; Malomed, Boris A.
2010-01-01
We investigate solitons and nonlinear Bloch waves in Bose-Einstein condensates trapped in optical lattices (OLs). By introducing specially designed localized profiles of the spatial modulation of the attractive nonlinearity, we construct an infinite set of exact soliton solutions in terms of Mathieu and elliptic functions, with the chemical potential belonging to the semi-infinite gap of the OL-induced spectrum. Starting from the particular exact solutions, we employ the relaxation method to construct generic families of soliton solutions in a numerical form. The stability of the solitons is investigated through the computation of the eigenvalues for small perturbations, and also by direct simulations. Finally, we demonstrate a virtually exact (in the numerical sense) composition relation between nonlinear Bloch waves and solitons.
International Nuclear Information System (INIS)
Wang Lei; Zhu Yujie; Wang Ziqi; Xu Tao; Qi Fenghua; Xue Yushan
2016-01-01
We study the nonlinear localized waves on constant backgrounds of the Hirota–Maxwell–Bloch (HMB) system arising from the erbium doped fibers. We derive the asymmetric breather, rogue wave (RW) and semirational solutions of the HMB system. We show that the breather and RW solutions can be converted into various soliton solutions. Under different conditions of parameters, we calculate the locus of the eigenvalues on the complex plane which converts the breathers or RWs into solitons. Based on the second-order solutions, we investigate the interactions among different types of nonlinear waves including the breathers, RWs and solitons. (author)
Wang, Lei; Zhu, Yu-Jie; Wang, Zi-Qi; Xu, Tao; Qi, Feng-Hua; Xue, Yu-Shan
2016-02-01
We study the nonlinear localized waves on constant backgrounds of the Hirota-Maxwell-Bloch (HMB) system arising from the erbium doped fibers. We derive the asymmetric breather, rogue wave (RW) and semirational solutions of the HMB system. We show that the breather and RW solutions can be converted into various soliton solutions. Under different conditions of parameters, we calculate the locus of the eigenvalues on the complex plane which converts the breathers or RWs into solitons. Based on the second-order solutions, we investigate the interactions among different types of nonlinear waves including the breathers, RWs and solitons.
Cioslowski, Jerzy
2018-04-01
The dependence of the natural amplitudes of the harmonium atom in its ground state on the confinement strength ω is thoroughly investigated. A combination of rigorous analysis and extensive, highly accurate numerical calculations reveals the presence of only one positive-valued natural amplitude ("the normal sign pattern") for all ω ≥1/2 . More importantly, it is shown that unusual, weakly occupied natural orbitals (NOs) corresponding to additional positive-valued natural amplitudes emerge upon sufficient weakening of the confinement. These solitonic NOs, whose shapes remain almost invariant as their radial positions drift toward infinity upon the critical values of ω being approached from below, exhibit strong radial localization. Their asymptotic properties are extracted from the numerical data and their relevance to calculations on fully Coulombic systems is discussed.
Gemini surfactant for fluorescent and stable quantum dots in aqueous solution
Energy Technology Data Exchange (ETDEWEB)
Li Haibing [Key Laboratory of Pesticide and Chemical Biology (CCNU), Ministry of Education, College of Chemistry, Central China Normal University, Wuhan 430079 (China); Wang Xiaoqiong [Key Laboratory of Pesticide and Chemical Biology (CCNU), Ministry of Education, College of Chemistry, Central China Normal University, Wuhan 430079 (China); Gao Zhinong [Department of Chemistry, Wuhan University, Wuhan 430072 (China); He Zhike [Department of Chemistry, Wuhan University, Wuhan 430072 (China)
2007-05-23
Highly fluorescent and stable CdSe/ZnS core/shell quantum dots (QDs) coated with gemini surfactant are successfully synthesized in aqueous media. Analyses of luminescence spectrometry, ultraviolet-visible (UV-vis) spectrophotometry, and transmission electron micrographs (TEMs) indicate that the water-soluble QDs are monodisperse and have a luminescence enhancement compared with the original hydrophobic QDs. The water-soluble QDs coated with gemini surfactant are shown to be biocompatible, photostable, and have been proven to be suitable for live cell imaging.
Gemini surfactant for fluorescent and stable quantum dots in aqueous solution
International Nuclear Information System (INIS)
Li Haibing; Wang Xiaoqiong; Gao Zhinong; He Zhike
2007-01-01
Highly fluorescent and stable CdSe/ZnS core/shell quantum dots (QDs) coated with gemini surfactant are successfully synthesized in aqueous media. Analyses of luminescence spectrometry, ultraviolet-visible (UV-vis) spectrophotometry, and transmission electron micrographs (TEMs) indicate that the water-soluble QDs are monodisperse and have a luminescence enhancement compared with the original hydrophobic QDs. The water-soluble QDs coated with gemini surfactant are shown to be biocompatible, photostable, and have been proven to be suitable for live cell imaging
All-solution processed polymer light-emitting diodes with air stable metal-oxide electrodes
Bruyn, P. de; Moet, D.J.D.; Blom, P.W.M.
2012-01-01
We present an all-solution processed polymer light-emitting diode (PLED) using spincoated zinc oxide (ZnO) and vanadium pentoxide (V2O5) as electron and hole injecting contact, respectively. We compare the performance of these devices to the standard PLED design using PEDOT:PSS as anode and Ba/Al as
Stable Isotope Analyses of water and Aqueous Solutions by Conventional Dual-inlet Mass Spectrometry
Energy Technology Data Exchange (ETDEWEB)
Horita, Juske [ORNL; Kendall, C. [U.S. Geological Survey, Menlo Park, CA
2004-01-01
The foundation of various analytical methods for the stable isotope composition of water and other aqueous samples (natural abundance, {sup 1}H : {sup 2}H (D) = 99.985 : 0.015 atom%, and {sup 16}O : {sup 17}O : {sup 18}O = 99.762 : 0.038 : 0.200 atom%) was established during the Manhatten Project in the U.S.A., when large amounts of heavy water were produced for nuclear reactors (see Kirshenbaum, 1951, for a detailed account). From early on, there was great interest in the oxygen and hydrogen isotopic compositions of water, because they are the ideal tracers of water sources and reactions. The increased analytical precisions made possible by the subsequent development of modern gas-source isotope-ratio mass spectrometers with dual-inlets and multi-collectors, have caused the proliferation of new analytical methods and applications for the oxygen and hydrogen isotopic compositions of water. These stable isotopes have found wide applications in basic as well as applied sciences (chemistry, geology, hydrology, biology, medical sciences, and food sciences). This is because water is ubiquitous, is an essential and predominant ingredient of living organisms, and is perhaps the most reactive compound in the Earth.
Mismatch management for optical and matter-wave quadratic solitons
International Nuclear Information System (INIS)
Driben, R.; Oz, Y.; Malomed, B. A.; Gubeskys, A.; Yurovsky, V. A.
2007-01-01
We propose a way to control solitons in χ (2) (quadratically nonlinear) systems by means of periodic modulation imposed on the phase-mismatch parameter ('mismatch management', MM). It may be realized in the cotransmission of fundamental-frequency (FF) and second-harmonic (SH) waves in a planar optical waveguide via a long-period modulation of the usual quasi-phase-matching pattern of ferroelectric domains. In an altogether different physical setting, the MM may also be implemented by dint of the Feshbach resonance in a harmonically modulated magnetic field in a hybrid atomic-molecular Bose-Einstein condensate (BEC), with the atomic and molecular mean fields (MFs) playing the roles of the FF and SH, respectively. Accordingly, the problem is analyzed in two different ways. First, in the optical model, we identify stability regions for spatial solitons in the MM system, in terms of the MM amplitude and period, using the MF equations for spatially inhomogeneous configurations. In particular, an instability enclave is found inside the stability area. The robustness of the solitons is also tested against variation of the shape of the input pulse, and a threshold for the formation of stable solitons is found in terms of the power. Interactions between stable solitons are virtually unaffected by the MM. The second method (parametric approximation), going beyond the MF description, is developed for spatially homogeneous states in the BEC model. It demonstrates that the MF description is valid for large modulation periods, while, at smaller periods, non-MF components acquire gain, which implies destruction of the MF under the action of the high-frequency MM
Quantization in presence of external soliton fields
International Nuclear Information System (INIS)
Grosse, H.; Karner, G.
1986-01-01
Quantization of a fermi field interacting with an external soliton protential is considered. Classes of interactions leading to unitarily equivalent representations of the canonical anticommutation relations are determined. Soliton-like potentials compared to trivial ones yield inequivalent representations. (Author)
Noise-induced perturbations of dispersion-managed solitons
International Nuclear Information System (INIS)
Li, Jinglai; Spiller, Elaine; Biondini, Gino
2007-01-01
We study noise-induced perturbations of dispersion-managed solitons. We do so by first developing soliton perturbation theory for the dispersion-managed nonlinear Schroedinger (DMNLS) equation, which governs the long-term behavior of optical fiber transmission systems and certain kinds of femtosecond lasers. We show that the eigenmodes and generalized eigenmodes of the linearized DMNLS equation around traveling-wave solutions can be generated from the invariances of the DMNLS equations, we quantify the perturbation-induced parameter changes of the solution in terms of the eigenmodes and the adjoint eigenmodes, and we obtain evolution equations for the solution parameters. We then apply these results to guide importance-sampled Monte Carlo (MC) simulations and reconstruct the probability density functions of the solution parameters under the effect of noise, and we compare with standard MC simulations of the unaveraged system. The comparison further validates the use of the DMNLS equation as a model for dispersion-managed systems
Grytskyy, Dmytro; Diesmann, Markus; Helias, Moritz
2016-06-01
Self-organized structures in networks with spike-timing dependent synaptic plasticity (STDP) are likely to play a central role for information processing in the brain. In the present study we derive a reaction-diffusion-like formalism for plastic feed-forward networks of nonlinear rate-based model neurons with a correlation sensitive learning rule inspired by and being qualitatively similar to STDP. After obtaining equations that describe the change of the spatial shape of the signal from layer to layer, we derive a criterion for the nonlinearity necessary to obtain stable dynamics for arbitrary input. We classify the possible scenarios of signal evolution and find that close to the transition to the unstable regime metastable solutions appear. The form of these dissipative solitons is determined analytically and the evolution and interaction of several such coexistent objects is investigated.
Experiment on dust acoustic solitons in strongly coupled dusty plasma
International Nuclear Information System (INIS)
Boruah, Abhijit; Sharma, Sumita Kumari; Bailung, Heremba
2015-01-01
Dusty plasma, which contains nanometer to micrometer sized dust particles along with electrons and ions, supports a low frequency wave called Dust Acoustic wave, analogous to ion acoustic wave in normal plasma. Due to high charge and low temperature of the dust particles, dusty plasma can easily transform into a strongly coupled state when the Coulomb interaction potential energy exceeds the dust kinetic energy. Dust acoustic perturbations are excited in such strongly coupled dusty plasma by applying a short negative pulse (100 ms) of amplitude 5 - 20 V to an exciter. The perturbation steepens due to nonlinear effect and forms a solitary structure by balancing dispersion present in the medium. For specific discharge conditions, excitation amplitude above a critical value, the perturbation is found to evolve into a number of solitons. The experimental results on the excitation of multiple dust acoustic solitons in the strongly coupled regime are presented in this work. The experiment is carried out in radio frequency discharged plasma produced in a glass chamber at a pressure 0.01 - 0.1 mbar. Few layers of dust particles (∼ 5 μm in diameter) are levitated above a grounded electrode inside the chamber. Wave evolution is observed with the help of green laser sheet and recorded in a high resolution camera at high frame rate. The high amplitude soliton propagates ahead followed by smaller amplitude solitons with lower velocity. The separation between the solitons increases as time passes by. The characteristics of the observed dust acoustic solitons such as amplitude-velocity and amplitude- Mach number relationship are compared with the solutions of Korteweg-de Vries (KdV) equation. (author)
Energy-exchange collisions of dark-bright-bright vector solitons.
