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.
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....
Stable solitons of quadratic ginzburg-landau equations
Crasovan; Malomed; Mihalache; Mazilu; Lederer
2000-07-01
We present a physical model based on coupled Ginzburg-Landau equations that supports stable temporal solitary-wave pulses. The system consists of two parallel-coupled cores, one having a quadratic nonlinearity, the other one being effectively linear. The former core is active, with bandwidth-limited amplification built into it, while the latter core has only losses. Parameters of the model can be easily selected so that the zero background is stable. The model has nongeneric exact analytical solutions in the form of solitary pulses ("dissipative solitons"). Direct numerical simulations, using these exact solutions as initial configurations, show that they are unstable; however, the evolution initiated by the exact unstable solitons ends up with nontrivial stable localized pulses, which are very robust attractors. Direct simulations also demonstrate that the presence of group-velocity mismatch (walkoff) between the two harmonics in the active core makes the pulses move at a constant velocity, but does not destabilize them.
Solitons in nonlocal nonlinear media: Exact solutions
DEFF Research Database (Denmark)
Krolikowski, Wieslaw; Bang, Ole
2001-01-01
We investigate the propagation of one-dimensional bright and dark spatial solitons in a nonlocal Kerr-like media, in which the nonlocality is of general form. We find an exact analytical solution to the nonlinear propagation equation in the case of weak nonlocality. We study the properties...... of these solitons and show their stability....
Geometric characteristics of the solitonic solution in the case of finite density
Zhunussova, Zhanat; Dosmagulova, Karlygash
2015-09-01
Some exact solutions of nonlinear partial differential equations are widely investigated both mathematical and physical points of view. Physically interesting solution as solitonic is well known. Also solitonic solution have simple behavior in bumping and are stable. There are various methods for searching of these exact solutions.
Topological and non-topological soliton solutions to some time ...
Indian Academy of Sciences (India)
topological soliton solutions to some time-fractional differential equations. M MIRZAZADEH ... Biswas et al [21,23–27] obtained optical solitons and soliton ..... nonlinear fractional partial differential equations in mathematical and physical sciences.
One-soliton solutions from Laplace's seed
Indian Academy of Sciences (India)
One-soliton solutions of axially symmetric vacuum Einstein ﬁeld equations are presented in this paper. Two sets of Laplace's solutions are used as seed and it is shown that the derived solutions reduce to some already known solutions when the constants are properly adjusted. An analysis of the solutions in terms of the ...
One-soliton solutions from Laplace's seed
Indian Academy of Sciences (India)
Abstract. One-soliton solutions of axially symmetric vacuum Einstein field equations are pre- sented in this paper. Two sets of Laplace's solutions are used as seed and it is shown that the derived solutions reduce to some already known solutions when the constants are properly adjusted. An analysis of the solutions in ...
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 helical solitons in optical media
Indian Academy of Sciences (India)
Besides that, these solitons are objects of fundamental interest. To fully examine their stability, it is crucially important to consider collisions between them, and their collisions with fundamental solitons, in (ordinary or hollow) optical ﬁbres. We introduce a system of coupled nonlinear Schrödinger equations for the ...
Stable helical solitons in optical media
Indian Academy of Sciences (India)
case is when the centres of the colliding solitons exactly coincide atz =0. In this case, δωl is found by straightforward integration of eq. (14) from z = 0 to z = +∞. The result can be presented in a more natural form, multiplying the net frequency shift by the soliton's temporal width (i.e., normalizing the frequency shift to the ...
Multi loop soliton solutions and their interactions in the Degasperis-Procesi equation
Stalin, S.; Senthilvelan, M.
2012-01-01
In this article, we construct loop soliton solutions and mixed soliton - loop soliton solution for the Degasperis-Procesi equation. To explore these solutions we adopt the procedure given by Matsuno. By appropriately modifying the $\\tau$-function given in the above paper we derive these solutions. We present the explicit form of one and two loop soliton solutions and mixed soliton - loop soliton solutions and investigate the interaction between (i) two loop soliton solutions in different para...
Stable Langmuir solitons in plasma with diatomic ions
Directory of Open Access Journals (Sweden)
M. Dvornikov
2013-08-01
Full Text Available We study stable axially and spherically symmetric spatial solitons in plasma with diatomic ions. The stability of a soliton against collapse is provided by the interaction of induced electric dipole moments of ions with the rapidly oscillating electric field of a plasmoid. We derive the new cubic-quintic nonlinear Schrödinger equation, which governs the soliton dynamics and numerically solve it. Then we discuss the possibility of implementation of such plasmoids in realistic atmospheric plasma. In particular, we suggest that spherically symmetric Langmuir solitons, described in the present work, can be excited at the formation stage of long-lived atmospheric plasma structures. The implication of our model for the interpretation of the results of experiments for the plasmoids generation is discussed.
Directory of Open Access Journals (Sweden)
Muhammad Arshad
Full Text Available The nonlinear Schrödinger equations (NLSEs describe the promulgation of ultra-short pluse in optical fibers. The modify unstable nonlinear Schrödinger equation (mUNLSE is a universal equation of the class of nonlinear integrable systems in NLSEs, which governs certain instabilities of modulated wave-trains. This equation also describes the time evolution of disturbances in marginally stable or unstable media. In the current work, the aim is to investigate the mUNLSE analytically by utilizing proposed modified extended mapping method. New exact solutions are constructed in the different form such as exact dark soliton, exact bright soliton, bright-dark soliton, solitary wave, elliptic function in different form and periodic solutions of mUNLSE. Furthermore, we also present the formation conditions of the bright soliton and dark soliton of this equation. The modulation instability analysis is implemented to discuss the stability analysis of the attained solutions and the movement role of the waves is examined, which confirms that all constructed solutions are exact and stable. Keywords: Modify unstable nonlinear schrödinger equation, Modified extended mapping method, bright and dark solitons, Solitary wave solutions, Elliptic function solutions, periodic solutions
Shozo, TAKENO; Department of Physics, Kyoto Technical University
1982-01-01
It is shown that for the two-and three-dimensional sine-Gordon equations there exist exact multi-(resonant-soliton)-soliton solutions and vortex-like solutions, in addition to exact multi-soliton and resonant-soliton solutions.
Bright and dark soliton solutions of the (3+ 1)-dimensional ...
Indian Academy of Sciences (India)
In this paper, we obtain the 1-soliton solutions of the (3 + 1)-dimensional generalized Kadomtsev–Petviashvili (gKP) equation and the generalized Benjamin equation. By using two solitary wave ansatz in terms of sech p and tanh p functions, we obtain exact analytical bright and dark soliton solutions for the considered ...
Soliton solutions of some nonlinear evolution equations with time ...
Indian Academy of Sciences (India)
Home; Journals; Pramana – Journal of Physics; Volume 80; Issue 2. Soliton solutions of some nonlinear evolution equations with time-dependent coefficients ... In this paper, we obtain exact soliton solutions of the modified KdV equation, inho-mogeneous nonlinear Schrödinger equation and (, ) equation with variable ...
Analytical multi-soliton solutions of a (2+1)-dimensional breaking soliton equation.
Wang, Shao-Fu
2016-01-01
The analytical solutions for a (2+1)-dimensional breaking solution equation is proposed in this paper by using mapping and projective method darboux transformation, and Some exact propagating solutions are constructed for this Breaking equation, and the M × N multi-soliton could be obtained by using Weierstrassp function and setting the perfect parameters. The potential application of breaking Soliton equation will be of great interest in future research.
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
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.
Euler potentials for the MHD Kamchatnov-Hopf soliton solution
Semenov, VS; Korovinski, DB; Biernat, HK
2002-01-01
In the MHD description of plasma phenomena the concept of magnetic helicity turns out to be very useful. We present here an example of introducing Euler potentials into a topological MHD soliton which has non-trivial helicity. The MHD soliton solution (Kamchatnov, 1982) is based on the Hopf
Lax Integrability and Soliton Solutions for a Nonisospectral Integrodifferential System
Directory of Open Access Journals (Sweden)
Sheng Zhang
2017-01-01
Full Text Available Searching for integrable systems and constructing their exact solutions are of both theoretical and practical value. In this paper, Ablowitz–Kaup–Newell–Segur (AKNS spectral problem and its time evolution equation are first generalized by embedding a new spectral parameter. Based on the generalized AKNS spectral problem and its time evolution equation, Lax integrability of a nonisospectral integrodifferential system is then verified. Furthermore, exact solutions of the nonisospectral integrodifferential system are formulated through the inverse scattering transform (IST method. Finally, in the case of reflectionless potentials, the obtained exact solutions are reduced to n-soliton solutions. When n=1 and n=2, the characteristics of soliton dynamics of one-soliton solutions and two-soliton solutions are analyzed with the help of figures.
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.
Static and stationary multiple soliton solutions to the Einstein equations
International Nuclear Information System (INIS)
Letelier, P.S.
1985-01-01
The application of the Belinsky--Zakharov solution-generating technique, i.e., the inverse scattering method, to generate stationary axially symmetric solutions to the vacuum Einstein equations is reduced to a single quadrature when the seed solution is diagonal. The possibility of having real odd-number soliton solutions is investigated. These solutions represent solitonic perturbations of Euclidean metrics. The possibility of using instantons as seed solutions is also investigated. The one- and two-soliton solutions generated from a diagonal seed solution are studied. As an application, a unified derivation of some well-known static solutions, like the Schwarzschild metric and the Chazy--Curzon metric, as well as other new metrics is presented. By using these metrics as seed solutions, some known stationary solutions, like the Kerr-NUT metric, the double Kerr metric, and the rotating Weyl C-metric, as well as other new metrics are also derived in a unified way
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.
The quasi-line soliton: Solutions to the Davey-Stewartson I equation
Arai, Takahito
2012-01-01
[Abstract] A periodic soliton is turned into a line soliton accordingly as a parameter point approaches to the boundary of the existing domain in the parameter space for a non-singular periodic soliton solution. We will call the periodic soliton solution with parameters of the neighborhood of the boundary a quasi-line soliton in this paper. We will examine that a periodic soliton turn into the line soliton as the parameter point of a periodic soliton approaches to the neighborhood of the boun...
Stable gray soliton pinned by a defect in a microcavity-polariton condensate.
Chen, Ting-Wei; Hsieh, Wen-Feng; Cheng, Szu-Cheng
2015-09-21
We study the spatially localized dark state, called dark soliton, in a one-dimensional system of the non-resonantly pumped microcavity-polariton condensate (MPC). From the recent work by Xue and Matuszewski [Phys. Rev. Lett. 112, 216401 (2014)], we know that the dark soliton in the pure MPC system is unstable. But we find that a dark soliton pinned by a defect in the impure MPC becomes a gray soliton and can be stabilized by the presence of a defect. Moreover, the stable regime of the gray soliton is given in terms of the defect strength and pump parameter.
Stable spatial and spatiotemporal optical soliton in the core of an optical vortex.
Adhikari, S K
2015-10-01
We demonstrate a robust, stable, mobile, two-dimensional (2D) spatial and three-dimensional (3D) spatiotemporal optical soliton in the core of an optical vortex, while all nonlinearities are of the cubic (Kerr) type. The 3D soliton can propagate with a constant velocity along the vortex core without any deformation. Stability of the soliton under a small perturbation is established numerically. Two such solitons moving along the vortex core can undergo a quasielastic collision at medium velocities. Possibilities of forming such a 2D spatial soliton in the core of a vortical beam are discussed.
Soliton solutions for some x-dependent nonlinear evolution equations
International Nuclear Information System (INIS)
Wang, Pan
2014-01-01
Under investigation in this paper are two x-dependent nonlinear evolution equations: the generalized x-dependent nonlinear Schrödinger (NLS) equation and the modified Korteweg–de Vries (KdV) equation. With the help of Hirota method and symbolic computation, the one- and two-soliton solutions have been obtained for the generalized x-dependent NLS and KdV equations. Propagation and evolution of one soliton have been investigated through the physical quantities of amplitude, width and velocity. The effects of the parameters in the equations on the interaction of two solitons have been studied analytically and graphically. (paper)
N-Soliton Solutions of the Nonisospectral Generalized Sawada-Kotera Equation
Directory of Open Access Journals (Sweden)
Jian Zhou
2014-01-01
Full Text Available The soliton interaction is investigated based on solving the nonisospectral generalized Sawada-Kotera (GSK equation. By using Hirota method, the analytic one-, two-, three-, and N-soliton solutions of this model are obtained. According to those solutions, the relevant properties and features of line-soliton and bright-soliton are illustrated. The results of this paper will be useful to the study of soliton resonance in the inhomogeneous media.
New types of exact quasi-soliton solutions in metamaterials
International Nuclear Information System (INIS)
Yang, Rongcao; Min, Xuemin; Tian, Jinping; Xue, Wenrui; Zhang, Wenmei
2016-01-01
We consider a generalized nonlinear Schrödinger equation describing the propagation of ultrashort pulses in metamaterials (MMs) and present three new types of exact bright, dark, bright-grey quasi-solitons with a free constant associated with their amplitudes, pulse widths and formation conditions. Based on the Drude model, we analyze the existence regions and characteristics of these quasi-solitons in MMs. The results show that these bright and dark (grey) quasi-solitons can exist in wider regions of MMs and their intensities and pulse widths can be adjusted by choosing a suitable free constant. Furthermore, we take the third type of quasi-soliton solution as an example to numerically discuss the stabilities under slight perturbations of the frequency and the initial pulse width. The obtained results are helpful in exploring more solitary waves in MMs and providing a new reference for experimental verification. (paper)
Stable two-dimensional dispersion-managed soliton
International Nuclear Information System (INIS)
Abdullaev, Fatkhulla Kh.; Baizakov, Bakhtiyor B.; Salerno, Mario
2003-01-01
The existence of a dispersion-managed soliton in two-dimensional nonlinear Schroedinger equation with periodically varying dispersion has been explored. The averaged equations for the soliton width and chirp are obtained which successfully describe the long time evolution of the soliton. The slow dynamics of the soliton around the fixed points for the width and chirp are investigated and the corresponding frequencies are calculated. Analytical predictions are confirmed by direct partial differential equation (PDE) and ordinary differential equation (ODE) simulations. Application to a Bose-Einstein condensate in optical lattice is discussed. The existence of a dispersion-managed matter-wave soliton in such system is shown
Indian Academy of Sciences (India)
generalized Korteweg–de Vries equations admit genuine soliton solutions besides com- pacton solitary waves. For models which admit stable compactons having a width which is independent of their amplitude and those which possess unstable compacton solutions the Painlevé test fails, such that no soliton solutions can ...
Energy Technology Data Exchange (ETDEWEB)
Lebedev, M. E., E-mail: gloriouslair@gmail.com, E-mail: galfimov@yahoo.com; Alfimov, G. L., E-mail: gloriouslair@gmail.com, E-mail: galfimov@yahoo.com [National Research University of Electronic Technology MIET, Zelenograd, Moscow 124498 (Russian Federation); Malomed, Boris A., E-mail: malomed@post.tau.ac.il [Department of Physical Electronics, School of Electrical Engineering, Faculty of Engineering, Tel Aviv University, Tel Aviv 69978 (Israel); Laboratory of Nonlinear-Optical Informatics, ITMO University, St. Petersburg 197101 (Russian Federation)
2016-07-15
We develop a general classification of the infinite number of families of solitons and soliton complexes in the one-dimensional Gross-Pitaevskii/nonlinear Schrödinger equation with a nonlinear lattice pseudopotential, i.e., periodically modulated coefficient in front of the cubic term, which takes both positive and negative local values. This model finds direct implementations in atomic Bose-Einstein condensates and nonlinear optics. The most essential finding is the existence of two branches of dipole solitons (DSs), which feature an antisymmetric shape, being essentially squeezed into a single cell of the nonlinear lattice. This soliton species was not previously considered in nonlinear lattices. We demonstrate that one branch of the DS family (namely, which obeys the Vakhitov-Kolokolov criterion) is stable, while unstable DSs spontaneously transform into stable fundamental solitons (FSs). The results are obtained in numerical and approximate analytical forms, the latter based on the variational approximation. Some stable bound states of FSs are found too.
Li, H. M.; Zhao, J. Q.; You, L. Y.
2015-10-01
We investigate the explicit matter-wave soliton solutions of the cubic-quintic nonlinear Schrödinger equation with spatiotemporal modulation of the nonlinearities and potentials. With a systematic way, we construct some integrable systems with localized cubic-quintic nonlinearities and an infinite number of potentials, including optical lattice potential and combined time-dependent magnetic-optical potentials in the form of linear-lattice, harmonic-lattice and harmonic-linear-lattice ones. Also, corresponding analytical localized soliton solutions in terms of Mathieu and elliptic functions are studied, such as snake solitons, moving breathing solitons and oscillating solitons. Finally, some stable solitons are found by means of the stability analysis of the exact solutions with the split-step Fourier transform method.
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)
Soliton solutions of some nonlinear evolution equations with time ...
Indian Academy of Sciences (India)
Dark and bright soliton; KdV equation; nonlinear Schrödinger equation; G(m, n) equation. PACS Nos 42.81.Dp; 42.65.Tg; 05.45.Yv. 1. Introduction. To find exact solutions of the nonlinear evolution equations (NLEEs) is one of the cen- tral themes in mathematics and physics. In recent years, many powerful methods have.
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 ...
Superregular solitonic solutions: a novel scenario for the nonlinear stage of modulation instability
International Nuclear Information System (INIS)
Gelash, A A; Zakharov, V E
2014-01-01
We describe a general N-solitonic solution of the focusing nonlinear Schrödinger equation in the presence of a condensate by using the dressing method. We give the explicit form of one- and two-solitonic solutions and study them in detail as well as solitonic atoms and degenerate solutions. We distinguish a special class of solutions that we call regular solitonic solutions. Regular solitonic solutions do not disturb phases of the condensate at infinity by coordinate. All of them can be treated as localized perturbations of the condensate. We find a broad class of superregular solitonic solutions which are small perturbations at a certain moment of time. Superregular solitonic solutions are generated by pairs of poles located on opposite sides of the cut. They describe the nonlinear stage of the modulation instability of the condensate and play an important role in the theory of freak waves. (invited article)
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
Soliton and Similarity Solutions of Ν = 2, 4 Supersymmetric Equations
Directory of Open Access Journals (Sweden)
Laurent Delisle
2012-08-01
Full Text Available We produce soliton and similarity solutions of supersymmetric extensions of Burgers, Korteweg–de Vries and modified KdV equations. We give new representations of the τ -functions in Hirota bilinear formalism. Chiral superfields are used to obtain such solutions. We also introduce new solitons called virtual solitons whose nonlinear interactions produce no phase shifts.
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.
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.
Quadratic solitons as nonlocal solitons
DEFF Research Database (Denmark)
Nikolov, Nikola Ivanov; Neshev, D.; Bang, Ole
2003-01-01
We show that quadratic solitons are equivalent to solitons of a nonlocal Kerr medium. This provides new physical insight into the properties of quadratic solitons, often believed to be equivalent to solitons of an effective saturable Kerr medium. The nonlocal analogy also allows for analytical...... solutions and the prediction of bound states of quadratic solitons....
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.
Cheng, Wen-Guang; Li, Biao; Chen, Yong
2015-05-01
In this paper, the truncated Painlevé analysis and the consistent tanh expansion (CTE) method are developed for the (2+1)-dimensional breaking soliton equation. As a result, the soliton-cnoidal wave interaction solution of the equation is explicitly given, which is difficult to be found by other traditional methods. When the value of the Jacobi elliptic function modulus m = 1, the soliton-cnoidal wave interaction solution reduces back to the two-soliton solution. The method can also be extended to other types of nonlinear evolution equations in mathematical physics. Supported by National Natural Science Foundation of China under Grant Nos. 11271211, 11275072, 11435005, and K.C. Wong Magna Fund in Ningbo University
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
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.
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)
A New Expression of Soliton Solution to the Ultradiscrete Toda Equation
Nagai, Hidetomo
2008-01-01
A new type of multi-soliton solution to the ultradiscrete Toda equation is proposed. The solution can be transformed into another expression of solution in a perturbation form. A direct proof of the solution is also given.
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.
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.
Approximate solutions for half-dark solitons in spinor non-equilibrium Polariton condensates
Energy Technology Data Exchange (ETDEWEB)
Pinsker, Florian, E-mail: florian.pinsker@gmail.com
2015-11-15
In this work I generalize and apply an analytical approximation to analyze 1D states of non-equilibrium spinor polariton Bose–Einstein condensates (BEC). Solutions for the condensate wave functions carrying black solitons and half-dark solitons are presented. The derivation is based on the non-conservative Lagrangian formalism for complex Ginzburg–Landau type equations (cGLE), which provides ordinary differential equations for the parameters of the dark soliton solutions in their dynamic environment. Explicit expressions for the stationary dark soliton solution are stated. Subsequently the method is extended to spin sensitive polariton condensates, which yields ordinary differential equations for the parameters of half-dark solitons. Finally a stationary case with explicit expressions for half-dark solitons is presented.
On Kaup-Kupershchmidt-type equations and their soliton solutions
Gerdjikov, V. S.
2016-09-01
We start with the Lax representation for the Kaup-Kupersschmidt equation (KKE). We outline the deep relation between the scalar Lax operator and the matrix Lax operators related to Kac-Moody algebras. Then we derive the MKdV equations gauge equivalent to the KKE. Next we outline the symmetry and the spectral properties of the relevant Lax operator. Using the dressing Zakharov-Shabat method we demonstrate that the MKdV and KKE have two types of one-soliton solutions and briefly comment on their properties.
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.
Multi-kink solutions and soliton fission and fusion of Sharma-Tasso-Olver equation
International Nuclear Information System (INIS)
Chen Aihua
2010-01-01
From the Levi spectral problem, we obtain two basic Darboux transformations of the Sharma-Tasso-Olver equation. Then from the trivial seed solution, we obtain multi-kink solutions and soliton fission and fusion solutions of this equation.
Chen, Yong; Yan, Zhenya
2018-04-01
We demonstrate the parity-time- (PT-) symmetric harmonic-Gaussian potential with unbounded gain-and-loss distribution can support entirely-real linear spectra, stable spatial and spatio-temporal solitons in an inhomogeneous nonlinear medium (e.g., cubic nonlinear Schrödinger equation with the self-focusing and defocusing cases). Exact analytical solitons are derived in both one-dimensional (1D) and higher-dimensional (e.g., 2D, 3D) geometries such that they are verified to be stable in the given parameters regions. Particularly, several families of numerical fundamental solitons (especially the 1D double-peaked solitons, 2D vortex solitons, and 3D double bullets) can be found to be stable around the propagation parameters for exact solitons. Other significant properties of solitons are also explored including the interactions of solitons, stable soliton excitations, and transverse power flows. The results may excite the corresponding theoretical analysis and experiment designs.