Radhakrishnan, R; Manikandan, N; Aravinthan, K
2015-12-01
We find a dark component guiding the practically interesting bright-bright vector one-soliton to two different parametric domains giving rise to different physical situations by constructing a more general form of three-component dark-bright-bright mixed vector one-soliton solution of the generalized Manakov model with nine free real parameters. Moreover our main investigation of the collision dynamics of such mixed vector solitons by constructing the multisoliton solution of the generalized Manakov model with the help of Hirota technique reveals that the dark-bright-bright vector two-soliton supports energy-exchange collision dynamics. In particular the dark component preserves its initial form and the energy-exchange collision property of the bright-bright vector two-soliton solution of the Manakov model during collision. In addition the interactions between bound state dark-bright-bright vector solitons reveal oscillations in their amplitudes. A similar kind of breathing effect was also experimentally observed in the Bose-Einstein condensates. Some possible ways are theoretically suggested not only to control this breathing effect but also to manage the beating, bouncing, jumping, and attraction effects in the collision dynamics of dark-bright-bright vector solitons. The role of multiple free parameters in our solution is examined to define polarization vector, envelope speed, envelope width, envelope amplitude, grayness, and complex modulation of our solution. It is interesting to note that the polarization vector of our mixed vector one-soliton evolves in sphere or hyperboloid depending upon the initial parametric choices.
Solitons of an envelope in an inhomogeneous medium
International Nuclear Information System (INIS)
Churilov, S.M.
1982-01-01
Solutions of the Schroedinger nonlinear equation (SNE) used for the description of evolution of a wave packet envelope has been investigated in inhomogeneous and nonstationary media. It is shown that the SNE solution possessing two important properties exists. Firstly, the wave packet remains localized when propagating in an inhomogeneous medium. Secondly, the soliton width and amplitude are determined only with local characteristics of medium and don't depend on the prehistory. Problem of limits of obtained result applicability has been considered
Solitons and the energy-momentum tensor for affine Toda theory
Olive, D. I.; Turok, N.; Underwood, J. W. R.
1993-07-01
Following Leznov and Saveliev, we present the general solution to Toda field theories of conformal, affine or conformal affine type, associated with a simple Lie algebra g. These depend on a free massless field and on a group element. By putting the former to zero, soliton solutions to the affine Toda theories with imaginary coupling constant result with the soliton data encoded in the group element. As this requires a reformulation of the affine Kac-Moody algebra closely related to that already used to formulate the physical properties of the particle excitations, including their scattering matrices, a unified treatment of particles and solitons emerges. The physical energy—momentum tensor for a general solution is broken into a total derivative plus a part dependent only on the derivatives of the free field. Despite the non-linearity of the field equations and their complex nature the energy and momentum of the N-soliton solution is shown to be real, equalling the sum of contributions from the individual solitons. There are rank-g species of soliton, with masses given by a generalisation of a formula due to Hollowood, being proportional to the components of the left Perron-Frobenius eigenvector of the Cartan matrix of g.
Solitons and the energy-momentum tensor for affine Toda theory
International Nuclear Information System (INIS)
Olive, D.I.; Turok, N.; Underwood, J.W.R.
1993-01-01
Following Leznov and Saveliev, we present the general solution to Toda field theories of conformal, affine or conformal affine type, associated with a simple Lie algebra g. These depend on a free massless field and on a group element. By putting the former to zero, soliton solutions to the affine Toda theories with imaginary coupling constant result with the soliton data encoded in the group element. As this requires a reformulation of the affine Kac-Moodyy algebra closely related to that already used to formulate the physical properties of the particle excitations, including their scattering matrices, a unified treatment of particles and solitons emerges. The physical energy-momentum tensor for a general solution is broken into a total derivative plus a part dependent only on the derivatives of the free field. Despite the non-linearity of the field equations and their complex nature the energy and momentum of the N-soliton solution is shown to be real, equalling the sum of contributions from the individual solitons. There are rank-g species of soliton, with masses given by a generalisation of a formula due to Hollowood, being proportional to the components of the left Perron-Frobenius eigenvector of the Cartan matrix of g. (orig.)
Glimpses of soliton theory the algebra and geometry of nonlinear PDEs
Kasman, Alex
2010-01-01
Solitons are explicit solutions to nonlinear partial differential equations exhibiting particle-like behavior. This is quite surprising, both mathematically and physically. Waves with these properties were once believed to be impossible by leading mathematical physicists, yet they are now not only accepted as a theoretical possibility but are regularly observed in nature and form the basis of modern fiber-optic communication networks. Glimpses of Soliton Theory addresses some of the hidden mathematical connections in soliton theory which have been revealed over the last half-century. It aims to convince the reader that, like the mirrors and hidden pockets used by magicians, the underlying algebro-geometric structure of soliton equations provides an elegant and surprisingly simple explanation of something seemingly miraculous. Assuming only multivariable calculus and linear algebra as prerequisites, this book introduces the reader to the KdV Equation and its multisoliton solutions, elliptic curves and Weierstr...
On the supersymmetric solitons and monopoles
International Nuclear Information System (INIS)
Hruby, J.
1978-01-01
The basic results in a new trend in supersymmetry and soliton theory are presented. It is shown that the soliton expectation value of the energy operator is mass of the soliton without the quantum corrections. A new supersymmetric monopole model in three dimensions is constructed by generalization of the supersymmetric sine-Gordon model in one space dimension
Soliton resonance in bose-einstein condensate
Zak, Michail; Kulikov, I.
2002-01-01
A new phenomenon in nonlinear dispersive systems, including a Bose-Einstein Condensate (BEC), has been described. It is based upon a resonance between an externally induced soliton and 'eigen-solitons' of the homogeneous cubic Schrodinger equation. There have been shown that a moving source of positive /negative potential induces bright /dark solitons in an attractive / repulsive Bose condensate.
Zhao, Xue-Hui; Tian, Bo; Xie, Xi-Yang; Wu, Xiao-Yu; Sun, Yan; Guo, Yong-Jiang
2018-04-01
Under investigation in this paper is a (2+1)-dimensional Davey-Stewartson system, which describes the transformation of a wave-packet on water of finite depth. By virtue of the bell polynomials, bilinear form, Bäcklund transformation and Lax pair are got. One- and two-soliton solutions are obtained via the symbolic computation and Hirota method. Velocity and amplitude of the one-soliton solutions are relevant with the wave number. Graphical analysis indicates that soliton shapes keep unchanged and maintain their original directions and amplitudes during the propagation. Elastic overtaking and head-on interactions between the two solitons are described.
Coupling between magnetic and optical properties of stable Au-Fe solid solution nanoparticles
Energy Technology Data Exchange (ETDEWEB)
De Julian Fernandez, C; Novak, R L; Bogani, L; Caneschi, A [INSTM RU at the Department of Chemistry of the University of Firenze, via della Lastruccia 3, 50019 Sesto Fiorentino (Italy); Mattei, G; Mazzoldi, P [Department of Physics, CNISM and University of Padova, via Marzolo 8, 35131 Padova (Italy); Paz, E; Palomares, F J [Instituto de Ciencia de Materiales de Madrid (CSIC), Cantoblanco, 28049 Madrid (Spain); Cavigli, L, E-mail: cesar.dejulian@unifi.it [Department of Physics-LENS, University of Florence, via Sansone 1, 50019 Sesto Fiorentino (Italy)
2010-04-23
Au-Fe nanoparticles constitute one of the simplest prototypes of a multifunctional nanomaterial that can exhibit both magnetic and optical (plasmonic) properties. This solid solution, not feasible in the bulk phase diagram in thermal equilibrium, can be formed as a nanostructure by out-of-equilibrium processes. Here, the novel magnetic, optical and magneto-optical properties of ion-implanted Au-Fe solid solution nanoparticles dispersed in a SiO{sub 2} matrix are investigated and correlated. The surface plasmon resonance of the Au-Fe nanoparticles with almost equicomposition is strongly damped when compared to pure Au and to Au-rich Au-Fe nanoparticles. In all cases, the Au atoms are magnetically polarized, as measured by x-ray magnetic circular dichroism, and ferromagnetically coupled with Fe atoms. Although the chemical stability of Au-Fe nanoparticles is larger than that of Fe nanoparticles, both the magnetic moment per Fe atom and the order temperature are smaller. These results suggest that electronic and magnetic properties are more influenced by the hybridization of the electronic bands in the Au-Fe solid solution than by size effects. On the other hand, the magneto-optical transitions allowed in the vis-nIR spectral regions are very similar. In addition, we also observe, after studying the properties of thermally treated samples, that the Au-Fe alloy is stabilized, not by surface effects, but by the combination of the out-of-equilibrium nature of the ion implantation technique and by changes in the properties due to size effects.
Coupling between magnetic and optical properties of stable Au-Fe solid solution nanoparticles
International Nuclear Information System (INIS)
De Julian Fernandez, C; Novak, R L; Bogani, L; Caneschi, A; Mattei, G; Mazzoldi, P; Paz, E; Palomares, F J; Cavigli, L
2010-01-01
Au-Fe nanoparticles constitute one of the simplest prototypes of a multifunctional nanomaterial that can exhibit both magnetic and optical (plasmonic) properties. This solid solution, not feasible in the bulk phase diagram in thermal equilibrium, can be formed as a nanostructure by out-of-equilibrium processes. Here, the novel magnetic, optical and magneto-optical properties of ion-implanted Au-Fe solid solution nanoparticles dispersed in a SiO 2 matrix are investigated and correlated. The surface plasmon resonance of the Au-Fe nanoparticles with almost equicomposition is strongly damped when compared to pure Au and to Au-rich Au-Fe nanoparticles. In all cases, the Au atoms are magnetically polarized, as measured by x-ray magnetic circular dichroism, and ferromagnetically coupled with Fe atoms. Although the chemical stability of Au-Fe nanoparticles is larger than that of Fe nanoparticles, both the magnetic moment per Fe atom and the order temperature are smaller. These results suggest that electronic and magnetic properties are more influenced by the hybridization of the electronic bands in the Au-Fe solid solution than by size effects. On the other hand, the magneto-optical transitions allowed in the vis-nIR spectral regions are very similar. In addition, we also observe, after studying the properties of thermally treated samples, that the Au-Fe alloy is stabilized, not by surface effects, but by the combination of the out-of-equilibrium nature of the ion implantation technique and by changes in the properties due to size effects.
Coupling between magnetic and optical properties of stable Au-Fe solid solution nanoparticles
de Julián Fernández, C.; Mattei, G.; Paz, E.; Novak, R. L.; Cavigli, L.; Bogani, L.; Palomares, F. J.; Mazzoldi, P.; Caneschi, A.
2010-04-01
Au-Fe nanoparticles constitute one of the simplest prototypes of a multifunctional nanomaterial that can exhibit both magnetic and optical (plasmonic) properties. This solid solution, not feasible in the bulk phase diagram in thermal equilibrium, can be formed as a nanostructure by out-of-equilibrium processes. Here, the novel magnetic, optical and magneto-optical properties of ion-implanted Au-Fe solid solution nanoparticles dispersed in a SiO2 matrix are investigated and correlated. The surface plasmon resonance of the Au-Fe nanoparticles with almost equicomposition is strongly damped when compared to pure Au and to Au-rich Au-Fe nanoparticles. In all cases, the Au atoms are magnetically polarized, as measured by x-ray magnetic circular dichroism, and ferromagnetically coupled with Fe atoms. Although the chemical stability of Au-Fe nanoparticles is larger than that of Fe nanoparticles, both the magnetic moment per Fe atom and the order temperature are smaller. These results suggest that electronic and magnetic properties are more influenced by the hybridization of the electronic bands in the Au-Fe solid solution than by size effects. On the other hand, the magneto-optical transitions allowed in the vis-nIR spectral regions are very similar. In addition, we also observe, after studying the properties of thermally treated samples, that the Au-Fe alloy is stabilized, not by surface effects, but by the combination of the out-of-equilibrium nature of the ion implantation technique and by changes in the properties due to size effects.