Trigonal curves and algebro-geometric solutions to soliton hierarchies I.
Ma, Wen-Xiu
2017-07-01
This is the first part of a study, consisting of two parts, on Riemann theta function representations of algebro-geometric solutions to soliton hierarchies. In this part, using linear combinations of Lax matrices of soliton hierarchies, we introduce trigonal curves by their characteristic equations, explore general properties of meromorphic functions defined as ratios of the Baker-Akhiezer functions, and determine zeros and poles of the Baker-Akhiezer functions and their Dubrovin-type equations. We analyse the four-component AKNS soliton hierarchy in such a way that it leads to a general theory of trigonal curves applicable to construction of algebro-geometric solutions of an arbitrary soliton hierarchy.
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)
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.)
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
Directory of Open Access Journals (Sweden)
Hongwei Yang
2016-01-01
Full Text Available The exact rational solutions, quasi-periodic wave solutions, and N-soliton solutions of 3 + 1 dimensional Jimbo-Miwa equation are acquired, respectively, by using the Hirota method, whereafter the rational solutions are also called algebraic solitary waves solutions and used to describe the squall lines phenomenon and explained possible formation mechanism of the rainstorm formation which occur in the atmosphere, so the study on the rational solutions of soliton equations has potential application value in the atmosphere field; the soliton fission and fusion are described based on the resonant solution which is a special form of the N-soliton solutions. At last, the interactions of the solitons are shown with the aid of N-soliton solutions.
Trigonal curves and algebro-geometric solutions to soliton hierarchies II.
Ma, Wen-Xiu
2017-07-01
This is a continuation of a study on Riemann theta function representations of algebro-geometric solutions to soliton hierarchies. In this part, we straighten out all flows in soliton hierarchies under the Abel-Jacobi coordinates associated with Lax pairs, upon determining the Riemann theta function representations of the Baker-Akhiezer functions, and generate algebro-geometric solutions to soliton hierarchies in terms of the Riemann theta functions, through observing asymptotic behaviours of the Baker-Akhiezer functions. We emphasize that we analyse the four-component AKNS soliton hierarchy in such a way that it leads to a general theory of trigonal curves applicable to construction of algebro-geometric solutions of an arbitrary soliton hierarchy.
Reduction and New Explicit Solutions of (2+1)-Dimensional Breaking Soliton Equation
Tian, Ying-Hui; Chen, Han-Lin; Liu, Xi-Qiang
2006-01-01
By applying the Lie group method, the (2+1)-dimensional breaking soliton equation is reduced to some (1+1)-dimensional nonlinear equations. Based upon some new explicit solutions of the (2+1)-dimensional breaking soliton equation are obtained.
Soliton solutions describing charged particle propagation in a system with self-induction
International Nuclear Information System (INIS)
Mitropol'skij, I.A.; Shuvaev, A.G.
1991-01-01
Soliton solutions of the equations describing charged particle motion in an inductive feedback system are derived for quantum and classical cases. Possible existence of soliton bound states is shown. Conditions of longitudinal focusing of particles which propagate at different initial velocities in a nonlinear medium are 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
Symmetry Reduction and Exact Solutions of the (3+1)-Dimensional Breaking Soliton Equation
Wang, Ling; Dong, Zhong-Zhou
2008-10-01
By means of the generalized direct method, a relationship is constructed between the new solutions and the old ones of the (3+1)-dimensional breaking soliton equation. Based on the relationship, a new solution is obtained by using a given solution of the equation. The symmetry is also obtained for the (3+1)-dimensional breaking soliton equation. By using the equivalent vector of the symmetry, we construct a seven-dimensional symmetry algebra and get the optimal system of group-invariant solutions. To every case of the optimal system, the (3+1)-dimensional breaking soliton equation is reduced and some solutions to the reduced equations are obtained. Furthermore, some new explicit solutions are found for the (3+1)-dimensional breaking soliton equation.
Symmetry Reduction and Exact Solutions of the (3+1)-Dimensional Breaking Soliton Equation
International Nuclear Information System (INIS)
Wang Ling; Dong Zhongzhou
2008-01-01
By means of the generalized direct method, a relationship is constructed between the new solutions and the old ones of the (3+1)-dimensional breaking soliton equation. Based on the relationship, a new solution is obtained by using a given solution of the equation. The symmetry is also obtained for the (3+1)-dimensional breaking soliton equation. By using the equivalent vector of the symmetry, we construct a seven-dimensional symmetry algebra and get the optimal system of group-invariant solutions. To every case of the optimal system, the (3+1)-dimensional breaking soliton equation is reduced and some solutions to the reduced equations are obtained. Furthermore, some new explicit solutions are found for the (3+1)-dimensional breaking soliton equation
Breathers and Soliton Solutions for a Generalization of the Nonlinear Schrödinger Equation
Directory of Open Access Journals (Sweden)
Hai-Feng Zhang
2013-01-01
Full Text Available A generalized nonlinear Schrödinger equation, which describes the propagation of the femtosecond pulse in single mode optical silica fiber, is analytically investigated. By virtue of the Darboux transformation method, some new soliton solutions are generated: the bright one-soliton solution on the zero background, the dark one-soliton solution on the continuous wave background, the Akhmediev breather which delineates the modulation instability process, and the breather evolving periodically along the straight line with a certain angle of x-axis and t-axis. Those results might be useful in the study of the femtosecond pulse in single mode optical silica fiber.
Holomorphic Vector Bundles Corresponding to some Soliton Solutions of the Ward Equation
Energy Technology Data Exchange (ETDEWEB)
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.
Polarons as stable solitary wave solutions to the Dirac-Coulomb system
Comech, Andrew; Zubkov, Mikhail
2013-11-01
We consider solitary wave solutions to the Dirac-Coulomb system both from physical and mathematical points of view. Fermions interacting with gravity in the Newtonian limit are described by the model of Dirac fermions with the Coulomb attraction. This model also appears in certain condensed matter systems with emergent Dirac fermions interacting via optical phonons. In this model, the classical soliton solutions of equations of motion describe the physical objects that may be called polarons, in analogy to the solutions of the Choquard equation. We develop analytical methods for the Dirac-Coulomb system, showing that the no-node gap solitons for sufficiently small values of charge are linearly (spectrally) stable.
Indian Academy of Sciences (India)
For models which admit stable compactons having a width which is independent of their amplitude and those which possess unstable compacton solutions the Painlevé test fails, such that no soliton solutions can be found. The Painlevé test is passed for models allowing for compacton solutions whose width is determined ...
The soliton solution of the PHI24 field theory in the Hartree approximation
International Nuclear Information System (INIS)
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
Lump Solutions and Resonance Stripe Solitons to the (2+1-Dimensional Sawada-Kotera Equation
Directory of Open Access Journals (Sweden)
Xian Li
2017-01-01
Full Text Available Based on the symbolic computation, a class of lump solutions to the (2+1-dimensional Sawada-Kotera (2DSK equation is obtained through making use of its Hirota bilinear form and one positive quadratic function. These solutions contain six parameters, four of which satisfy two determinant conditions to guarantee the analyticity and rational localization of the solutions, while the others are free. Then by adding an exponential function into the original positive quadratic function, the interaction solutions between lump solutions and one stripe soliton are derived. Furthermore, by extending this method to a general combination of positive quadratic function and hyperbolic function, the interaction solutions between lump solutions and a pair of resonance stripe solitons are provided. Some figures are given to demonstrate the dynamical properties of the lump solutions, interaction solutions between lump solutions, and stripe solitons by choosing some special parameters.
New multi-soliton solutions for generalized Burgers-Huxley equation
Directory of Open Access Journals (Sweden)
Liu Jun
2013-01-01
Full Text Available The double exp-function method is used to obtain a two-soliton solution of the generalized Burgers-Huxley equation. The wave has two different velocities and two different frequencies.
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.
Soliton solutions and their stability for the flow of relativistic fluids through channels
Lerche, I.; Wiita, P. J.
1980-01-01
The flow of a perfect relativistic fluid through channels of various cross-sections is considered with reference to models of radio galaxies. Soliton-like solutions are found and their topologies are discussed. The calculations show that these solutions are unstable. It is suggested that under realistic astrophysical conditions the growth rate of the instabilities is so slow that soliton-type blobs may persist for a significant time.
Soliton solutions and conservation laws for lossy nonlinear transmission line equation
Tchier, Fairouz; Yusuf, Abdullahi; Aliyu, Aliyu Isa; Inc, Mustafa
2017-07-01
In this article, the Lie symmetry and Ricatti-Bernoulli (RB) sub-ODE method are applied to obtain soliton solutions for nonlinear transmission line equation (NLTLs). The NLTLs is defined to be a structure whereby a short-duration pulses known as electrical solitons can be invented and disseminated. We compute conservation laws (Cls) via a non-linear self-adjointness approach. A suitable substitution for NLTLs is found and the obtained substitution makes the NLTLs equation a non-linearly self-adjoint. We establish Cls for NLTLs equation by the new Cls theorem presented by Ibragimov. We obtain trigonometric, algebraic and soliton solutions. The obtained solutions can be useful for describing the concentrations of transmission lines problems, for NLTLs. The parameters of the transmission line play a significant role in managing the original form of the soliton.
How many soliton solutions are there in the Landau-Lifshits equation for uniaxial ferromagnetic?
International Nuclear Information System (INIS)
Ostrovskaya, Natalia
2010-01-01
The well-known Akhiezer-Borovik soliton is only the simplest solution in the set of solitons in this problem. In our work the general traveling-wave solution of the Landau-Lifshits equation was found in the form of elliptic integral of the first kind avoiding the inverse scattering method. The solution contains four independent constants of integration, two of which are just shearing ones, and the additional parameter - the wave velocity. The bifurcation manifold for the solution in three-dimensional bifurcation space consists of five surfaces. On four of them there are the regions, where the soliton solutions of the classical localized form do exist. For the parameter combinations out of these surfaces there are the regions of periodic cnoidal solutions and the regions without any real solutions, but with complex ones only.
New soliton solutions of the system of equations for the ion sound and Langmuir waves
Directory of Open Access Journals (Sweden)
Seyma Tuluce Demiray
2016-11-01
Full Text Available This study is based on new soliton solutions of the system of equations for the ion sound wave under the action of the ponderomotive force due to high-frequency field and for the Langmuir wave. The generalized Kudryashov method (GKM, which is one of the analytical methods, has been tackled for finding exact solutions of the system of equations for the ion sound wave and the Langmuir wave. By using this method, dark soliton solutions of this system of equations have been obtained. Also, by using Mathematica Release 9, some graphical simulations were designed to see the behavior of these solutions.
Double Wronskian Solution and Soliton Properties of the Nonisospectral BKP Equation
Wang, Deng-Shan; Li, Xiang-Gui; Chan, C. K.; Zhou, Jian
2016-03-01
Based on the Wronskian technique and Lax pair, double Wronskian solution of the nonisospectral BKP equation is presented explicitly. The speed and dynamical influence of the one soliton are discussed. Soliton resonances of two soliton are shown by means of density distributions. Soliton properties are also investigated in the inhomogeneous media. Supported by the Research Committee of The Hong Kong Polytechnic University under Grant No. G-YM37, the AMSS-PolyU Joint Research Institute for Engineering and Management Mathematics under Grant No. 1-ZVA8, National Natural Science Foundation of China under Grant Nos. 11271362 and 11375030, Beijing Natural Science Fund Project and Beijing City Board of Education Science and Technology Key Project under Grant No. KZ201511232034, Beijing Natural Science Foundation under Grant No. 1153004, Beijing Nova Program No. Z131109000413029, and Beijing Finance Funds of Natural Science Program for Excellent Talents under Grant No. 2014000026833ZK19
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...... mechanically without approximations, and their numerical solutions at different temperatures are presented. Our conclusion is that the Davydov soliton is stable at 310 K....