Efficient and stable solution-processed planar perovskite solar cells via contact passivation
Tan, Hairen; Jain, Ankit; Voznyy, Oleksandr; Lan, Xinzheng; Garcí a de Arquer, F. Pelayo; Fan, James Z.; Quintero-Bermudez, Rafael; Yuan, Mingjian; Zhang, Bo; Zhao, Yicheng; Fan, Fengjia; Li, Peicheng; Quan, Li Na; Zhao, Yongbiao; Lu, Zheng-Hong; Yang, Zhenyu; Hoogland, Sjoerd; Sargent, Edward H.
2017-01-01
Planar perovskite solar cells (PSCs) made entirely via solution processing at low temperatures (<150°C) offer promise for simple manufacturing, compatibility with flexible substrates, and perovskite-based tandem devices. However, these PSCs require an electron-selective layer that performs well with similar processing. We report a contact-passivation strategy using chlorine-capped TiO2 colloidal nanocrystal film that mitigates interfacial recombination and improves interface binding in low-temperature planar solar cells. We fabricated solar cells with certified efficiencies of 20.1 and 19.5% for active areas of 0.049 and 1.1 square centimeters, respectively, achieved via low-temperature solution processing. Solar cells with efficiency greater than 20% retained 90% (97% after dark recovery) of their initial performance after 500 hours of continuous room-temperature operation at their maximum power point under 1-sun illumination (where 1 sun is defined as the standard illumination at AM1.5, or 1 kilowatt/square meter).
Efficient and stable solution-processed planar perovskite solar cells via contact passivation
Tan, Hairen
2017-02-03
Planar perovskite solar cells (PSCs) made entirely via solution processing at low temperatures (<150°C) offer promise for simple manufacturing, compatibility with flexible substrates, and perovskite-based tandem devices. However, these PSCs require an electron-selective layer that performs well with similar processing. We report a contact-passivation strategy using chlorine-capped TiO2 colloidal nanocrystal film that mitigates interfacial recombination and improves interface binding in low-temperature planar solar cells. We fabricated solar cells with certified efficiencies of 20.1 and 19.5% for active areas of 0.049 and 1.1 square centimeters, respectively, achieved via low-temperature solution processing. Solar cells with efficiency greater than 20% retained 90% (97% after dark recovery) of their initial performance after 500 hours of continuous room-temperature operation at their maximum power point under 1-sun illumination (where 1 sun is defined as the standard illumination at AM1.5, or 1 kilowatt/square meter).
Sun, Yan; Tian, Bo; Wu, Xiao-Yu; Liu, Lei; Yuan, Yu-Qiang
2017-04-01
Under investigation in this paper is a variable-coefficient higher-order nonlinear Schrödinger equation, which has certain applications in the inhomogeneous optical fiber communication. Through the Hirota method, bilinear forms, dark one- and two-soliton solutions for such an equation are obtained. We graphically study the solitons with d1(z), d2(z) and d3(z), which represent the variable coefficients of the group-velocity dispersion, third-order dispersion and fourth-order dispersion, respectively. With the different choices of the variable coefficients, we obtain the parabolic, periodic and V-shaped dark solitons. Head-on and overtaking collisions are depicted via the dark two soliton solutions. Velocities of the dark solitons are linearly related to d1(z), d2(z) and d3(z), respectively, while the amplitudes of the dark solitons are not related to such variable coefficients.
KP solitons and the Grassmannians combinatorics and geometry of two-dimensional wave patterns
Kodama, Yuji
2017-01-01
This is the first book to treat combinatorial and geometric aspects of two-dimensional solitons. Based on recent research by the author and his collaborators, the book presents new developments focused on an interplay between the theory of solitons and the combinatorics of finite-dimensional Grassmannians, in particular, the totally nonnegative (TNN) parts of the Grassmannians. The book begins with a brief introduction to the theory of the Kadomtsev–Petviashvili (KP) equation and its soliton solutions, called the KP solitons. Owing to the nonlinearity in the KP equation, the KP solitons form very complex but interesting web-like patterns in two dimensions. These patterns are referred to as soliton graphs. The main aim of the book is to investigate the detailed structure of the soliton graphs and to classify these graphs. It turns out that the problem has an intimate connection with the study of the TNN part of the Grassmannians. The book also provides an elementary introduction to the recent development of ...
Lyapunov Functions and Solutions of the Lyapunov Matrix Equation for Marginally Stable Systems
DEFF Research Database (Denmark)
Kliem, Wolfhard; Pommer, Christian
2000-01-01
We consider linear systems of differential equations $I \\ddot{x}+B \\dot{x}+C{x}={0}$ where $I$ is the identity matrix and $B$ and $C$ are general complex $n$ x $n$ matrices. Our main interest is to determine conditions for complete marginalstability of these systems. To this end we find solutions...... of the Lyapunov matrix equation and characterize the set of matrices $(B, C)$ which guarantees marginal stability. The theory is applied to gyroscopic systems, to indefinite damped systems, and to circulatory systems, showing how to choose certain parameter matrices to get sufficient conditions for marginal...... stability.Comparison is made with some known results for equations with real system matrices.Moreover more general cases are investigated and several examples are given....
Fermion: field nontopological solitons. II. Models for hadrons
International Nuclear Information System (INIS)
Friedberg, R.; Lee, T.D.
1977-01-01
The possibility, and its consequences, are examined that in a relativistic local field theory, consisting of color quarks q, scalar gluon sigma, color gauge field V/sub mu/ and color Higgs field phi, the mass of the soliton solution may be much lower than any mass of the plane wave solutions; i.e., m/sub q/ the quark mass, m/sub sigma/ the gluon mass, etc. There appears a rather clean separation between the physics of these low mass solitons and that of the high energy excitations, in the range of m/sub q/ and m/sub sigma/, provided that the parameters xi identical with (μ/m/sub q/) 2 and eta identical with μ/m/sub sigma/ are both much less than 1, where μ is an overall low energy scale appropriate for the solitons (but the ratio eta/xi is assumed to be O(1), though otherwise arbitrary). Under very general assumptions, it is shown that independently of the number of parameters in the original Lagrangian, the mathematical problem of finding the quasiclassical soliton solutions reduces, through scaling, to that of a simple set of two coupled first-order differential equations, neither of which contains any explicit free parameters. The general properties and the numerical solutions of this reduced set of differential equations are given. The resulting solitons exhibit physical characteristics very similar to those of a ''gas bubble'' immersed in a ''medium'': there is a constant surface tension and a constant pressure exerted by the medium on the gas; in addition, there are the ''thermodynamical'' energy of the gas and the related gas pressure, which are determined by the solutions of the reduced equations. Both a SLAC-like bag and the Creutz-Soh version of the MIT bag may appear, but only as special limiting cases. These soliton solutions are applied to the physical hadrons; their static properties are calculated and, within a 10 to 15 percent accuracy, agree with observations
Interaction of Langmuir solitons with sound
International Nuclear Information System (INIS)
Kurin, V.V.; Fraiman, G.M.
1981-01-01
The adiabatic approximation is used to study the interaction of Langmuir solitons with long ion-acoustic waves. The finite acoustic velocity gives rise to an effective mass for the soliton which is quite different from that in the approximation of a local nonlinearity. The force acting on a soliton, averaged over the period of the acoustic wave, is derived. The system of kinetic equations is analyzed in the approximation of random phases of the acoustic waves. The interaction of acoustic waves with solitons causes the acoustic spectrum to become more nearly isotropic, and the solitons are effectively damped
Gap states of charged soliton in polyacetylene
International Nuclear Information System (INIS)
Lu Dingwei; Liu Jie; Fu Rouli
1988-10-01
By considering the electron interaction in polyacetylene, it is found that two gap states in charged solitons of trans-polyacetylene exist: one is deep level, another is shallow level. The deep one shifts 0.23 ev down (for positive soliton) or up (for negative soliton) from the center of the gap; while the shallow one is 0.06 ev under the bottom of conduction band (positive soliton) or above the top of valence band (negative soliton). These results agree with the absorption spectra of trans-polyacetylene. (author). 5 refs, 4 figs
Solitons in the Peierls condensate
International Nuclear Information System (INIS)
Horowitz, B.; Krumhansl, J.A.
1983-05-01
The electron-phonon system in one dimension is studied within the adiabatic (Hartree) and Hartree-Fock approximations. The equations of motion for the Peierls order parameter at zero temperature are derived from a microscopic Hamiltonian and an effective Lagrangian is constructed. Charged phase solitons describe systems whose electron density is at or near M fold commensurability with M >= 3. For M = 2 the order parameter is real in the adiabatic approximation, but becomes complex when both acoustic and optical phonons are coupled, or for a non-adiabatic theory. The latter is studied with Coulomb exchange force and phase solitons are derived. The soliton charge is 2/M for all M > = 2. When M = 4 the pinning potential can be anomalously low, in agreement with data on TaS 3 and similar compounds. (author)
Solitons, envelope solitons in collisonless plasmas
International Nuclear Information System (INIS)
Ichikawa, Y.H.; Watanabe, S.
1977-08-01
A review is given to extensive development of theoretical, computational and experimental studies of nonlinear wave propagation in collisionless plasmas. Firstly, the historical experiment of Ikezi et al. is discussed in comparison with theoretical analysis based on the Korteweg-de Vries equation. Systematic discrepancy between the observation and the theoretical prediction suggests that it is necessary to examine such as higher order mode coupling effect and contribution of trapped particles. Secondly, effects of the nonlinear Landau damping on the envelope solution of ion plasma wave is discussed on the basis of theoretical study of Ichikawa-Taniuti, experimental observation of Watanabe and numerical analysis of Yajima et al. Finally, a new type of evolution equation derived for the Alfven wave is examined in some detail. The rigorous solution obtained for this mode represents a new kind of envelope solution, in which both of its phase and amplitude are subject to modulation of comparable spatial extension. In conclusion, the emphasis will be placed on the fact that much more intensive experimental researches are expected to be done, since the powerful methods to disentangle various nonlinear evolution equations are now available for theoretical approach. (auth.)
Deceleration of solitons in molecular chains
International Nuclear Information System (INIS)
Davydov, A.S.; Eremko, A.A.
1980-01-01
Effects of external actions on solitons arising under local excitations in molecular quasi-one-dimensional chains are investigated. The main formulas describing free solitons are presented. The motion of solitons in the presence of the force of friction proportional to their velocity is studied. It is shown that in this case the soliton velocity decreases with time in an exponential manner. It is shown that if the forces of friction are proportional to the square of velocity, the velocity decreases with time according to a linear law. The motion of solitons is investigated an the presence of small local non-uniformities or external fields. It is shown that an this case the soliton centre moves according to the Newton law in which however the force is determined by the integral expression. The conclusion is made that it is impossible to describe correctly the dynamic properties of solitons without taking into account physical factors causing the nonlinearity
Solitonic Dispersive Hydrodynamics: Theory and Observation
Maiden, Michelle D.; Anderson, Dalton V.; Franco, Nevil A.; El, Gennady A.; Hoefer, Mark A.
2018-04-01
Ubiquitous nonlinear waves in dispersive media include localized solitons and extended hydrodynamic states such as dispersive shock waves. Despite their physical prominence and the development of thorough theoretical and experimental investigations of each separately, experiments and a unified theory of solitons and dispersive hydrodynamics are lacking. Here, a general soliton-mean field theory is introduced and used to describe the propagation of solitons in macroscopic hydrodynamic flows. Two universal adiabatic invariants of motion are identified that predict trapping or transmission of solitons by hydrodynamic states. The result of solitons incident upon smooth expansion waves or compressive, rapidly oscillating dispersive shock waves is the same, an effect termed hydrodynamic reciprocity. Experiments on viscous fluid conduits quantitatively confirm the soliton-mean field theory with broader implications for nonlinear optics, superfluids, geophysical fluids, and other dispersive hydrodynamic media.
Soliton robustness in optical fibers
International Nuclear Information System (INIS)
Menyuk, C.R.
1993-01-01
Simulations and experiments indicate that solitons in optical fibers are robust in the presence of Hamiltonian deformations such as higher-order dispersion and birefringence but are destroyed in the presence of non-Hamiltonian deformations such as attenuation and the Raman effect. Two hypotheses are introduced that generalize these observations and give a recipe for when deformations will be Hamiltonian. Concepts from nonlinear dynamics are used to make these two hypotheses plausible. Soliton stabilization with frequency filtering is also briefly discussed from this point of view
Multiphase averaging of periodic soliton equations
International Nuclear Information System (INIS)
Forest, M.G.
1979-01-01
The multiphase averaging of periodic soliton equations is considered. Particular attention is given to the periodic sine-Gordon and Korteweg-deVries (KdV) equations. The periodic sine-Gordon equation and its associated inverse spectral theory are analyzed, including a discussion of the spectral representations of exact, N-phase sine-Gordon solutions. The emphasis is on physical characteristics of the periodic waves, with a motivation from the well-known whole-line solitons. A canonical Hamiltonian approach for the modulational theory of N-phase waves is prescribed. A concrete illustration of this averaging method is provided with the periodic sine-Gordon equation; explicit averaging results are given only for the N = 1 case, laying a foundation for a more thorough treatment of the general N-phase problem. For the KdV equation, very general results are given for multiphase averaging of the N-phase waves. The single-phase results of Whitham are extended to general N phases, and more importantly, an invariant representation in terms of Abelian differentials on a Riemann surface is provided. Several consequences of this invariant representation are deduced, including strong evidence for the Hamiltonian structure of N-phase modulational equations
Exact periodic and solitonic states of the spinor condensates in a uniform external potential
Energy Technology Data Exchange (ETDEWEB)
Zhang, Zhi-Hai [School of Physics and Electronics, Yancheng Teachers University, Yancheng 224051 (China); Yang, Shi-Jie, E-mail: yangshijie@tsinghua.org.cn [Department of Physics, Beijing Normal University, Beijing 100875 (China)
2016-08-15
We propose a method to analytically solve the one-dimensional coupled nonlinear Gross–Pitaevskii equations which govern the motion of the spinor Bose–Einstein condensates. In a uniform external potential, several classes of exact periodic and solitonic solutions, either in real or in complex forms, are obtained for both the F=1 and F=2 condensates for the Hamiltonian comprising the kinetic energy, the linear and the quadratic Zeeman energies. Real solutions take the form of composite soliton trains. Complex solutions correspond to the mass counter-flows as well as spin currents. These solutions are general that contains neither approximations nor constraints on the system parameters.
Soliton generation from a multi-frequency optical signal
International Nuclear Information System (INIS)
Panoiu, N-C; Mel'nikov, I V; Mihalache, D; Etrich, C; Lederer, F
2002-01-01
We present a comprehensive analysis of the generation of optical solitons in a monomode optical fibre from a superposition of soliton-like optical pulses at different frequencies. It is demonstrated that the structure of the emerging optical field is highly dependent on the number of input channels, the inter-channel frequency separation, the time shift between the pulses belonging to adjacent channels, and the polarization of the pulses. Also, it is found that there exists a critical frequency separation above which wavelength-division multiplexing with solitons is feasible and that this critical frequency increases with the number of transmission channels. Moreover, for the case in which only two channels are considered, we analyse the propagation of the emerging two-soliton solutions in the presence of several perturbations important for optical networks: bandwidth-limited amplification, nonlinear amplification, and amplitude and phase modulation. Finally, the influence of the birefringence of the fibre on the structure of the emerging optical field is discussed. (review article)
Interaction of charged 3D soliton with Coulomb center
International Nuclear Information System (INIS)
Rybakov, Yu.P.
1996-03-01
The Einstein - de Broglie particle-soliton concept is applied to simulate stationary states of an electron in a hydrogen atom. According to this concept, the electron is described by the localized regular solutions to some nonlinear equations. In the framework of Synge model for interacting scalar and electromagnetic fields a system of integral equations has been obtained, which describes the interaction between charged 3D soliton and Coulomb center. The asymptotic expressions for physical fields, describing soliton moving around the fixed Coulomb center, have been obtained with the help of integral equations. It is shown that the electron-soliton center travels along some stationary orbit around the Coulomb center. The electromagnetic radiation is absent as the Poynting vector has non-wave asymptote O(r -3 ) after averaging over angles, i.e. the existence of spherical surface corresponding to null Poynting vector stream, has been proved. Vector lines for Poynting vector are constructed in asymptotical area. (author). 22 refs, 2 figs
Motion of a magnetic soliton about a lattice soliton in a Heisenberg chain
International Nuclear Information System (INIS)
Nayyar, A.H.; Murtaza, G.
1981-08-01
As an example of interaction between two solitons belonging to different species, a semiclassical study of the nonlinear dynamics of a coupled magnon-phonon system in a one-dimensional Heisenberg ferromagnet is made, where both the lattice and the spin systems are taken with their respective nonlinear interactions. The lattice soliton is shown to introduce spatial inhomogeneities into the propagation of the magnetic soliton resulting in (a) the trapping of the magnetic soliton in the harmonic field of the lattice soliton and (b) the amplitude and the width of the magnetic soliton becoming time-dependent. (author)
Xiao, Zi-Jian; Tian, Bo; Sun, Yan
2018-01-01
In this paper, we investigate a (2+1)-dimensional variable-coefficient modified Kadomtsev-Petviashvili (mKP) equation in fluid dynamics. With the binary Bell-polynomial and an auxiliary function, bilinear forms for the equation are constructed. Based on the bilinear forms, multi-soliton solutions and Bell-polynomial-type Bäcklund transformation for such an equation are obtained through the symbolic computation. Soliton interactions are presented. Based on the graphic analysis, Parametric conditions for the existence of the shock waves, elevation solitons and depression solitons are given, and it is shown that under the condition of keeping the wave vectors invariable, the change of α(t) and β(t) can lead to the change of the solitonic velocities, but the shape of each soliton remains unchanged, where α(t) and β(t) are the variable coefficients in the equation. Oblique elastic interactions can exist between the (i) two shock waves, (ii) two elevation solitons, and (iii) elevation and depression solitons. However, oblique interactions between (i) shock waves and elevation solitons, (ii) shock waves and depression solitons are inelastic.
DEFF Research Database (Denmark)
D'ovidio, Francesco; Bohr, Henrik; Lindgård, Per-Anker
2005-01-01
We study the propagation of solitons along the hydrogen bonds of an alpha helix. Modeling the hydrogen and peptide bonds with Lennard-Jones potentials, we show that the solitons can appear spontaneously and have long lifetimes. Remarkably, even if no explicit solution is known for the Lennard-Jones...... potential, the solitons can be characterized analytically with a good quantitative agreement using formulas for a Toda potential with parameters fitted to the Lennard-Jones potential. We also discuss and show the robustness of the family of periodic solutions called cnoidal waves, corresponding to phonons...
Spangenberg, Jorge E
2012-11-30
The choice of containers for storage of aqueous samples between their collection, transport and water hydrogen ((2)H) and oxygen ((18)O) stable isotope analysis is a topic of concern for a wide range of fields in environmental, geological, biomedical, food, and forensic sciences. The transport and separation of water molecules during water vapor or liquid uptake by sorption or solution and the diffusive transport of water molecules through organic polymer material by permeation or pervaporation may entail an isotopic fractionation. An experiment was conducted to evaluate the extent of such fractionation. Sixteen bottle-like containers of eleven different organic polymers, including low and high density polyethylene (LDPE and HDPE), polypropylene (PP), polycarbonate (PC), polyethylene terephthalate (PET), and perfluoroalkoxy-Teflon (PFA), of different wall thickness and size were completely filled with the same mineral water and stored for 659 days under the same conditions of temperature and humidity. Particular care was exercised to keep the bottles tightly closed and prevent loss of water vapor through the seals. Changes of up to +5‰ for δ(2)H values and +2.0‰ for δ(18)O values were measured for water after more than 1 year of storage within a plastic container, with the magnitude of change depending mainly on the type of organic polymer, wall thickness, and container size. The most important variations were measured for the PET and PC bottles. Waters stored in glass bottles with Polyseal™ cone-lined PP screw caps and thick-walled HDPE or PFA containers with linerless screw caps having an integrally molded inner sealing ring preserved their original δ(2)H and δ(18)O values. The carbon, hydrogen, and oxygen stable isotope compositions of the organic polymeric materials were also determined. The results of this study clearly show that for precise and accurate measurements of the water stable isotope composition in aqueous solutions, rigorous sampling and
International Nuclear Information System (INIS)
Olsen, M.; Smith, H.; Scott, A.C.
1984-01-01
A wave tank experiment (first described by the nineteenth-century engineer and naval architect John Scott Russell) relates a linear eigenvalue problem from elementary quantum mechanics to a striking feature of modern nonlinear wave theory: multiple generation of solitons. The tank experiment is intended for lecture demonstrations. 19 references, 6 figures
Oscillating solitons in nonlinear optics
Indian Academy of Sciences (India)
The study of solitons in those physical systems reveals some exciting .... With the following power series expansions for g(z,t) and f(z,t): g(z,t) = εg1(z,t) + ... If nonlinearity γ (z) is also taken as a function in figure 1b, the periodic and oscillation.
Wen, Lin; Zhang, Xiao-Fei; Hu, Ai-Yuan; Zhou, Jing; Yu, Peng; Xia, Lei; Sun, Qing; Ji, An-Chun
2018-03-01
We investigate the dynamics of bright-bright solitons in one-dimensional two-component Bose-Einstein condensates with Raman-induced spin-orbit coupling, via the variational approximation and the numerical simulation of Gross-Pitaevskii equations. For the uniform system without trapping potential, we obtain two population balanced stationary solitons. By performing the linear stability analysis, we find a Goldstone eigenmode and an oscillation eigenmode around these stationary solitons. Moreover, we derive a general dynamical solution to describe the center-of-mass motion and spin evolution of the solitons under the action of spin-orbit coupling. The effects of a harmonic trap have also been discussed.
Li, Ming-Zhen; Tian, Bo; Qu, Qi-Xing; Chai, Han-Peng; Liu, Lei; Du, Zhong
2017-12-01
In this paper, under investigation is a coupled variable-coefficient higher-order nonlinear Schrödinger system, which describes the simultaneous propagation of optical pulses in an inhomogeneous optical fiber. Based on the Lax pair and binary Darboux transformation, we present the nondegenerate N-dark-dark soliton solutions. With the graphical simulation, soliton propagation and interaction are discussed with the group velocity dispersion and fourth-order dispersion effects, which affect the velocity but have no effect on the amplitude. Linear, parabolic and periodic one dark-dark solitons are displayed. Interactions between the two solitons are presented as well, which are all elastic.
Zhang, Jie-Fang; Li, Yi-Shen; Meng, Jianping; Wu, Lei; Malomed, Boris A.
2010-01-01
We investigate solitons and nonlinear Bloch waves in Bose-Einstein condensates trapped in optical lattices. By introducing specially designed localized profiles of the spatial modulation of the attractive nonlinearity, we construct an infinite number of exact soliton solutions in terms of the Mathieu and elliptic functions, with the chemical potential belonging to the semi-infinite bandgap of the optical-lattice-induced spectrum. Starting from the exact solutions, we employ the relaxation met...
Spinning solitons in cubic-quintic nonlinear media
Indian Academy of Sciences (India)
Spinning solitons in cubic-quintic nonlinear media ... features of families of bright vortex solitons (doughnuts, or 'spinning' solitons) in both conservative and dissipative cubic-quintic nonlinear media. ... Pramana – Journal of Physics | News.
Solitons, gauge theories and the 'great Einstein theorem'
International Nuclear Information System (INIS)
Dresden, M.; Chen, S.F.
1976-01-01
A field theory is said to be of 'Einstein type' if it has the property that the field equations imply the equations of motion. It is known that general relativity is of Einstein type, it is demonstrated here that the Yang-Mills gauge theory is of Einstein type. The relationship between the singularities in the solutions of the field equations and soliton type is analyzed. (Auth.)