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 ...
Solitons and periodic solutions to a couple of fractional nonlinear ...
Indian Academy of Sciences (India)
2014-02-26
Feb 26, 2014 ... Home; Journals; Pramana – Journal of Physics; Volume 82; Issue 3 ... First integral method; solitons; foam drainage equation; Klein–Gordon equation. ... East of Guilan, University of Guilan, Rudsar, Iran; Department of Mathematics, Faculty of Mathematical Sciences, University of Mazandaran, Babolsar, Iran ...
Soliton solutions for a quasilinear Schrödinger equation via Morse ...
Indian Academy of Sciences (India)
weak solutions to a class of quasilinear Schrödinger equation of the form. − pu − p. 2p−1 u p(u. 2. ) = f (x, u) in a bounded smooth domain. ⊂ RN with Dirichlet boundary condition. Keywords. Quasilinear Schrödinger equation; soliton solution; critical point; Morse theory; local linking. 1991 Mathematics Subject Classification.
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.
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.
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
Takahiro, AZUMA; Makoto, ENDO; Takao, KOIKAWA; Department of Mathematics, King's College London; Faculty of Liberal Arts, Dokkyo University; Department of Physics, Tokyo Metropolitan University
1991-01-01
We study a stationary and axisymmetric solution to the higher-dimensional Einstein equations and investigate its singularity structure. The solution consists of two solitons in the four-dimensional part (i.e., the Kerr solution) and n solitons in the extra dimensions. Naked singularities appear on the symmetry axis (z-axis) and/or at the event horizons of the Kerr solution. In a certain choice of integration constants there are solutions with regular event horizons.
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
Soliton-based ultra-high speed optical communications
Indian Academy of Sciences (India)
evolution of information and introduction of optical soliton solution as the stable nonlinear solution. The paper ... aged solitons will be presented to demonstrate the effectiveness of dispersion management techniques both .... Most high speed transmission systems at present use an all optical scheme with loss compensated ...
Solitons in an isolated helix chain
DEFF Research Database (Denmark)
Christiansen, Peter Leth; Zolotaryuk, Alexander; Savin, A.V.
1997-01-01
-, and third-nearest neighbors. The set of nonlinear field equations with respect to the longitudinal and transverse (torsional and radial) displacements of the chain molecules has been derived and treated. Stable nontopological soliton solutions which describe supersonic pulses of longitudinal compression...... propagating together with localized transverse thickening (bulge) and torsional stretching (untwisting) have been found. The stability properties of these (three-component) soliton solutions have been studied by using numerical techniques developed for seeking solitary-wave solutions in complex molecular...
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.
Da-Quan, Xian
2010-08-01
In this paper, the new idea of a combination of Lie group method and homoclinic test technique is first proposed to seek non-traveling wave solutions of (2 + 1)-dimensional breaking soliton equation. The system is reduced to some (1 + 1)-dimensional nonlinear equations by applying the Lie group method and solves reduced equation with homoclinic test technique. Based on this idea and with the aid of symbolic computation, some new explicit solutions of similar systems can be obtained.
Energy Technology Data Exchange (ETDEWEB)
Chen, Yang, E-mail: yayangchen@umac.mo [Department of Mathematics, University of Macau, Macau (China); Fan, Engui, E-mail: faneg@fudan.edu.cn [School of Mathematics and Key Laboratory of Mathematics for Nonlinear Science, Fudan University, Shanghai 200433 (China); Yuen, Manwai, E-mail: nevetsyuen@hotmail.com [Department of Mathematics and Information Technology, The Hong Kong Institute of Education, 10 Lo Ping Road, Tai Po, New Territories (Hong Kong)
2016-01-08
We show that, under an irrotational condition, there exists an n-dimensional Hopf–Cole transformation between the n-dimensional Burgers system and an n-dimensional heat equation. Further, as application of the Hopf–Cole transformation, two kinds of physically interesting exact solutions for the n-dimensional Burgers equations are found. In the first kind of solutions, the velocity fields are topological solitons. In the second kind of solutions, velocity fields are all multiple fusion soliton solutions. - Highlights: • Find an irrotational condition to linearize n-dimensional Burgers system. • Generalize classical Hopf–Cole transformation to n-dimensional Burgers system. • Present topological solitons and multiple fusion soliton solutions.
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.
Manikandan, N; Radhakrishnan, R; Aravinthan, K
2014-08-01
We have constructed a dark-bright N-soliton solution with 4N+3 real parameters for the physically interesting system of mixed coupled nonlinear Schrödinger equations. Using this as well as an asymptotic analysis we have investigated the interaction between dark-bright vector solitons. Each colliding dark-bright one-soliton at the asymptotic limits includes more coupling parameters not only in the polarization vector but also in the amplitude part. Our present solution generalizes the dark-bright soliton in the literature with parametric constraints. By exploiting the role of such coupling parameters we are able to control certain interaction effects, namely beating, breathing, bouncing, attraction, jumping, etc., without affecting other soliton parameters. Particularly, the results of the interactions between the bound state dark-bright vector solitons reveal oscillations in their amplitudes under certain parametric choices. A similar kind of effect was also observed experimentally in the BECs. We have also characterized the solutions with complicated structure and nonobvious wrinkle to define polarization vector, envelope speed, envelope width, envelope amplitude, grayness, and complex modulation. It is interesting to identify that the polarization vector of the dark-bright one-soliton evolves on a spherical surface instead of a hyperboloid surface as in the bright-bright case of the mixed coupled nonlinear Schrödinger equations.
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.
Extended Soliton Solutions in an Effective Action for SU(2 Yang-Mills Theory
Directory of Open Access Journals (Sweden)
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.
Soliton Perturbations, Revisited.
Herman, Russell Leland
Starting with an 'integrable' nonlinear evolution equation, we are investigating perturbations about a one soliton solution, through the inversion of a linear equation for the first order correction. This differs from the methods based on the perturbation of certain 'scattering data', as the proposed method takes place in coordinate space, and not spectral space. The method is tested on several perturbed Korteweg -DeVries equations. The damped KdV equation is studied in detail, resulting in the resolution of the controversy over the shift in the center of the soliton in favor of the results of Karpman and Maslov. Using a finite difference scheme, a numerically induced shift in the damped soliton's position is predicted through the use of perturbation theory. We extend the results of Ott and Sudan for other damped KdV equations, giving expressions for the shift in soliton position and the asymptotic form of the first order correction to the solution. Next we investigate Menyuk's case of a solution consisting of a soliton plus arbitrary initial radiation, which is subject to a Hamiltonian perturbation; and we show that the radiation must start out small. After these preliminary investigations, we turn to the stochastic KdV equation with external Gaussian white noise, zeta(x,t). For the cases of damping and no damping, the averaged soliton asymptotically becomes a Gaussian wave packet, which decays and broadens according to the same power laws as found by Wadati and Akutsu for the noise zeta(t). Next, we investigate the propagation of a modulated KP soliton and compare our results to the work of Chang. We find that singular perturbation theory cannot explain the evolution of this profile, but we can obtain good qualitative results from the solution of the Cauchy problem for the linearized KP equation. The modulations travel away from the soliton peak and decay in time, leaving a stable planar soliton behind. Finally, we discuss the application of the method to the
Singular and non-topological soliton solutions for nonlinear fractional differential equations
Ozkan, Guner
2015-10-01
In this article, the fractional derivatives are described in the modified Riemann-Liouville sense. We propose a new approach, namely an ansatz method, for solving fractional differential equations (FDEs) based on a fractional complex transform and apply it to solve nonlinear space-time fractional equations. As a result, the non-topological as well as the singular soliton solutions are obtained. This method can be suitable and more powerful for solving other kinds of nonlinear fractional FDEs arising in mathematical physics.
Ozkan, Guner; Ahmet, Bekir
2016-04-01
In this article, we establish exact solutions for the variable-coefficient Fisher-type equation. The solutions are obtained by the modified sine-cosine method and ansatz method. The soliton and periodic solutions and topological as well as the singular 1-soliton solution are obtained with the aid of the ansatz method. These solutions are important for the explanation of some practical physical problems. The obtained results show that these methods provide a powerful mathematical tool for solving nonlinear equations with variable coefficients.
Multi-soliton solutions of the Einstein equation and the Tomimatsu-Sato metric
International Nuclear Information System (INIS)
Tomimatsu, Akira; Sato, Humitaka.
1982-01-01
We present a new recognition about the Tomimatsu-Sato metric through reviewing the recent study of the stationary and axially symmetric Einstein field equation. We describe some powerful methods of solving the Einstein equation; the Baecklund transformation, the inverse scattering method and any other. These methods derive the so-called multi-soliton solution, which represents the Kerr-NUT metric or a non-linear superposition of several Kerr-NUT metrics aligned along their common rotational axis. The Tomimatsu-Sato metric of delta = N is constructed via a limiting process that the N Kerr metrics with the same mass and angular momentum approach mutually towards their complete overlapping. We investigate the space-time properties of the multi-soliton metric, by taking the two Kerr case as a typical example. (author)
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
Constructing Soliton and Kink Solutions of PDE Models in Transport and Biology
Directory of Open Access Journals (Sweden)
Vsevolod A. Vladimirov
2006-06-01
Full Text Available We present a review of our recent works directed towards discovery of a periodic, kink-like and soliton-like travelling wave solutions within the models of transport phenomena and the mathematical biology. Analytical description of these wave patterns is carried out by means of our modification of the direct algebraic balance method. In the case when the analytical description fails, we propose to approximate invariant travelling wave solutions by means of an infinite series of exponential functions. The effectiveness of the method of approximation is demonstrated on a hyperbolic modification of Burgers equation.
Jaradat, H. M.; Syam, Muhammed; Jaradat, M. M. M.; Mustafa, Zead; Moman, S.
2018-03-01
In this paper, we investigate the multiple soliton solutions and multiple singular soliton solutions of a class of the fifth order nonlinear evolution equation with variable coefficients of t using the simplified bilinear method based on a transformation method combined with the Hirota's bilinear sense. In addition, we present analysis for some parameters such as the soliton amplitude and the characteristic line. Several equation in the literature are special cases of the class which we discuss such as Caudrey-Dodd-Gibbon equation and Sawada-Kotera. Comparison with several methods in the literature, such as Helmholtz solution of the inverse variational problem, rational exponential function method, tanh method, homotopy perturbation method, exp-function method, and coth method, are made. From these comparisons, we conclude that the proposed method is efficient and our solutions are correct. It is worth mention that the proposed solution can solve many physical problems.
Chakraborty, Sushmita; Nandy, Sudipta; Barthakur, Abhijit
2015-02-01
We investigate coupled nonlinear Schrödinger equations (NLSEs) with variable coefficients and gain. The coupled NLSE is a model equation for optical soliton propagation and their interaction in a multimode fiber medium or in a fiber array. By using Hirota's bilinear method, we obtain the bright-bright, dark-bright combinations of a one-soliton solution (1SS) and two-soliton solutions (2SS) for an n-coupled NLSE with variable coefficients and gain. Crucial properties of two-soliton (dark-bright pair) interactions, such as elastic and inelastic interactions and the dynamics of soliton bound states, are studied using asymptotic analysis and graphical analysis. We show that a bright 2-soliton, in addition to elastic interactions, also exhibits multiple inelastic interactions. A dark 2-soliton, on the other hand, exhibits only elastic interactions. We also observe a breatherlike structure of a bright 2-soliton, a feature that become prominent with gain and disappears as the amplitude acquires a minimum value, and after that the solitons remain parallel. The dark 2-soliton, however, remains parallel irrespective of the gain. The results found by us might be useful for applications in soliton control, a fiber amplifier, all optical switching, and optical computing.