Hirota's solitons in the affine and the conformal affine Toda models
International Nuclear Information System (INIS)
Aratyn, H.; Constantinidis, C.P.; Ferreira, L.A.; Gomes, J.F.; Zimerman, A.H.
1993-01-01
We use Hirota's method formulated as a recursive scheme to construct a complete set of soliton solutions for the affine Toda field theory based on an arbitrary Lie algebra. Our solutions include a new class of solitons connected with two different types of degeneracies encountered in Hirota's perturbation approach. We also derive an universal mass formula for all Hirota's solutions to the affine Toda model valid for all underlying Lie groups. Embedding of the affine Toda model in the conformal affine Toda model plays a crucial role in this analysis. (orig.)
Time-dependent gravitating solitons in five dimensional warped space-times
Giovannini, Massimo
2007-01-01
Time-dependent soliton solutions are explicitly derived in a five-dimensional theory endowed with one (warped) extra-dimension. Some of the obtained geometries, everywhere well defined and technically regular, smoothly interpolate between two five-dimensional anti-de Sitter space-times for fixed value of the conformal time coordinate. Time dependent solutions containing both topological and non-topological sectors are also obtained. Supplementary degrees of freedom can be also included and, in this case, the resulting multi-soliton solutions may describe time-dependent kink-antikink systems.
Matter-Wave Solitons In Optical Superlattices
International Nuclear Information System (INIS)
Louis, Pearl J. Y.; Ostrovskaya, Elena A.; Kivshar, Yuri S.
2006-01-01
In this work we show that the properties of both bright and dark Bose-Einstein condensate (BEC) solitons trapped in optical superlattices can be controlled by changing the shape of the trapping potential whilst maintaining a constant periodicity and lattice height. Using this method we can control the properties of bright gap solitons by dispersion management. We can also control the interactions between dark lattice solitons. In addition we demonstrate a method for controlled generation of matter-wave gap solitons in stationary optical lattices by interfering two condensate wavepackets, producing a single wavepacket at a gap edge with properties similar to a gap soliton. As this wavepacket evolves, it forms a bright gap soliton
Rogue waves and W-shaped solitons in the multiple self-induced transparency system.
Wang, Xin; Liu, Chong; Wang, Lei
2017-09-01
We study localized nonlinear waves on a plane wave background in the multiple self-induced transparency (SIT) system, which describes an important enhancement of the amplification and control of optical waves compared to the single SIT system. A hierarchy of exact multiparametric rational solutions in a compact determinant representation is presented. We demonstrate that this family of solutions contain known rogue wave solutions and unusual W-shaped soliton solutions. State transitions between the fundamental rogue waves and W-shaped solitons as well as higher-order nonlinear superposition modes are revealed in the zero-frequency perturbation region by the suitable choice for the background wavenumber of the electric field component. Particularly, it is found that the multiple SIT system can admit both stationary and nonstationary W-shaped solitons in contrast to the stationary results in the single SIT system. Moreover, the W-shaped soliton complex which is formed by a certain number of fundamental W-shaped solitons with zero phase parameters and its decomposition mechanism in the case of the nonzero phase parameters are shown. Meanwhile, some important characteristics of the nonlinear waves including trajectories and spectrum are discussed through the numerical and analytical methods.
Warped solitonic deformations and propagation of black holes in 5D vacuum gravity
International Nuclear Information System (INIS)
Vacaru, Sergiu I; Singleton, D
2002-01-01
In this paper we use the anholonomic frames method to construct exact solutions for vacuum 5D gravity with metrics having off-diagonal components. The solutions are, in general, anisotropic and possess interesting features such as an anisotropic warp factor with respect to the extra dimension, or a gravitational scaling/running of some of the physical parameters associated with the solutions. A certain class of solutions is found to describe Schwarzschild black holes which 'solitonically' propagate in spacetime. The solitonic character of these black-hole solutions arises from the embedding of the sine-Gordon soliton configuration into certain ansatz functions of the 5D metric. These solitonic solutions may either violate or preserve local Lorentz invariance. In addition, there is a connection between these solutions and non-commutative field theory. In addition to the possible physical applications of the solutions presented here, this paper is meant to illustrate the strength of the anholonomic frames method in handling anisotropic solutions of the gravitational field equations
Walking solitons in quadratic nonlinear media
Torner Sabata, Lluís; Mazilu, D; Mihalache, Dumitru
1996-01-01
We study self-action of light in parametric wave interactions in nonlinear quadratic media. We show the existence of stationary solitons in the presence of Poynting vector beam walk-off or different group velocities between the waves. We discover that the new solitons constitute a two-parameter family, and they exist for different wave intensities and transverse velocities. We discuss the properties of the walking solitons and their experimental implications. Peer Reviewed
Solitons in a random force field
International Nuclear Information System (INIS)
Bass, F.G.; Konotop, V.V.; Sinitsyn, Y.A.
1985-01-01
We study the dynamics of a soliton of the sine-Gordon equation in a random force field in the adiabatic approximation. We obtain an Einstein-Fokker equation and find the distribution function for the soliton parameters which we use to evaluate its statistical characteristics. We derive an equation for the averaged functions of the soliton parameters. We determine the limits of applicability of the delta-correlated in time random field approximation
Certain bright soliton interactions of the Sasa-Satsuma equation in a monomode optical fiber
Liu, Lei; Tian, Bo; Chai, Han-Peng; Yuan, Yu-Qiang
2017-03-01
Under investigation in this paper is the Sasa-Satsuma equation, which describes the propagation of ultrashort pulses in a monomode fiber with the third-order dispersion, self-steepening, and stimulated Raman scattering effects. Based on the known bilinear forms, through the modified expanded formulas and symbolic computation, we construct the bright two-soliton solutions. Through classifying the interactions under different parameter conditions, we reveal six cases of interactions between the two solitons via an asymptotic analysis. With the help of the analytic and graphic analysis, we find that such interactions are different from those of the nonlinear Schrödinger equation and Hirota equation. When those solitons interact with each other, the singular-I soliton is shape-preserving, while the singular-II and nonsingular solitons may be shape preserving or shape changing. Such elastic and inelastic interaction phenomena in a scalar equation might enrich the knowledge of soliton behavior, which could be expected to be experimentally observed.
A unified view of acoustic-electrostatic solitons in complex plasmas
McKenzie, J. F.; Doyle, T. B.
2003-03-01
A fluid dynamic approach is used in a unified fully nonlinear treatment of the properties of the dust-acoustic, ion-acoustic and Langmuir-acoustic solitons. The analysis, which is carried out in the wave frame of the soliton, is based on total momentum conservation and Bernoulli-like energy equations for each of the particle species in each wave type, and yields the structure equation for the `heavy' species flow speed in each case. The heavy (cold or supersonic) species is always compressed in the soliton, requiring concomitant contraints on the potential and on the flow speed of the electrons and protons in the wave. The treatment clearly elucidates the crucial role played by the heavy species sonic point in limiting the collective species Mach number, which determines the upper limit for the existence of the soliton and its amplitude, and also shows the essentially similar nature of each soliton type. An exact solution, which highlights these characteristic properties, shows that the three acoustic solitons are in fact the same mathematical entity in different physical disguises.
A unified view of acoustic-electrostatic solitons in complex plasmas
International Nuclear Information System (INIS)
McKenzie, J F; Doyle, T B
2003-01-01
A fluid dynamic approach is used in a unified fully nonlinear treatment of the properties of the dust-acoustic, ion-acoustic and Langmuir-acoustic solitons. The analysis, which is carried out in the wave frame of the soliton, is based on total momentum conservation and Bernoulli-like energy equations for each of the particle species in each wave type, and yields the structure equation for the 'heavy' species flow speed in each case. The heavy (cold or supersonic) species is always compressed in the soliton, requiring concomitant constraints on the potential and on the flow speed of the electrons and protons in the wave. The treatment clearly elucidates the crucial role played by the heavy species sonic point in limiting the collective species Mach number, which determines the upper limit for the existence of the soliton and its amplitude, and also shows the essentially similar nature of each soliton type. An exact solution, which highlights these characteristic properties, shows that the three acoustic solitons are in fact the same mathematical entity in different physical disguises
Induced mitochondrial membrane potential for modeling solitonic conduction of electrotonic signals.
Directory of Open Access Journals (Sweden)
R R Poznanski
Full Text Available A cable model that includes polarization-induced capacitive current is derived for modeling the solitonic conduction of electrotonic potentials in neuronal branchlets with microstructure containing endoplasmic membranes. A solution of the nonlinear cable equation modified for fissured intracellular medium with a source term representing charge 'soakage' is used to show how intracellular capacitive effects of bound electrical charges within mitochondrial membranes can influence electrotonic signals expressed as solitary waves. The elastic collision resulting from a head-on collision of two solitary waves results in localized and non-dispersing electrical solitons created by the nonlinearity of the source term. It has been shown that solitons in neurons with mitochondrial membrane and quasi-electrostatic interactions of charges held by the microstructure (i.e., charge 'soakage' have a slower velocity of propagation compared with solitons in neurons with microstructure, but without endoplasmic membranes. When the equilibrium potential is a small deviation from rest, the nonohmic conductance acts as a leaky channel and the solitons are small compared when the equilibrium potential is large and the outer mitochondrial membrane acts as an amplifier, boosting the amplitude of the endogenously generated solitons. These findings demonstrate a functional role of quasi-electrostatic interactions of bound electrical charges held by microstructure for sustaining solitons with robust self-regulation in their amplitude through changes in the mitochondrial membrane equilibrium potential. The implication of our results indicate that a phenomenological description of ionic current can be successfully modeled with displacement current in Maxwell's equations as a conduction process involving quasi-electrostatic interactions without the inclusion of diffusive current. This is the first study in which solitonic conduction of electrotonic potentials are generated by
Temperature effects on the Davydov soliton
DEFF Research Database (Denmark)
Cruzeiro, L.; Halding, J.; Christiansen, Peter Leth
1988-01-01
As a possible mechanism for energy storage and transport in proteins, Davydov has proposed soliton formation and propagation. In this paper we investigate the stability of Davydov solitons at biological temperatures. From Davydov’s original theory evolution equations are derived quantum mechanica......As a possible mechanism for energy storage and transport in proteins, Davydov has proposed soliton formation and propagation. In this paper we investigate the stability of Davydov solitons at biological temperatures. From Davydov’s original theory evolution equations are derived quantum...
Solitons in one-dimensional antiferromagnetic chains
International Nuclear Information System (INIS)
Pires, A.S.T.; Talim, S.L.; Costa, B.V.
1989-01-01
We study the quantum-statistical mechanics, at low temperatures, of a one-dimensional antiferromagnetic Heisenberg model with two anisotropies. In the weak-coupling limit we determine the temperature dependences of the soliton energy and the soliton density. We have found that the leading correction to the sine-Gordon (SG) expression for the soliton density and the quantum soliton energy comes from the out-of-plane magnon mode, not present in the pure SG model. We also show that when an external magnetic field is applied, the chain supports a new type of kink, where the sublattices rotate in opposite directions
Soliton coding for secured optical communication link
Amiri, Iraj Sadegh; Idrus, Sevia Mahdaliza
2015-01-01
Nonlinear behavior of light such as chaos can be observed during propagation of a laser beam inside the microring resonator (MRR) systems. This Brief highlights the design of a system of MRRs to generate a series of logic codes. An optical soliton is used to generate an entangled photon. The ultra-short soliton pulses provide the required communication signals to generate a pair of polarization entangled photons required for quantum keys. In the frequency domain, MRRs can be used to generate optical millimetre-wave solitons with a broadband frequency of 0?100 GHz. The soliton signals are multi
Cuevas-Maraver, J.; Malomed, Boris A.; Kevrekidis, P. G.; Frantzeskakis, D. J.