Topological and non-topological soliton solutions to some time ...
Indian Academy of Sciences (India)
While there are other relativistic wave equations, Klein–Gordon equation has been the most frequently studied equation for describing particle dynamics in quantum field theory [4,5]. The construction of exact and analytical travelling wave solutions of nonlinear fractional partial differential equations is one of the most impor-.
Topological and non-topological soliton solutions to some time ...
Indian Academy of Sciences (India)
This paper investigates, for the first time, the applicability and effectiveness of He's semi-inverse variational principle method and the ansatz method on systems of nonlinear fractional partial differential equations. He's semi-inverse variational principle method and the ansatz method are used to construct exact solutions of ...
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
Energy Technology Data Exchange (ETDEWEB)
Batool, Nazia; Jahangir, R. [Theoretical Plasma Physics Group, Department of Physics, Quaid-i-Azam University, Islamabad 45320 (Pakistan); National Center of Physics (NCP), Quaid-i-Azam University Campus, Islamabad (Pakistan); Masood, W. [National Center of Physics (NCP), Quaid-i-Azam University Campus, Islamabad (Pakistan); COMSATS Institute of Information Technology, Islamabad (Pakistan); Siddiq, M. [National Center of Physics (NCP), Quaid-i-Azam University Campus, Islamabad (Pakistan)
2016-08-15
In the present investigation, cylindrical Kadomstev-Petviashvili (CKP) equation is derived in pair-ion-electron plasmas to study the propagation and interaction of two solitons. Using a novel gauge transformation, two soliton solutions of CKP equation are found analytically by using Hirota's method and to the best of our knowledge have been used in plasma physics for the first time. Interestingly, it is observed that unlike the planar Kadomstev-Petviashvili (KP) equation, the CKP equation admits horseshoe-like solitary structures. Another non-trivial feature of CKP solitary solution is that the interaction parameter gets modified by the plasma parameters contrary to the one obtained for Korteweg–de Vries equation. The importance of the present investigation to understand the formation and interaction of solitons in laboratory produced pair plasmas is also highlighted.
Chiu, Hong-Yee
1990-01-01
The theory of Lee and Pang (1987), who obtained solutions for soliton stars composed of zero-temperature fermions and bosons, is applied here to quark soliton stars. Model soliton stars based on a simple physical model of the proton are computed, and the properties of the solitons are discussed, including the important problem of the existence of a limiting mass and thus the possible formation of black holes of primordial origin. It is shown that there is a definite mass limit for ponderable soliton stars, so that during cooling a soliton star might reach a stage beyond which no equilibrium configuration exists and the soliton star probably will collapse to become a black hole. The radiation of ponderable soliton stars may alter the short-wavelength character of the cosmic background radiation, and may be observed as highly redshifted objects at z of about 100,000.
Observation of Two-Dimensional Localized Jones-Roberts Solitons in Bose-Einstein Condensates
Meyer, Nadine; Proud, Harry; Perea-Ortiz, Marisa; O'Neale, Charlotte; Baumert, Mathis; Holynski, Michael; Kronjäger, Jochen; Barontini, Giovanni; Bongs, Kai
2017-10-01
Jones-Roberts solitons are the only known class of stable dark solitonic solutions of the nonlinear Schrödinger equation in two and three dimensions. They feature a distinctive elongated elliptical shape that allows them to travel without change of form. By imprinting a triangular phase pattern, we experimentally generate two-dimensional Jones-Roberts solitons in a three-dimensional atomic Bose-Einstein condensate. We monitor their dynamics, observing that this kind of soliton is indeed not affected by dynamic (snaking) or thermodynamic instabilities, that instead make other classes of dark solitons unstable in dimensions higher than one. Our results confirm the prediction that Jones-Roberts solitons are stable solutions of the nonlinear Schrödinger equation and promote them for applications beyond matter wave physics, like energy and information transport in noisy and inhomogeneous environments.
Bright and dark soliton solutions for some nonlinear fractional differential equations
Ozkan, Guner; Ahmet, Bekir
2016-03-01
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.
Kanna, T; Sakkaravarthi, K; Tamilselvan, K
2013-12-01
We consider the multicomponent Yajima-Oikawa (YO) system and show that the two-component YO system can be derived in a physical setting of a three-coupled nonlinear Schrödinger (3-CNLS) type system by the asymptotic reduction method. The derivation is further generalized to the multicomponent case. This set of equations describes the dynamics of nonlinear resonant interaction between a one-dimensional long wave and multiple short waves. The Painlevé analysis of the general multicomponent YO system shows that the underlying set of evolution equations is integrable for arbitrary nonlinearity coefficients which will result in three different sets of equations corresponding to positive, negative, and mixed nonlinearity coefficients. We obtain the general bright N-soliton solution of the multicomponent YO system in the Gram determinant form by using Hirota's bilinearization method and explicitly analyze the one- and two-soliton solutions of the multicomponent YO system for the above mentioned three choices of nonlinearity coefficients. We also point out that the 3-CNLS system admits special asymptotic solitons of bright, dark, anti-dark, and gray types, when the long-wave-short-wave resonance takes place. The short-wave component solitons undergo two types of energy-sharing collisions. Specifically, in the two-component YO system, we demonstrate that two types of energy-sharing collisions-(i) energy switching with opposite nature for a particular soliton in two components and (ii) similar kind of energy switching for a given soliton in both components-result for two different choices of nonlinearity coefficients. The solitons appearing in the long-wave component always exhibit elastic collision whereas those of short-wave components exhibit standard elastic collisions only for a specific choice of parameters. We have also investigated the collision dynamics of asymptotic solitons in the original 3-CNLS system. For completeness, we explore the three-soliton interaction
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)
Wazwaz, Abdul-Majid
2012-06-01
In this work, we explore a variety of solitary wave ansatze and periodic wave ansatze to some nonlinear equations. Three complex systems of nonlinear equations that appear in mathematical physics are investigated. We derive abundant soliton and periodic wave solutions for the coupled Higgs field equation, the Maccari system and the Hirota-Maccari system. The results obtained show that these three coupled equations exhibit the richness of explicit solutions: solitons, periodic and rational wave solutions.
Guner, Ozkan; Korkmaz, Alper; Bekir, Ahmet
2017-02-01
Dark soliton solutions for space-time fractional Sharma-Tasso-Olver and space-time fractional potential Kadomtsev-Petviashvili equations are determined by using the properties of modified Riemann-Liouville derivative and fractional complex transform. After reducing both equations to nonlinear ODEs with constant coefficients, the \\tanh ansatz is substituted into the resultant nonlinear ODEs. The coefficients of the solutions in the ansatz are calculated by algebraic computer computations. Two different solutions are obtained for the Sharma-Tasso-Olver equation as only one solution for the potential Kadomtsev-Petviashvili equation. The solution profiles are demonstrated in 3D plots in finite domains of time and space.
Bednyakova, Anastasia; Turitsyn, Sergei K
2015-03-20
The key to generating stable optical pulses is mastery of nonlinear light dynamics in laser resonators. Modern techniques to control the buildup of laser pulses are based on nonlinear science and include classical solitons, dissipative solitons, parabolic pulses (similaritons) and various modifications and blending of these methods. Fiber lasers offer remarkable opportunities to apply one-dimensional nonlinear science models for the design and optimization of very practical laser systems. Here, we propose a new concept of a laser based on the adiabatic amplification of a soliton pulse in the cavity-the adiabatic soliton laser. The adiabatic change of the soliton parameters during evolution in the resonator relaxes the restriction on the pulse energy inherent in traditional soliton lasers. Theoretical analysis is confirmed by extensive numerical modeling.
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
Breaking soliton equations and negative-order breaking soliton ...
Indian Academy of Sciences (India)
Home; Journals; Pramana – Journal of Physics; Volume 87; Issue 5. Breaking soliton ... We use the simplified Hirota's method to obtain multiple soliton solutions for each developed breaking soliton equation. We also develop ... WAZWAZ1. Department of Mathematics, Saint Xavier University, Chicago, IL 60655, USA ...
Guner, Ozkan; Bekir, Ahmet; Unsal, Omer; Cevikel, Adem C.
2017-01-01
In this paper, we pay attention to the analytical method named, ansatz method for finding the exact solutions of the variable-coefficient modified KdV equation and variable coefficient diffusion-reaction equation. As a result the singular 1-soliton solution is obtained. These solutions are important for the explanation of some practical physical problems. The obtained results show that these methods provides a powerful mathematical tool for solving nonlinear equations with variable coefficients. This method can be extended to solve other variable coefficient nonlinear partial differential equations.
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.
Oscillating solitons in nonlinear optics
Indian Academy of Sciences (India)
Abstract. Oscillating solitons are obtained in nonlinear optics. Analytical study of the variable- coefficient nonlinear Schrödinger equation, which is used to describe the soliton propagation in those systems, is carried out using the Hirota's bilinear method. The bilinear forms and analytic soliton solutions are derived, and the ...
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.)
Indian Academy of Sciences (India)
Home; Journals; Pramana – Journal of Physics; Volume 74; Issue 6. Compactons versus solitons ... by their amplitude. Consequently, these models admit soliton solutions in addition to compactons and are integrable. ... Centre for Mathematical Science, City University London, Northampton Square, London EC1V 0HB, UK ...
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
Stability of nonlinear ion sound waves and solitons in plasmas
International Nuclear Information System (INIS)
Infeld, E.; Rowlands, G.
1979-01-01
Large amplitude ion acoustic waves and solitons in two component plasmas are investigated for stability. The soliton solutions are found to be stable, while the nonlinear waves are always unstable, though for a significant range of parameters they are only unstable to fully three-dimensional perturbations. The results in one dimension are compared with those obtained from the Korteweg-de Vries equation, which gives stability for non linear waves and solitons. Agreement is surprisingly good for Mach numbers less than about 1.5 A three-dimensional generalization of the Korteweg-de Vries equation is considered but this leads to stability for all non linear solutions and hence is not a good model for nonlinear waves. It is, however, reasonable in the soliton limit. (author)
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.
Chiu, Hong-Yee
1990-01-01
The structure of nontopological solutions of Einstein field equations as proposed by Friedberg, Lee, and Pang (1987) is examined. This analysis incorporates finite temperature effects and pair creation. Quarks are assumed to be the only species that exist in interior of soliton stars. The possibility of primordial creation of soliton stars in the incomplete decay of the degenerate vacuum in early universe is explored. Because of dominance of pair creation inside soliton stars, the luminosity of soliton stars is not determined by its radiative transfer characteristics, and the surface temperature of soliton stars can be the same as its interior temperature. It is possible that soliton stars are intense X-ray radiators at large distances. Soliton stars are nearly 100 percent efficient energy converters, converting the rest energy of baryons entering the interior into radiation. It is possible that a sizable number of baryons may also be trapped inside soliton stars during early epochs of the universe. In addition, if soliton stars exist they could assume the role played by massive black holes in galactic centers.
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.