2018-04-01
We demonstrate a possibility to make rogue waves (RWs) in the form of the Peregrine soliton (PS) and Kuznetsov-Ma breathers (KMBs) effectively stable objects, with the help of properly defined dispersion or nonlinearity management applied to the continuous-wave (CW) background supporting the RWs. In particular, it is found that either management scheme, if applied along the longitudinal coordinate, making the underlying nonlinear Schrödinger equation (NLSE) self-defocusing in the course of disappearance of the PS, indeed stabilizes the global solution with respect to the modulational instability of the background. In the process, additional excitations are generated, namely, dispersive shock waves and, in some cases, also a pair of slowly separating dark solitons. Further, the nonlinearity-management format, which makes the NLSE defocusing outside of a finite domain in the transverse direction, enables the stabilization of the KMBs, in the form of confined oscillating states. On the other hand, a nonlinearity-management format applied periodically along the propagation direction, creates expanding patterns featuring multiplication of KMBs through their cascading fission.
A Coupled Korteweg-de Vries System and Mass Exchanges among Solitons
DEFF Research Database (Denmark)
Miller, P. D.; Christiansen, Peter Leth
2000-01-01
V and the solution of a linear equation with nonconstant coefficients. The coupled KdV system may be viewed as a phenomenological model for the sharing of mass among interacting solitons of the (one-component) KdV equation. Results for the scattering theory of solutions of the nonconstant coefficient linear equation...
Soliton condensation in some self-dual Chern-Simons theories
International Nuclear Information System (INIS)
Olesen, P.
1991-05-01
We show that the gauged non-linear Schroedinger equation has a closely packed soliton-condensate as a solution. We also show that the abelian Chern-Simons Higgs theory has a vortex condensate as an approximate solution whent he vortex cells are very small. (orig.)
Ion temperature gradient mode driven solitons and shocks
Zakir, U.; Adnan, Muhammad; Haque, Q.; Qamar, Anisa; Mirza, Arshad M.
2016-04-01
Ion temperature gradient (ITG) driven solitons and shocks are studied in a plasma having gradients in the equilibrium number density and equilibrium ion temperature. In the linear regime, it is found that the ion temperature and the ratio of the gradient scale lengths, ηi=Ln/LT , affect both the real frequency and the growth rate of the ITG driven wave instability. In the nonlinear regime, for the first time we derive a Korteweg de Vries-type equation for the ITG mode, which admits solitary wave solution. It is found that the ITG mode supports only compressive solitons. Further, it is noticed that the soliton amplitude and width are sensitive to the parameter ηi=Ln/LT . Second, in the presence of dissipation in the system, we obtain a Burger type equation, which admits the shock wave solution. This work may be useful to understand the low frequency electrostatic modes in inhomogeneous electron-ion plasma having density and ion temperature gradients. For illustration, the model has been applied to tokamak plasma.
Soliton Gases and Generalized Hydrodynamics
Doyon, Benjamin; Yoshimura, Takato; Caux, Jean-Sébastien
2018-01-01
We show that the equations of generalized hydrodynamics (GHD), a hydrodynamic theory for integrable quantum systems at the Euler scale, emerge in full generality in a family of classical gases, which generalize the gas of hard rods. In this family, the particles, upon colliding, jump forward or backward by a distance that depends on their velocities, reminiscent of classical soliton scattering. This provides a "molecular dynamics" for GHD: a numerical solver which is efficient, flexible, and which applies to the presence of external force fields. GHD also describes the hydrodynamics of classical soliton gases. We identify the GHD of any quantum model with that of the gas of its solitonlike wave packets, thus providing a remarkable quantum-classical equivalence. The theory is directly applicable, for instance, to integrable quantum chains and to the Lieb-Liniger model realized in cold-atom experiments.
Polarization Properties of Laser Solitons
Directory of Open Access Journals (Sweden)
Pedro Rodriguez
2017-04-01
Full Text Available The objective of this paper is to summarize the results obtained for the state of polarization in the emission of a vertical-cavity surface-emitting laser with frequency-selective feedback added. We start our research with the single soliton; this situation presents two perpendicular main orientations, connected by a hysteresis loop. In addition, we also find the formation of a ring-shaped intensity distribution, the vortex state, that shows two homogeneous states of polarization with very close values to those found in the soliton. For both cases above, the study shows the spatially resolved value of the orientation angle. It is important to also remark the appearance of a non-negligible amount of circular light that gives vectorial character to all the different emissions investigated.
Nonlinear mode conversion with chaotic soliton generation at plasma resonance
International Nuclear Information System (INIS)
Pietsch, H.; Laedke, E.W.; Spatschek, K.H.
1993-01-01
The resonant absorption of electromagnetic waves near the critical density in inhomogeneous plasmas is studied. A driven nonlinear Schroedinger equation for the mode-converted oscillations is derived by multiple-scaling techniques. The model is simulated numerically. The generic transition from a stationary to a time-dependent solution is investigated. Depending on the parameters, a time-chaotic behavior is found. By a nonlinear analysis, based on the inverse scattering transform, solitons of a corresponding integrable equation are identified as the dominant coherent structures of the chaotic dynamics. Finally, a map is presented which predicts chaotic soliton generation and emission at the critical density. Its qualitative behavior, concerning the bifurcation points, is in excellent agreement with the numerical simulations
CP-Violating solitons in the early universe
International Nuclear Information System (INIS)
Tornkvist, O.; Riotto, A.
1997-07-01
Solitons in extensions of the Standard Model can serve as localized sources of CP violation. Depending on their stability properties, they may serve either to create or to deplete the baryon asymmetry. The conditions for existence of a particular soliton candidate, the membrane solution of the two-Higgs model, are presented. In the generic case, investigated by Bachas and Tomaras, membranes exist and are metastable for a wide range of parameters. For the more viable supersymmetric case, it is shown that the present-day existence of CP-violating membranes is experimentally excluded, but preliminary studies suggest that they may have existed in the early universe soon after the electroweak phase transition, with important consequences for the baryon asymmetry of the universe
Soliton collapse during ionospheric heating
International Nuclear Information System (INIS)
Sheerin, J.P.; Nicholson, D.R.; Payne, G.L.; Duncan, L.M.
1984-01-01
We present analytical and numerical work which indicates that during ionospheric heating with high-powered hf radio waves, the oscillating two-stream instability may dominate the parametric decay instability. The oscillating two-stream instability saturates nonlinearly through the formation of solitons which undergo a collisionally damped collapse. Using the heater and radar facilities at Arecibo Observatory, we have investigated this phenomenon experimentally. Recent results from our theoretical and experimental investigations are presented
Nucleon-nucleon interaction in the soliton bag model
International Nuclear Information System (INIS)
Schuh, A.
1985-01-01
In the framework of the Soliton Bag Model introduced by Friedberg and Lee we treat S-wave nucleon-nucleon scattering. Our system consists of six quarks and the nontopological soliton field which represents an average colorfree interaction between the quarks and yields their (relative) confinement. The dynamical problem is treated by means of the Generator coordinate Method (GCM) where the total wave function is the weighted sum over static configurations of prescribed bag deformation. The static configurations needed for the GCM ansatz are generated starting from a potential well of prescribed deformation wherein we solve the Dirac equation for the quarks. The single particle quark orbitals are properly coupled with respect to orbital, color, spin, and isospin quantum numbers to form a totally antisymmetric 6-quark state. A mean field solution for the soliton field is then calculated and turned into a quantum mechanical state by a coherent state approximation. Since these static configurations are only to be seen as wave function generators for the GCM no selfconsistency between quark and soliton solution is enforced. With these configurations we then evaluate the norm and Hamiltonian kernels appearing in the GCM treatment. The Hill-Wheeler integral equation for the weight functions is transformed into a Schroedinger-type differential equation by an expansion into symmetric moments of up to second order. This equation is brought into a form where we can identify the interaction potential unambiguously. We find an intermediate range attraction of about 120 MeV and no attraction in the vicinity of the spherically symmetric shape of the system, in contradiction to the naive adiabatic potentials widely used in quark models for the nucleon-nucleon interaction up to now. (orig./HSI) [de
Analytic description of Raman-induced frequency shift in the case of non-soliton ultrashort pulses
International Nuclear Information System (INIS)
Bugay, Aleksandr N.; Khalyapin, Vyacheslav A.
2017-01-01
Raman-induced frequency shift of ultrashort pulses have been studied extensively for the soliton propagation regime. Here we derive explicit analytic expressions for the evolution of Raman-induced frequency shift in much less studied case of non-soliton ultrashort pulses. Pulse spectra may belong to any region of group velocity dispersion including zero group dispersion point. The analysis is based on the moment method. Obtained expressions fit well to the numerical solution of the nonlinear wave equation. - Highlights: • Explicit analytic formulas for the evolution of Raman-induced frequency shift are derived in the case of non-soliton pulses. • Dynamics of non-soliton ultrashort pulses in the cases of positive and zero group dispersion is considered. • The deceleration and the saturation of Raman-induced frequency shift are analyzed. • The calculation relies on the moment method and fit well to the numerical solution of the nonlinear wave equation.
A modified KdV equation with self-consistent sources in non-uniform media and soliton dynamics
International Nuclear Information System (INIS)
Zhang Dajun; Bi Jinbo; Hao Honghai
2006-01-01
Two non-isospectral modified KdV equations with self-consistent sources are derived, which correspond to the time-dependent spectral parameter λ satisfying λ t = λ and λ t = λ 3 , respectively. Gauge transformation between the first non-isospectral equation (corresponding to λ t = λ) and its isospectral counterpart is given, from which exact solutions and conservation laws for the non-isospectral one are easily listed. Besides, solutions to the two non-isospectral modified KdV equations with self-consistent sources are derived by means of the Hirota method and the Wronskian technique, respectively. Non-isospectral dynamics and source effects, including one-soliton characteristics in non-uniform media, two-solitons scattering and special behaviours related to sources (for example, the 'ghost' solitons in the degenerate two-soliton case), are investigated analytically
Analytic description of Raman-induced frequency shift in the case of non-soliton ultrashort pulses
Energy Technology Data Exchange (ETDEWEB)
Bugay, Aleksandr N., E-mail: bugay_aleksandr@mail.ru [Joint Institute for Nuclear Research, Joliot-Curie 6, 141980, Dubna, Moscow Region (Russian Federation); Khalyapin, Vyacheslav A., E-mail: slavasxi@gmail.com [Immanuel Kant Baltic Federal University, Kaliningrad, 236041 (Russian Federation); Kaliningrad State Technical University, Kaliningrad, 236000 (Russian Federation)
2017-01-30
Raman-induced frequency shift of ultrashort pulses have been studied extensively for the soliton propagation regime. Here we derive explicit analytic expressions for the evolution of Raman-induced frequency shift in much less studied case of non-soliton ultrashort pulses. Pulse spectra may belong to any region of group velocity dispersion including zero group dispersion point. The analysis is based on the moment method. Obtained expressions fit well to the numerical solution of the nonlinear wave equation. - Highlights: • Explicit analytic formulas for the evolution of Raman-induced frequency shift are derived in the case of non-soliton pulses. • Dynamics of non-soliton ultrashort pulses in the cases of positive and zero group dispersion is considered. • The deceleration and the saturation of Raman-induced frequency shift are analyzed. • The calculation relies on the moment method and fit well to the numerical solution of the nonlinear wave equation.
Stability of black holes and solitons in Anti-de Sitter space-time
Energy Technology Data Exchange (ETDEWEB)
Hartmann, Betti
2014-06-15
The stability of black holes and solitons in d-dimensional Anti-de Sitter (AdS{sub d}) space-time against scalar field condensation is discussed. The resulting solutions are “hairy” black holes and solitons, respectively. In particular, we will discuss static black hole solutions with hyperbolic, flat and spherical horizon topology and emphasize that two different type of instabilities exist depending on whether the scalar field is charged or uncharged, respectively. We will also discuss the influence of Gauss-Bonnet curvature terms. The results have applications within the AdS/CFT correspondence and describe e.g. holographic insulator/conductor/superconductor phase transitions.