Energy Technology Data Exchange (ETDEWEB)
Trogdon, Thomas, E-mail: trogdon@cims.nyu.edu [Courant Institute of Mathematical Sciences, New York University, 251 Mercer St., New York, NY 10012 (United States); Deconinck, Bernard [Department of Applied Mathematics, University of Washington, Campus Box 352420, Seattle, WA 98195 (United States)
2014-01-31
All solutions of the Korteweg–de Vries equation that are bounded on the real line are physically relevant, depending on the application area of interest. Usually, both analytical and numerical approaches consider solution profiles that are either spatially localized or (quasi-)periodic. In this paper, we discuss a class of solutions that is a nonlinear superposition of these two cases: their asymptotic state for large |x| is (quasi-)periodic, but they may contain solitons, with or without dispersive tails. Such scenarios might occur in the case of localized perturbations of previously present sea swell, for instance. Such solutions have been discussed from an analytical point of view only recently. We numerically demonstrate different features of these solutions.
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....
Salerno, Mario; Quintero, Niurka R.
2001-01-01
The mechanism underlying the soliton ratchet, both in absence and in presence of noise, is investigated. We show the existence of an asymmetric internal mode on the soliton profile that couples, through the damping in the system, to the soliton translational mode. Effective soliton transport is achieved when the internal mode and the external force are phase locked. We use as a working model a generalized double sine-Gordon equation. The phenomenon is expected to be valid for generic soliton ...
One- and two-dimensional gap solitons in spin-orbit-coupled systems with Zeeman splitting
Sakaguchi, Hidetsugu; Malomed, Boris A.
2018-01-01
We elaborate a mechanism for the formation of stable solitons of the semivortex type (with vorticities 0 and 1 in their two components), populating a finite band gap in the spectrum of the spin-orbit-coupled binary Bose-Einstein condensate with the Zeeman splitting, in the two-dimensional (2D) free space, under conditions which make the kinetic-energy terms in the respective coupled Gross-Pitaevskii equations negligible. Unlike a recent work which used long-range dipole-dipole interactions to construct stable gap solitons in a similar setting, we here demonstrate that stable solitons are supported by generic local interactions of both attractive and repulsive signs, provided that the relative strength of the cross- and self-interactions in the two-component system does not exceed a critical value ≈0.77 . A boundary between stable and unstable fundamental 2D gap solitons is precisely predicted by the Vakhitov-Kolokolov criterion, while all excited states of the 2D solitons, with vorticities (m ,1 +m ) in the two components, m =1 ,2 ,... , are unstable. The analysis of the one-dimensional (1D) reduction of the system produces an exact analytical solution for the family of gap solitons which populate the entire band gap, the family being fully stable. Motion of the 1D solitons in the trapping potential is considered too, showing that their effective mass is positive or negative if the cubic nonlinearity is attractive or repulsive, respectively.
Energy Technology Data Exchange (ETDEWEB)
Ganguly, A., E-mail: gangulyasish@rediffmail.com, E-mail: aganguly@maths.iitkgp.ernet.in; Das, A., E-mail: amiya620@gmail.com [Department of Mathematics, IIT Kharagpur, Kharagpur, 721302 West Bengal (India)
2014-11-15
We consider one-dimensional stationary position-dependent effective mass quantum model and derive a generalized Korteweg-de Vries (KdV) equation in (1+1) dimension through Lax pair formulation, one being the effective mass Schrödinger operator and the other being the time-evolution of wave functions. We obtain an infinite number of conserved quantities for the generated nonlinear equation and explicitly show that the new generalized KdV equation is an integrable system. Inverse scattering transform method is applied to obtain general solution of the nonlinear equation, and then N-soliton solution is derived for reflectionless potentials. Finally, a special choice has been made for the variable mass function to get mass-deformed soliton solution. The influence of position and time-dependence of mass and also of the different representations of kinetic energy operator on the nature of such solitons is investigated in detail. The remarkable features of such solitons are demonstrated in several interesting figures and are contrasted with the conventional KdV-soliton associated with constant-mass quantum model.
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.
International Nuclear Information System (INIS)
Gai Xiaoling; Gao Yitian; Meng Dexin; Wang Lei; Sun Zhiyuan; Feng Qian; Wang Mingzhen; Yu Xin; Zhu Shunhui; Lue Xing
2010-01-01
This paper is to investigate a variable-coefficient modified Kortweg-de Vries (vc-mKdV) model, which describes some situations from fluid mechanics, ocean dynamics, and plasma mechanics. By the Ablowitz-Kaup-Newell-Segur procedure and symbolic computation, the Lax pair of the vc-MKdV model is derived. Then, based on the aforementioned Lax pair, the Darboux transformation is constructed and a new one-soliton-like solution is obtained as well. Features of the one-soliton-like solution are analyzed and graphically discussed to illustrate the influence of the variable coefficients in the solitonlike propagation. (general)
Directory of Open Access Journals (Sweden)
Xiangrong Wang
2015-01-01
Full Text Available A generalized (2+1-dimensional variable-coefficient KdV equation is introduced, which can describe the interaction between a water wave and gravity-capillary waves better than the (1+1-dimensional KdV equation. The N-soliton solutions of the (2+1-dimensional variable-coefficient fifth-order KdV equation are obtained via the Bell-polynomial method. Then the soliton fusion, fission, and the pursuing collision are analyzed depending on the influence of the coefficient eAij; when eAij=0, the soliton fusion and fission will happen; when eAij≠0, the pursuing collision will occur. Moreover, the Bäcklund transformation of the equation is gotten according to the binary Bell-polynomial and the period wave solutions are given by applying the Riemann theta function method.
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.
Self-trapped optical beams: Spatial solitons
Indian Academy of Sciences (India)
as
tons, including the soliton stability in non-Kerr media, the instability-induced soliton dynamics, and collision of solitary ... suggested as a way to stabilize such a catastrophic self-focusing and produce stable solitary waves of ...... cations of spatial optical solitons towards creating a novel generation of nonlinear optical devices ...
Breaking soliton equations and negative-order breaking soliton ...
Indian Academy of Sciences (India)
2016-10-06
Oct 6, 2016 ... as optical fibres, fluid dynamics, plasma physics, ocean engineering, chemical physics etc. are described by nonlinear equations where soliton solutions may appear. Some of these nonlinear evolution equations are integrable which give multiple soliton solutions. The study of integrable equations, that ...
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.)
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
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)
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
Chowdury, Amdad; Krolikowski, Wieslaw; Akhmediev, N
2017-10-01
We present one- and two-breather solutions of the fourth-order nonlinear Schrödinger equation. With several parameters to play with, the solution may take a variety of forms. We consider most of these cases including the general form and limiting cases when the modulation frequencies are 0 or coincide. The zero-frequency limit produces a combination of breather-soliton structures on a constant background. The case of equal modulation frequencies produces a degenerate solution that requires a special technique for deriving. A zero-frequency limit of this degenerate solution produces a rational second-order rogue wave solution with a stretching factor involved. Taking, in addition, the zero limit of the stretching factor transforms the second-order rogue waves into a soliton. Adding a differential shift in the degenerate solution results in structural changes in the wave profile. Moreover, the zero-frequency limit of the degenerate solution with differential shift results in a rogue wave triplet. The zero limit of the stretching factor in this solution, in turn, transforms the triplet into a singlet plus a low-amplitude soliton on the background. A large value of the differential shift parameter converts the triplet into a pure singlet.
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
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.
Chai, Jun; Tian, Bo; Chai, Han-Peng
2018-02-01
Investigation in this paper is given to the reduced Maxwell-Bloch equations with variable coefficients, describing the propagation of the intense ultra-short optical pulses through an inhomogeneous two-level dielectric medium. We apply the Hirota method and symbolic computation to study such equations. With the help of the dependent variable transformations, we present the variable-coefficient-dependent bilinear forms. Then, we construct the one-, two- and N-soliton solutions in analytic forms for them. Supported by the National Natural Science Foundation of China under Grant Nos. 11772017, 11272023, 11471050, the Fund of State Key Laboratory of Information Photonics and Optical Communications (Beijing University of Posts and Telecommunications), China (IPOC: 2017ZZ05), and the Fundamental Research Funds for the Central Universities of China under Grant No. 2011BUPTYB02
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.
Soliton model for elementary electric charge
International Nuclear Information System (INIS)
Chepilko, N.M.; Kobushkin, A.P.
1988-01-01
The existence and topological stability of three-dimensional solitons in Klein-Gordon field electrodynamics are proved. The central-symmetric solution to field equations, which can be interpreted as soliton model of elementary electric charge with zero spin, is constructed. The electrostatic soliton rotation is shown to result in the charge having its own magnetic-dipole field. 9 refs.; 2 figs
Scale symmetry of quantum solitons
International Nuclear Information System (INIS)
Chepilko, N.M.; Fujii, K.; Kobushkin, A.P.
1991-01-01
A collective-coordinate Lagrangian for a rotating and vibrating quantum soliton in the nonlinear σ-model is shown to possess a symmetry under scale transformation of the chiral field. Using this symmetry an integrodifferential equation for the chiral angle is obtained. A consistency condition between this equation and the Schroedinger equation for the quantum soliton is also discussed. At limiting cases (a vibrating, but not rotating soliton; or a rotating, but not vibrating soliton) the integrodifferential ones and the chiral angle becomes independent of the solution of the Schroedinger equation. 7 refs
Baskonus, Haci Mehmet; Sulaiman, Tukur Abdulkadir; Bulut, Hasan; Aktürk, Tolga
2018-03-01
In this study, using the extended sinh-Gordon equation expansion method, we construct the dark, bright, combined dark-bright optical, singular, combined singular solitons and singular periodic waves solutions to the complex cubic nonlinear Schrödinger equation with δ-potential. The conditions for the existence of the obtained solutions are given. To present the physical feature of the acquired result, the 2D and 3D graphs are plotted under the choice of suitable values of the parameters.
Soliton star in FL-non-topological soliton model and its behavior at high temperature
International Nuclear Information System (INIS)
Xiong Hejin; Li Jiarong
1992-01-01
Based on the FL-non-topological soliton model, the possibility of the formation of the FL-soliton star and its behavior at high temperature are discussed. It is found that the stable, cold and spherical FL-soliton star can be formed, under the necessary condition W > 3B. At high temperature, the FL-soliton bag disappears by the phase transition, but there may be some stellar configuration
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.
Two-dimensional matter-wave solitons and vortices in competing cubic-quintic nonlinear lattices
Gao, Xuzhen; Zeng, Jianhua
2018-02-01
The nonlinear lattice — a new and nonlinear class of periodic potentials — was recently introduced to generate various nonlinear localized modes. Several attempts failed to stabilize two-dimensional (2D) solitons against their intrinsic critical collapse in Kerr media. Here, we provide a possibility for supporting 2D matter-wave solitons and vortices in an extended setting — the cubic and quintic model — by introducing another nonlinear lattice whose period is controllable and can be different from its cubic counterpart, to its quintic nonlinearity, therefore making a fully "nonlinear quasi-crystal". A variational approximation based on Gaussian ansatz is developed for the fundamental solitons and in particular, their stability exactly follows the inverted Vakhitov-Kolokolov stability criterion, whereas the vortex solitons are only studied by means of numerical methods. Stability regions for two types of localized mode — the fundamental and vortex solitons — are provided. A noteworthy feature of the localized solutions is that the vortex solitons are stable only when the period of the quintic nonlinear lattice is the same as the cubic one or when the quintic nonlinearity is constant, while the stable fundamental solitons can be created under looser conditions. Our physical setting (cubic-quintic model) is in the framework of the Gross-Pitaevskii equation or nonlinear Schrödinger equation, the predicted localized modes thus may be implemented in Bose-Einstein condensates and nonlinear optical media with tunable cubic and quintic nonlinearities.