Combined solitary-wave solution for coupled higher-order nonlinear Schroedinger equations
International Nuclear Information System (INIS)
Tian Jinping; Tian Huiping; Li Zhonghao; Zhou Guosheng
2004-01-01
Coupled nonlinear Schroedinger equations model several interesting physical phenomena. We used a trigonometric function transform method based on a homogeneous balance to solve the coupled higher-order nonlinear Schroedinger equations. We obtained four pairs of exact solitary-wave solutions including a dark and a bright-soliton pair, a bright- and a dark-soliton pair, a bright- and a bright-soliton pair, and the last pair, a combined bright-dark-soliton pair
Bifurcations and new exact travelling wave solutions for the ...
Indian Academy of Sciences (India)
By using the method of dynamical system, the bidirectional wave equations are considered. Based on this method, all kinds of phase portraits of the reduced travelling wave system in the parametric space are given. All possible bounded travelling wave solutions such as dark soliton solutions, bright soliton solutions and ...
The ion-acoustic soliton: A gas-dynamic viewpoint
McKenzie, J. F.
2002-03-01
The properties of fully nonlinear ion-acoustic solitons are investigated by interpreting conservation of total momentum as the structure equation for the proton flow in the wave. In most studies momentum conservation is regarded as the first integral of the Poisson equation for the electric potential and is interpreted as being analogous to a particle moving in a pseudo-potential well. By adopting an essentially gas-dynamic viewpoint, which emphasizes momentum conservation and the properties of the Bernoulli-type energy equations, the crucial role played by the proton sonic point becomes apparent. The relationship (implied by energy conservation) between the electron and proton speeds in the transition yields a locus—the hodograph of the system-which shows that, in the first half of the soliton, the electrons initially lag behind the protons until the charge neutral point is reached, after which they run ahead of the protons. The system reaches an equilibrium point (the center of the soliton) before the proton flow goes sonic. It follows that the critical ion-acoustic Mach number, Mc, above which smooth, continuous solitons cannot be constructed, stems from the requirement that the two equilibrium points of the structure equation coalesce at the proton sonic point of the flow. In general the range of the ion-acoustic Mach numbers, Mep, in which solitons exist, is extended beyond the classical range 1
Reversible decay of ring dark solitons
International Nuclear Information System (INIS)
Toikka, L A; Suominen, K-A
2014-01-01
We show how boundary effects can cause a Bose–Einstein condensate to periodically oscillate between a (circular) array of quantized vortex–antivortex pairs and a (ring) dark soliton. If the boundary is restrictive enough, the ring dark soliton becomes long-lived. (paper)
Dissipative Solitons that Cannot be Trapped
International Nuclear Information System (INIS)
Pardo, Rosa; Perez-Garcia, Victor M.
2006-01-01
We show that dissipative solitons in systems with high-order nonlinear dissipation cannot survive in the presence of trapping potentials of the rigid wall or asymptotically increasing type. Solitons in such systems can survive in the presence of a weak potential but only with energies out of the interval of existence of linear quantum mechanical stationary states
Observation of attraction between dark solitons
DEFF Research Database (Denmark)
Dreischuh, A.; Neshev, D.N.; Petersen, D.E.
2006-01-01
We demonstrate a dramatic change in the interaction forces between dark solitons in nonlocal nonlinear media. We present what we believe is the first experimental evidence of attraction of dark solitons. Our results indicate that attraction should be observable in other nonlocal systems...
Dark Solitons in FPU Lattice Chain
Wang, Deng-Long; Yang, Ru-Shu; Yang, You-Tian
2007-11-01
Based on multiple scales method, we study the nonlinear properties of a new Fermi-Pasta-Ulam lattice model analytically. It is found that the lattice chain exhibits a novel nonlinear elementary excitation, i.e. a dark soliton. Moreover, the modulation depth of dark soliton is increasing as the anharmonic parameter increases.
Dark Solitons in FPU Lattice Chain
International Nuclear Information System (INIS)
Wang Denglong; Yang Youtian; Yang Rushu
2007-01-01
Based on multiple scales method, we study the nonlinear properties of a new Fermi-Pasta-Ulam lattice model analytically. It is found that the lattice chain exhibits a novel nonlinear elementary excitation, i.e. a dark soliton. Moreover, the modulation depth of dark soliton is increasing as the anharmonic parameter increases.
Modification of Plasma Solitons by Resonant Particles
DEFF Research Database (Denmark)
Karpman, Vladimir; Lynov, Jens-Peter; Michelsen, Poul
1979-01-01
Experimental and numerical results are compared with new theoretical results describing soliton propagation and deformation in a strongly magnetized, plasma-loaded waveguide.......Experimental and numerical results are compared with new theoretical results describing soliton propagation and deformation in a strongly magnetized, plasma-loaded waveguide....
The soliton content of classical Jackiw-Teitelboim gravity
Energy Technology Data Exchange (ETDEWEB)
Reyes, Enrique G [Departamento de Matematicas y Ciencia de la Computacion, Universidad de Santiago de Chile, Casilla 307 Correo 2, Santiago, Chile (Chile)
2006-01-13
It is pointed out that every generic-in a sense to be made precise in section 2-solution to an arbitrary equation describing pseudo-spherical surfaces (or, equivalently, an arbitrary equation which is the integrability condition of a sl(2, R)-valued linear problem) determines pseudo-Riemannian surfaces of constant scalar curvature, and therefore, classical solutions to the Jackiw-Teitelboim field equations for two-dimensional gravity. In particular, this observation explains why some standard soliton equations appear in this theory. (letter to the editor)
Solitons and bubbles in models with Chern-Simons term
International Nuclear Information System (INIS)
Masperi, L.
1992-07-01
It is shown that a gauge theory for complex scalar field with up to sextic self-interactions and a Chern-Simons term in 2 + 1 dimensions has solitons which may become bubbles of the stable broken-symmetry phase in a medium of the symmetric one producing the first-order phase transition. In the non-relativistic limit scale invariance prevents the determination of an optimal bubble size. Possible extensions to 3 + 1 dimensions of bubbles of string type are indicated. (author). 8 refs
Induced waveform transitions of dissipative solitons
Kochetov, Bogdan A.; Tuz, Vladimir R.
2018-01-01
The effect of an externally applied force upon the dynamics of dissipative solitons is analyzed in the framework of the one-dimensional cubic-quintic complex Ginzburg-Landau equation supplemented by a potential term with an explicit coordinate dependence. The potential accounts for the external force manipulations and consists of three symmetrically arranged potential wells whose depth varies along the longitudinal coordinate. It is found out that under an influence of such potential a transition between different soliton waveforms coexisting under the same physical conditions can be achieved. A low-dimensional phase-space analysis is applied in order to demonstrate that by only changing the potential profile, transitions between different soliton waveforms can be performed in a controllable way. In particular, it is shown that by means of a selected potential, stationary dissipative soliton can be transformed into another stationary soliton as well as into periodic, quasi-periodic, and chaotic spatiotemporal dissipative structures.
Kinetic slow mode-type solitons
Directory of Open Access Journals (Sweden)
K. Baumgärtel
2005-01-01
Full Text Available One-dimensional hybrid code simulations are presented, carried out in order both to study solitary waves of the slow mode branch in an isotropic, collisionless, medium-β plasma (βi=0.25 and to test the fluid based soliton interpretation of Cluster observed strong magnetic depressions (Stasiewicz et al., 2003; Stasiewicz, 2004 against kinetic theory. In the simulations, a variety of strongly oblique, large amplitude, solitons are seen, including solitons with Alfvenic polarization, similar to those predicted by the Hall-MHD theory, and robust, almost non-propagating, solitary structures of slow magnetosonic type with strong magnetic field depressions and perpendicular ion heating, which have no counterpart in fluid theory. The results support the soliton-based interpretation of the Cluster observations, but reveal substantial deficiencies of Hall-MHD theory in describing slow mode-type solitons in a plasma of moderate beta.
Brownian motion of solitons in a Bose-Einstein condensate.
Aycock, Lauren M; Hurst, Hilary M; Efimkin, Dmitry K; Genkina, Dina; Lu, Hsin-I; Galitski, Victor M; Spielman, I B
2017-03-07
We observed and controlled the Brownian motion of solitons. We launched solitonic excitations in highly elongated [Formula: see text] Bose-Einstein condensates (BECs) and showed that a dilute background of impurity atoms in a different internal state dramatically affects the soliton. With no impurities and in one dimension (1D), these solitons would have an infinite lifetime, a consequence of integrability. In our experiment, the added impurities scatter off the much larger soliton, contributing to its Brownian motion and decreasing its lifetime. We describe the soliton's diffusive behavior using a quasi-1D scattering theory of impurity atoms interacting with a soliton, giving diffusion coefficients consistent with experiment.
Solitons and protein folding: An In Silico experiment
International Nuclear Information System (INIS)
Ilieva, N.; Dai, J.; Sieradzan, A.; Niemi, A.
2015-01-01
Protein folding [1] is the process of formation of a functional 3D structure from a random coil — the shape in which amino-acid chains leave the ribosome. Anfinsen’s dogma states that the native 3D shape of a protein is completely determined by protein’s amino acid sequence. Despite the progress in understanding the process rate and the success in folding prediction for some small proteins, with presently available physics-based methods it is not yet possible to reliably deduce the shape of a biologically active protein from its amino acid sequence. The protein-folding problem endures as one of the most important unresolved problems in science; it addresses the origin of life itself. Furthermore, a wrong fold is a common cause for a protein to lose its function or even endanger the living organism. Soliton solutions of a generalized discrete non-linear Schrödinger equation (GDNLSE) obtained from the energy function in terms of bond and torsion angles κ and τ provide a constructive theoretical framework for describing protein folds and folding patterns [2]. Here we study the dynamics of this process by means of molecular-dynamics simulations. The soliton manifestation is the pattern helix–loop–helix in the secondary structure of the protein, which explains the importance of understanding loop formation in helical proteins. We performed in silico experiments for unfolding one subunit of the core structure of gp41 from the HIV envelope glycoprotein (PDB ID: 1AIK [3]) by molecular-dynamics simulations with the MD package GROMACS. We analyzed 80 ns trajectories, obtained with one united-atom and two different all-atom force fields, to justify the side-chain orientation quantification scheme adopted in the studies and to eliminate force-field based artifacts. Our results are compatible with the soliton model of protein folding and provide first insight into soliton-formation dynamics
Solitons and protein folding: An In Silico experiment
Energy Technology Data Exchange (ETDEWEB)
Ilieva, N., E-mail: nevena.ilieva@parallel.bas.bg [Institute of Information and Communication Technologies, Bulgarian Aacademy of Sciences, Sofia (Bulgaria); Dai, J., E-mail: daijing491@gmail.com [School of Physics, Beijing Institute of Technology, Beijing (China); Sieradzan, A., E-mail: adams86@wp.pl [Faculty of Chemistry, University of Gdańsk, Gdańsk (Poland); Niemi, A., E-mail: Antti.Niemi@physics.uu.se [Department of Physics and Astronomy, Uppsala University, Uppsala (Sweden); LMPT–CNRS, Université de Tours, Tours (France)
2015-10-28
Protein folding [1] is the process of formation of a functional 3D structure from a random coil — the shape in which amino-acid chains leave the ribosome. Anfinsen’s dogma states that the native 3D shape of a protein is completely determined by protein’s amino acid sequence. Despite the progress in understanding the process rate and the success in folding prediction for some small proteins, with presently available physics-based methods it is not yet possible to reliably deduce the shape of a biologically active protein from its amino acid sequence. The protein-folding problem endures as one of the most important unresolved problems in science; it addresses the origin of life itself. Furthermore, a wrong fold is a common cause for a protein to lose its function or even endanger the living organism. Soliton solutions of a generalized discrete non-linear Schrödinger equation (GDNLSE) obtained from the energy function in terms of bond and torsion angles κ and τ provide a constructive theoretical framework for describing protein folds and folding patterns [2]. Here we study the dynamics of this process by means of molecular-dynamics simulations. The soliton manifestation is the pattern helix–loop–helix in the secondary structure of the protein, which explains the importance of understanding loop formation in helical proteins. We performed in silico experiments for unfolding one subunit of the core structure of gp41 from the HIV envelope glycoprotein (PDB ID: 1AIK [3]) by molecular-dynamics simulations with the MD package GROMACS. We analyzed 80 ns trajectories, obtained with one united-atom and two different all-atom force fields, to justify the side-chain orientation quantification scheme adopted in the studies and to eliminate force-field based artifacts. Our results are compatible with the soliton model of protein folding and provide first insight into soliton-formation dynamics.