Solitonic fullerene structures in light atomic nuclei.
Battye, R A; Sutcliffe, P M
2001-04-30
The Skyrme model is a classical field theory which has topological soliton solutions. These solitons are candidates for describing nuclei, with an identification between the numbers of solitons and nucleons. We have computed numerically, using two different minimization algorithms, minimum energy configurations for up to 22 solitons. We find, remarkably, that the solutions for seven or more solitons have nucleon density isosurfaces in the form of polyhedra made of hexagons and pentagons. Precisely these structures arise, though at the much larger molecular scale, in the chemistry of carbon shells, where they are known as fullerenes.
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
Indian Academy of Sciences (India)
The Painlevé test is passed for models allowing for compacton solutions whose width is determined by their amplitude. Consequently, these models admit soliton solutions in ... Compactons; PT -symmetry; KdV equation; Painlevé test. .... Cooper et al [25] found that in the generalized KdV equation, i.e. m = 2, a necessary.
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
Eslami, M.; Mirzazadeh, M.; Biswas, Anjan
2013-11-01
In this paper, the resonant nonlinear Schrödinger's equation is studied with four forms of nonlinearity. This equation is also considered with time-dependent coefficients. The simplest equation method is applied to solve the governing equations and then exact 1-soliton solutions are obtained. It is shown that this method provides us with a powerful mathematical tool for solving nonlinear evolution equations with time-dependent coefficients in mathematical physics.
KP solitons, total positivity, and cluster algebras
Kodama, Yuji; Williams, Lauren K.
2011-01-01
Soliton solutions of the KP equation have been studied since 1970, when Kadomtsev and Petviashvili [Kadomtsev BB, Petviashvili VI (1970) Sov Phys Dokl 15:539–541] proposed a two-dimensional nonlinear dispersive wave equation now known as the KP equation. It is well-known that the Wronskian approach to the KP equation provides a method to construct soliton solutions. The regular soliton solutions that one obtains in this way come from points of the totally nonnegative part of the Grassmannian. In this paper we explain how the theory of total positivity and cluster algebras provides a framework for understanding these soliton solutions to the KP equation. We then use this framework to give an explicit construction of certain soliton contour graphs and solve the inverse problem for soliton solutions coming from the totally positive part of the Grassmannian. PMID:21562211
International Nuclear Information System (INIS)
Fujioka, J.; Espinosa C, A.; Rodriguez, R.F.
2006-01-01
At the end of the nineties a brand-new type of soliton was discovered: the embedded solitons. Initially they were found in optical systems, and afterwards they were also found in hydrodynamic models, liquid crystal theory and discrete systems. These peculiar solitary waves are interesting because they exist under conditions in which, until recently, the propagation ol solitons was thought to be impossible. At first these nonlinear waves were believed to be necessarily isolated and unstable, but later on it was found that they can be stable and may exist in families. This paper explains what these embedded solitons are, in which models they have been found, and what variants exist (stable, unstable, continuous, discrete, etc.) (Author)
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
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
International Nuclear Information System (INIS)
Hause, A.; Mitschke, F.
2010-01-01
Two solitons in an optical fiber can form pairs in which the double-humped shape is maintained even when the pair is shifted in frequency by the Raman effect. We show here analytically that this is possible even when the two solitons have unequal power. We discuss the forces that cause relative motion of the two solitons, and determine a condition for balance, i.e., for a pair to maintain their separation while the phase keeps evolving. At a specific parameter point we find a solution in which even the phase profile of the pulse pair is maintained. We then discuss that this special point exists also for multipeak structures, or soliton trains. These trains can move as an entity due to Raman shifting. The results are tested by numerical simulation. A comparison to literature reveals that both the rotating phase pair and the constant phase soliton pair apparently have been seen before by others in numerical simulations. Our treatment provides the general framework.
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)
Soliton solutions of the generalized sinh-Gordon equation by the ...
Indian Academy of Sciences (India)
substituting αm,...,v and the general solutions of eq. (8) into (7) we have more travelling wave solutions of the nonlinear evolution eq. (1). 3. Application to the generalized sinh-Gordon equation. First, consider the following transformation: ξ = λ(x + ct), η = λ (x + a ct) , a = c2,. (9) where λ, c are two parameters to be determined.
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.
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
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
Inelastic Vector Soliton Collisions: A Lattice-Based Quantum Representation
National Research Council Canada - National Science Library
Vahala, George; Vahala, Linda; Yepez, Jeffrey
2004-01-01
.... Under appropriate conditions the exact 2-soliton vector solutions yield in elastic soliton collisions, in agreement with the theoretical predictions of Radhakrishnan et al. (1997 Phys. Rev. E56, 2213...
Abelian solutions of the soliton equations and Riemann-Schottky problems
Krichever, Igor M.
2008-12-01
The present article is an exposition of the author's talk at the conference dedicated to the 70th birthday of S.P. Novikov. The talk contained the proof of Welters' conjecture which proposes a solution of the classical Riemann-Schottky problem of characterizing the Jacobians of smooth algebraic curves in terms of the existence of a trisecant of the associated Kummer variety, and a solution of another classical problem of algebraic geometry, that of characterizing the Prym varieties of unramified covers.
Soliton equations and pseudospherical surfaces
International Nuclear Information System (INIS)
Sasaki, R.
1979-03-01
All the soliton equations in 1+1 dimensions that can be solved by the AKNS 2x2 inverse scattering method (for example, the sine-Gordon, KdV or Modified KdV equations) are shown to describe pseudospherical surfaces, i.e. surfaces of constant negative Gaussian curvature. This result provides a unified picture of all these soliton equations. Geometrical interpretations of characteristic properties like infinite numbers of conservation laws, and Baecklund transformations and of the soliton solutions themselves are presented. The important role of scale transformations as generating one parameter families of pseudospherical surfaces is pointed out. (Auth.)
Soliton turbulence in shallow water ocean surface waves.
Costa, Andrea; Osborne, Alfred R; Resio, Donald T; Alessio, Silvia; Chrivì, Elisabetta; Saggese, Enrica; Bellomo, Katinka; Long, Chuck E
2014-09-05
We analyze shallow water wind waves in Currituck Sound, North Carolina and experimentally confirm, for the first time, the presence of soliton turbulence in ocean waves. Soliton turbulence is an exotic form of nonlinear wave motion where low frequency energy may also be viewed as a dense soliton gas, described theoretically by the soliton limit of the Korteweg-deVries equation, a completely integrable soliton system: Hence the phrase "soliton turbulence" is synonymous with "integrable soliton turbulence." For periodic-quasiperiodic boundary conditions the ergodic solutions of Korteweg-deVries are exactly solvable by finite gap theory (FGT), the basis of our data analysis. We find that large amplitude measured wave trains near the energetic peak of a storm have low frequency power spectra that behave as ∼ω-1. We use the linear Fourier transform to estimate this power law from the power spectrum and to filter densely packed soliton wave trains from the data. We apply FGT to determine the soliton spectrum and find that the low frequency ∼ω-1 region is soliton dominated. The solitons have random FGT phases, a soliton random phase approximation, which supports our interpretation of the data as soliton turbulence. From the probability density of the solitons we are able to demonstrate that the solitons are dense in time and highly non-Gaussian.
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
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.
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
Soliton solutions of coupled systems by improved (G'/G)-expansion method
Mohyud-Din, Syed Tauseef; Shakeel, Muhammad
2013-10-01
The paper witnesses the extension of improved (G'/G)-expansion method to generate traveling wave solutions of coupled systems. The proposed algorithm is extremely effective and is tested on two very important systems (namely coupled Higgs and Maccari equations) in mathematical physics. Numerical results reflect complete compatibility of suggested scheme.
Lie symmetry analysis and soliton solutions of time-fractional K (m, n ...
Indian Academy of Sciences (India)
In this note, method of Lie symmetries is applied to investigate symmetry properties of timefractional K ( m , n ) equation with the Riemann–Liouville derivatives. Reduction of time-fractional K ( m , n ) equation is done by virtue of the Erdélyi–Kober fractional derivative which depends on a parameter α. Thensoliton solutions ...
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...
280 GHz dark soliton fiber laser.
Song, Y F; Guo, J; Zhao, L M; Shen, D Y; Tang, D Y
2014-06-15
We report on an ultrahigh repetition rate dark soliton fiber laser. We show both numerically and experimentally that by taking advantage of the cavity self-induced modulation instability and the dark soliton formation in a net normal dispersion cavity fiber laser, stable ultrahigh repetition rate dark soliton trains can be formed in a dispersion-managed cavity fiber laser. Stable dark soliton trains with a repetition rate as high as ∼280 GHz have been generated in our experiment. Numerical simulations have shown that the effective gain bandwidth limitation plays an important role on the stabilization of the formed dark solitons in the laser.
Dissipative soliton acceleration in nonlinear optical lattices.
Kominis, Yannis; Papagiannis, Panagiotis; Droulias, Sotiris
2012-07-30
An effective mechanism for dissipative soliton acceleration in nonlinear optical lattices under the presence of linear gain and nonlinear loss is presented. The key idea for soliton acceleration consists of the dynamical reduction of the amplitude of the effective potential experienced by the soliton so that its kinetic energy eventually increases. This is possible through the dependence of the effective potential amplitude on the soliton mass, which can be varied due to the presence of gain and loss mechanisms. In contrast to the case where either the linear or the nonlinear refractive index is spatially modulated, we show that when both indices are modulated with the same period we can have soliton acceleration and mass increasing as well as stable soliton propagation with constant non-oscillating velocity. The acceleration mechanism is shown to be very robust for a wide range of configurations.
Carlson, Glenn Andrew
This dissertation develops details of Handel's Maser-Soliton Theory of ball lightning. The atmosphere between a thundercloud and the Earth's surface is modeled as an idealized stable open resonator with water vapor as the active medium and the thundercloud and Earth's surface as reflecting surfaces. The stable resonator generates a maser beam that narrows to the beam waist at the Earth's surface, which is assumed to be planar. Two candidate rotational transitions are identified within the ν1ν 2ν3 = 010 vibrational band of water having wavelengths of 13.9 cm and 1.12 cm, and relevant spectroscopic parameters are retrieved from the HITRAN 2008 molecular spectroscopic database. The maser is modeled as a continuously pumped four-level maser that includes the effects of nonradiative relaxation due to molecular collisions and of microwave absorption in atmospheric oxygen. Since maser spiking is highly unlikely to occur due to the high rate of collisional relaxation at normal atmospheric pressure, the electrical breakdown of air must be achieved by the steady state output of the atmospheric maser. A parametric analysis is performed to relate the size of the atmospheric maser to the pumping rate needed to create a steady state population inversion sufficient to generate maser radiation intense enough at the beam waist to result in the electrical breakdown of air. The analysis suggests that electric field intensities at the beam waist sufficient to cause electrical breakdown of air could only be created through huge pumping rates (˜105 to 107 times the critical pumping rate) and only for the most highly curved clouds (g ≈ 0) that give the narrowest beam waists.
Nodal soliton solutions for quasilinear Schrödinger equations with critical exponent
Deng, Yinbin; Peng, Shuangjie; Wang, Jixiu
2013-01-01
This paper is concerned with constructing nodal radial solutions for quasilinear Schrödinger equations in {R}^N with critical growth which have appeared as several models in mathematical physics. For any given integer k ⩾ 0, by using a change of variables and minimization argument, we obtain a sign-changing minimizer with k nodes of a minimization problem. Since the critical exponent appears and the lower order term may change sign, we should use more delicate arguments.