Chiral soliton models for baryons
International Nuclear Information System (INIS)
Weigel, H.
2008-01-01
This concise research monograph introduces and reviews the concept of chiral soliton models for baryons. In these models, baryons emerge as (topological) defects of the chiral field. The many applications shed light on a number of baryon properties, ranging from static properties via nucleon resonances and deep inelastic scattering to even heavy ion collisions. As far as possible, the theoretical investigations are confronted with experiment. Conceived to bridge the gap between advanced graduate textbooks and the research literature, this volume also features a number of appendices to help nonspecialist readers to follow in more detail some of the calculations in the main text. (orig.)
Soliton equations and Hamiltonian systems
Dickey, L A
2002-01-01
The theory of soliton equations and integrable systems has developed rapidly during the last 30 years with numerous applications in mechanics and physics. For a long time, books in this field have not been written but the flood of papers was overwhelming: many hundreds, maybe thousands of them. All this output followed one single work by Gardner, Green, Kruskal, and Mizura on the Korteweg-de Vries equation (KdV), which had seemed to be merely an unassuming equation of mathematical physics describing waves in shallow water. Besides its obvious practical use, this theory is attractive also becau
Wave Physics Oscillations - Solitons - Chaos
Nettel, Stephen
2009-01-01
This textbook is intended for those second year undergraduates in science and engineering who will later need an understanding of electromagnetic theory and quantum mechanics. The classical physics of oscillations and waves is developed at a more advanced level than has been customary for the second year, providing a basis for the quantum mechanics that follows. In this new edition the Green's function is explained, reinforcing the integration of quantum mechanics with classical physics. The text may also form the basis of an "introduction to theoretical physics" for physics majors. The concluding chapters give special attention to topics in current wave physics: nonlinear waves, solitons, and chaotic behavior.
Thermodynamics of Non-Topological Solitons
Laine, Mikko
1998-01-01
In theories with low energy supersymmetry breaking, the effective potential for squarks and sleptons has generically nearly flat directions, V(phi) ~ M^4 (log(phi/M))^n. This guarantees the existence of stable non-topological solitons, Q-balls, that carry large baryon number, B >> (M/m_p)^4, where m_p is the proton mass. We study the behaviour of these objects in a high temperature plasma. We show that in an infinitely extended system with a finite density of the baryon charge, the equilibrium state is not homogeneous and contains Q-balls at any temperature. In a system with a finite volume, Q-balls evaporate at a volume dependent temperature. In the cosmological context, we formulate the conditions under which Q-balls, produced in the Early Universe, survive till the present time. Finally, we estimate the baryon to cold dark matter ratio in a cosmological scenario in which Q-balls are responsible for both the net baryon number of the Universe and its dark matter. We find out naturally the correct orders of m...
Su, Jing-Jing; Gao, Yi-Tian
2018-03-01
Under investigation in this paper is a higher-order nonlinear Schrödinger equation with space-dependent coefficients, related to an optical fiber. Based on the self-similarity transformation and Hirota method, related to the integrability, the N-th-order bright and dark soliton solutions are derived under certain constraints. It is revealed that the velocities and trajectories of the solitons are both affected by the coefficient of the sixth-order dispersion term while the amplitudes of the solitons are determined by the gain function. Amplitudes increase when the gain function is positive and decrease when the gain function is negative. Furthermore, we find that the intensities of dark solitons are presented as a superposition of the solitons and stationary waves.
Interaction of ion-acoustic solitons in multi-dimensional space, 2
International Nuclear Information System (INIS)
Kako, Fujio; Yajima, Nobuo
1981-08-01
Numerical computations are made to study the collision process between two cylindrical or spherical solitons. The soliton resonance is found to play an important role in collision processes between two curved solitons as well as between two plane solitons. (author)
Energy Technology Data Exchange (ETDEWEB)
Blyakhman, L.G.; Gromov, E.M.; Onosova, I.V.; Tyutin, V.V., E-mail: vtyutin@hse.ru
2017-05-03
The dynamics of a two-component Davydov–Scott (DS) soliton with a small mismatch of the initial location or velocity of the high-frequency (HF) component was investigated within the framework of the Zakharov-type system of two coupled equations for the HF and low-frequency (LF) fields. In this system, the HF field is described by the linear Schrödinger equation with the potential generated by the LF component varying in time and space. The LF component in this system is described by the Korteweg–de Vries equation with a term of quadratic influence of the HF field on the LF field. The frequency of the DS soliton's component oscillation was found analytically using the balance equation. The perturbed DS soliton was shown to be stable. The analytical results were confirmed by numerical simulations. - Highlights: • The dynamics of the Davydov–Scott soliton with initial location or velocity mismatch of the HF component was investigated. • The study was performed within the framework of coupled linear Schrödinger and KdV equations for the HF and LF fields. • Analytical and numerical approaches were used. • The frequency of the DS soliton component oscillation was found. • Stability of the perturbed DS solitons was demonstrated.
Soliton and polaron generation in polyacetylene
International Nuclear Information System (INIS)
Su, Zhao-bin; Yu, Lu.
1984-07-01
The nonradiative decay of an e-h pair into soliton pair and that of an electron (hole) into polaron as well as the photoproduction of soliton pairs are considered using the lattice relaxation theory of multiphonon processes generalized to include the self-consistency of the multi-electron states with the lattice symmetry breaking. The selection rule which forbids the direct process of photogeneration for neutral pair is derived from the symmetry arguments. The branching ratio of the photogenerated neutral to charged soliton pairs is estimated. The recent related experiments are discussed. (author)
Form factors and excitations of topological solitons
International Nuclear Information System (INIS)
Weir, David J.; Rajantie, Arttu
2011-01-01
We show how the interaction properties of topological solitons in quantum field theory can be calculated with lattice Monte Carlo simulations. Topologically nontrivial field configurations are key to understanding the nature of the QCD vacuum through, for example, the dual superconductor picture. Techniques that we have developed to understand the excitations and form factors of topological solitons, such as kinks and 't Hooft-Polyakov monopoles, should be equally applicable to chromoelectric flux tubes. We review our results for simple topological solitons and their agreement with exact results, then discuss our progress towards studying objects of interest to high energy physics.
Soliton pair creation at finite temperatures
International Nuclear Information System (INIS)
Grigoriev, D.Yu.; Rubakov, V.A.
1988-01-01
Creation of soliton-antisoliton pairs at finite temperature is considered within a (1+1)-dimensional model of a real scalar field. It is argued that at certain temperatures, the soliton pair creation in quantum theory can be investigated by studying classical field evolution in real time. The classical field equations are solved numerically, and the pair creation rate and average number of solitons are evaluated. No peculiar suppression of the rate is observed. Some results on the sphaleron transitions in (1+1)-dimensional abelian Higgs model are also presented. (orig.)
Spectral tunneling of lattice nonlocal solitons
International Nuclear Information System (INIS)
Kartashov, Yaroslav V.; Torner, Lluis; Vysloukh, Victor A.
2010-01-01
We address spectral tunneling of walking spatial solitons in photorefractive media with nonlocal diffusion component of the nonlinear response and an imprinted shallow optical lattice. In contrast to materials with local nonlinearities, where solitons traveling across the lattice close to the Bragg angle suffer large radiative losses, in photorefractive media with diffusion nonlinearity resulting in self-bending, solitons survive when their propagation angle approaches and even exceeds the Bragg angle. In the spatial frequency domain this effect can be considered as tunneling through the band of spatial frequencies centered around the Bragg frequency where the spatial group velocity dispersion is positive.
Laser generated soliton waveguides in photorefractive crystals
International Nuclear Information System (INIS)
Vlad, V.I.; Fazio, E.; Bertolotti, M.; Bosco, A.; Petris, A.
2005-01-01
Non-linear photo-excited processes using the photorefractive effect are revisited with emphasis on spatial soliton generation in special laser beam propagation conditions. The soliton beams can create reversible or irreversible single-mode waveguides in the propagating materials. The important features are the 3D orientation and graded index profile matched to the laser fundamental mode. Bright spatial solitons are theoretically demonstrated and experimentally observed for the propagation of c.w. and pulsed femtosecond laser beams in photorefractive materials such as Bi 12 SiO 20 (BSO) and lithium niobate crystals. Applications in high coupling efficiency, adaptive optical interconnections and photonic crystal production are possible
Soliton Compton Mass from Auto-Parametric Wave-Soliton Coupling
Binder, B
2002-01-01
In this paper a self-excited Rayleigh-type system models the auto-parametric wave-soliton coupling via phase fluctuations. The parameter of dissipative terms determine not only the most likely quantum coupling between solitons and linear waves but also the most likely mass of the solitons. Phase fluctuations are mediated by virtual photons coupling at light-velocity in a permanent Compton scattering process. With a reference to the SI-units and proper scaling relations in length and velocity, the final result shows a highly interesting sequence: the likely soliton Compton mass is about 1.00138 times the neutron and 1.00276 times the proton mass.
Interaction between counter-streaming ion-acoustic solitons and the Langmuir waves
International Nuclear Information System (INIS)
Basovich, A.Ya.; Gromov, E.M.; Talanov, V.I.
1984-01-01
The interaction between strong counter-streaming ion-acoustic solitons and the Langmuir waves is considered. At first the Langmuir waves spectrum transformation by counter-streaming ion-acoustic solutions of a preset amplitude e has been found. An increase in the frequency and number of the Langmuir waves due to the Doppler effect in the course of multiple reflection from the f front soliton slope has been determined and the wave number range in which the confinement of the Langmuir waves by counter-streaning solitons is possible has s been found. It is shown that the time of the Langmuir wave transformation into the short-wave region under the effect of the counter-streaming soliton may y be short as compared with the time of the Langmuir wave diffusion into the Landau damping region under the effect of random fields of ion-acoustic waves. In the adiabatic fpproximation changes in the counter-streaming ion acoustic parameters of solitons owing to the Langmuir waves have been
Dark-dark-soliton dynamics in two density-coupled Bose-Einstein condensates
Morera, I.; Mateo, A. Muñoz; Polls, A.; Juliá-Díaz, B.
2018-04-01
We study the one-dimensional dynamics of dark-dark solitons in the miscible regime of two density-coupled Bose-Einstein condensates having repulsive interparticle interactions within each condensate (g >0 ). By using an adiabatic perturbation theory in the parameter g12/g , we show that, contrary to the case of two solitons in scalar condensates, the interactions between solitons are attractive when the interparticle interactions between condensates are repulsive g12>0 . As a result, the relative motion of dark solitons with equal chemical potential μ is well approximated by harmonic oscillations of angular frequency wr=(μ /ℏ ) √{(8 /15 ) g12/g } . We also show that, in finite systems, the resonance of this anomalous excitation mode with the spin-density mode of lowest energy gives rise to alternating dynamical instability and stability fringes as a function of the perturbative parameter. In the presence of harmonic trapping (with angular frequency Ω ) the solitons are driven by the superposition of two harmonic motions at a frequency given by w2=(Ω/√{2 }) 2+wr2 . When g12<0 , these two oscillators compete to give rise to an overall effective potential that can be either single well or double well through a pitchfork bifurcation. All our theoretical results are compared with numerical solutions of the Gross-Pitaevskii equation for the dynamics and the Bogoliubov equations for the linear stability. A good agreement is found between them.
Non-linear Evolution of the Transverse Instability of Plane-Envelope Solitons
DEFF Research Database (Denmark)
Janssen, Peter A. E. M.; Juul Rasmussen, Jens
1983-01-01
The nonlinear evolution of the transverse instability of plane envelope soliton solutions of the nonlinear Schrödinger equation is investigated. For the case where the spatial derivatives in the two‐dimensional nonlinear Schrödinger equation are elliptic a critical transverse wavenumber is found...