Nodal soliton solutions for generalized quasilinear Schrödinger equations
Energy Technology Data Exchange (ETDEWEB)
Deng, Yinbin, E-mail: ybdeng@mail.ccnu.edu.cn; Peng, Shuangjie, E-mail: sjpeng@mail.ccnu.edu.cn [School of Mathematics and Statistics, Huazhong Normal University, Wuhan 430079 (China); Wang, Jixiu, E-mail: wangjixiu127@aliyun.com [School of Mathematics and Computer Science, Hubei University of Arts and Science, Xiangyang 441053 (China)
2014-05-15
This paper is concerned with constructing nodal radial solutions for generalized quasilinear Schrödinger equations in R{sup N} which arise from plasma physics, fluid mechanics, as well as high-power ultashort laser in matter. For any given integer k ⩾ 0, by using a change of variables and minimization argument, we obtain a sign-changing minimizer with k nodes of a minimization problem.
Uniform strongly interacting soliton gas in the frame of the Nonlinear Schrodinger Equation
Gelash, Andrey; Agafontsev, Dmitry
2017-04-01
The statistical properties of many soliton systems play the key role in the fundamental studies of integrable turbulence and extreme sea wave formation. It is well known that separated solitons are stable nonlinear coherent structures moving with constant velocity. After collisions with each other they restore the original shape and only acquire an additional phase shift. However, at the moment of strong nonlinear soliton interaction (i.e. when solitons are located close) the wave field are highly complicated and should be described by the theory of inverse scattering transform (IST), which allows to integrate the KdV equation, the NLSE and many other important nonlinear models. The usual approach of studying the dynamics and statistics of soliton wave field is based on relatively rarefied gas of solitons [1,2] or restricted by only two-soliton interactions [3]. From the other hand, the exceptional role of interacting solitons and similar coherent structures - breathers in the formation of rogue waves statistics was reported in several recent papers [4,5]. In this work we study the NLSE and use the most straightforward and general way to create many soliton initial condition - the exact N-soliton formulas obtained in the theory of the IST [6]. We propose the recursive numerical scheme for Zakharov-Mikhailov variant of the dressing method [7,8] and discuss its stability with respect to increasing the number of solitons. We show that the pivoting, i.e. the finding of an appropriate order for recursive operations, has a significant impact on the numerical accuracy. We use the developed scheme to generate statistical ensembles of 32 strongly interacting solitons, i.e. solve the inverse scattering problem for the high number of discrete eigenvalues. Then we use this ensembles as initial conditions for numerical simulations in the box with periodic boundary conditions and study statics of obtained uniform strongly interacting gas of NLSE solitons. Author thanks the
International Nuclear Information System (INIS)
Vigier, J.P.
1991-01-01
Starting from a nonlinear relativistic Klein-Gordon equation derived from the stochastic interpretation of quantum mechanics (proposed by Bohm-Vigier, Nelson, de Broglie, Guerra et al.), one can construct joint wave and particle, soliton-like solutions, which follow the average de Broglie-Bohm real trajectories associated with linear solutions of the usual Schroedinger and Klein-Gordon equations
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.
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)
Gromov, Evgeny; Malomed, Boris
2017-11-01
New two-component soliton solutions of the coupled high-frequency (HF)—low-frequency (LF) system, based on Schrödinger-Korteweg-de Vries (KdV) system with the Zakharov's coupling, are obtained for arbitrary relative strengths of the nonlinearity and dispersion in the LF component. The complex HF field is governed by the linear Schrödinger equation with a potential generated by the real LF component, which, in turn, is governed by the KdV equation including the ponderomotive coupling term, representing the feedback of the HF field onto the LF component. First, we study the evolution of pulse-shaped pulses by means of direct simulations. In the case when the dispersion of the LF component is weak in comparison to its nonlinearity, the input gives rise to several solitons in which the HF component is much broader than its LF counterpart. In the opposite case, the system creates a single soliton with approximately equal widths of both components. Collisions between stable solitons are studied too, with a conclusion that the collisions are inelastic, with a greater soliton getting still stronger, and the smaller one suffering further attenuation. Robust intrinsic modes are excited in the colliding solitons. A new family of approximate analytical two-component soliton solutions with two free parameters is found for an arbitrary relative strength of the nonlinearity and dispersion of the LF component, assuming weak feedback of the HF field onto the LF component. Further, a one-parameter (non-generic) family of exact bright-soliton solutions, with mutually proportional HF and LF components, is produced too. Intrinsic dynamics of the two-component solitons, induced by a shift of their HF component against the LF one, is also studied, by means of numerical simulations, demonstrating excitation of a robust intrinsic mode. In addition to the above-mentioned results for LF-dominated two-component solitons, which always run in one (positive) velocities, we produce HF
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.
Modulation instability and solitons in two-color nematic crystals
Energy Technology Data Exchange (ETDEWEB)
Horikis, Theodoros P., E-mail: horikis@uoi.gr
2016-10-14
The conditions under which stable evolution of two nonlinear interacting waves are derived within the context of nematic liquid crystals. Two cases are considered: plane waves and solitons. In the first case, the modulation instability analysis reveals that while the nonlocal term suppresses the growth rates, substantially, the coupled system exhibits significantly higher growth rates than its scalar counterpart. In the soliton case, the necessary conditions are derived that lead the solitons to exhibit stable, undistorted evolution, suppressing any breathing behavior and radiation, leading to soliton mutual guiding. - Highlights: • Modulation instability analysis for two-color nematic crystals. • Stable soliton propagation for two-color nematic crystals. • Conditions for stable propagation of continuous waves and solitons in two-color nematic crystals.
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....
Infinite soliton and kink-soliton trains for nonlinear Schrödinger equations
Le Coz, Stefan; Tsai, Tai-Peng
2014-11-01
We look for solutions to general nonlinear Schrödinger equations built upon solitons and kinks. Solitons are localized solitary waves, and kinks are their non-localized counter-parts. We prove the existence of infinite soliton trains, i.e. solutions behaving at large time as the sum of infinitely many solitons. We also show that one can attach a kink at one end of the train. Our proofs proceed by fixed point arguments around the desired profile. We present two approaches leading to different results, one based on a combination of Lp - Lp‧ dispersive estimates and Strichartz estimates, the other based only on Strichartz estimates.
Generation of two-soliton and three-soliton molecules in a circular fiber array laser
Niknafs, Akram; Rooholamininejad, Hossein; Bahrampour, Alireza
2018-04-01
In this work, the generation of two-soliton and three-soliton molecules in a circular fiber array laser with an active optical central fiber is studied. Certain fibers of the array are excited by Gaussian and super-Gaussian pulses. The central fiber of the circular fiber laser is a rare-earth doped fiber. A circular fiber array is employed as a saturable absorber in a soliton mode locked fiber laser. Generation of two-soliton and three-soliton molecules are observed in our simulation. Numerical calculation of binding energy shows that the super-Gaussian pulse tends to be more stable, and therefore it would be a proper choice for the generation of soliton molecules in the circular fiber array laser.
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
Inelastic soliton-soliton interaction in coninin models
International Nuclear Information System (INIS)
Simonov, Yu.A.; Veselov, A.I.
1980-01-01
The field equations with nonlinearity proportional to |PSI|sup(-α)PSI, α>0 (model 1 of Simonov-Tjon) are solved in one spatial dimension with initial conditions corresponding to two colliding solitons. One or several breathers are generated during the collision process and the solitons remain stable after collision. An extensive study is done of the collision process and the breather generation for different values of the interaction parameter α, velocities and relative phase in the initial state. In addition the collision of two breathers is considered. Some comparative study of one dimensional model of the Werle type is also done
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.
Elliptic-type soliton combs in optical ring microresonators
Dikandé Bitha, Rodrigues D.; Dikandé, Alain M.
2018-03-01
Soliton crystals are periodic patterns of multispot optical fields formed from either time or space entanglements of equally separated identical high-intensity pulses. These specific nonlinear optical structures have gained interest in recent years with the advent and progress in nonlinear optical fibers and fiber lasers, photonic crystals, wave-guided wave systems, and most recently optical ring microresonator devices. In this work an extensive analysis of characteristic features of soliton crystals is carried out, with an emphasis on their one-to-one correspondence with elliptic solitons. With this purpose in mind, we examine their formation, their stability, and their dynamics in ring-shaped nonlinear optical media within the framework of the Lugiato-Lefever equation. The stability analysis deals with internal modes of the system via a 2 ×2 -matrix Lamé-type eigenvalue problem, the spectrum of which is shown to possess a rich set of bound states consisting of stable zero-fequency modes and unstable decaying as well as growing modes. Turning towards the dynamics of elliptic solitons in ring-shaped fiber resonators with Kerr nonlinearity, we first propose a collective-coordinate approach, based on a Lagrangian formalism suitable for elliptic-soliton solutions to the nonlinear Schrödinger equation with an arbitrary perturbation. Next we derive time evolutions of elliptic-soliton parameters in the specific context of ring-shaped optical fiber resonators, where the optical field evolution is thought to be governed by the Lugiato-Lefever equation. By solving numerically the collective-coordinate equations an analysis of the amplitude, the position, the phase of internal oscillations, the phase velocity, the energy, and phase portraits of the amplitude is carried out and reveals a complex dynamics of the elliptic soliton in ring-shaped optical microresonators. Direct numerical simulations of the Lugiato-Lefever equation are also carried out seeking for stationary
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
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
Topological solitons in DNA with modified potential
Directory of Open Access Journals (Sweden)
E Behjat
2010-06-01
Full Text Available DNA is not only an essential research subject for biologists, but also it raises very interesting questions for physicists.The open states in DNA double helix can lead to topological solitons. Since DNA is a very long molecule of order a meter or so long and nano-scale width, solitons can propagate along the molecule. In this paper, considering a correction term in the interaction potential between two chains, we study the dispersion relation analytically, and obtain the soliton solutions using a new relaxation method. Then we compare our solutions and its energy with those obtained by others without the proposed correction term.
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
Nonlinear Dynamics: Maps, Integrators and Solitons
Energy Technology Data Exchange (ETDEWEB)
Parsa, Z.
1998-10-01
For many physical systems of interest in various disciplines, the solution to nonlinear differential equations describing the physical systems can be generated using maps, symplectic integrators and solitons. We discuss these methods and apply them for various examples.
Vacuum-induced jitter in spatial solitons.
Nagasako, E; Boyd, R; Agarwal, G S
1998-08-31
We perform a calculation to determine how quantum mechanical fluctuations influence the propagation of a spatial soliton through a nonlinear material. To do so, we derive equations of motion for the linearized operators describing the deviation of the soliton position and transverse momentum from those of a corresponding classical solution to the nonlinear wave equation, and from these equations we determine the quantum uncertainty in the soliton position and transverse momentum. We find that under realistic laboratory conditions the quantum uncertainty in position is several orders of magnitude smaller the classical width of the soliton. This result suggests that the reliability of photonic devices based on spatial solitons is not compromised by quantum fluctuations.
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
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.
Soliton interactions and complexes for coupled nonlinear Schrödinger equations.
Jiang, Yan; Tian, Bo; Liu, Wen-Jun; Sun, Kun; Li, Min; Wang, Pan
2012-03-01
Under investigation in this paper are the coupled nonlinear Schrödinger (CNLS) equations, which can be used to govern the optical-soliton propagation and interaction in such optical media as the multimode fibers, fiber arrays, and birefringent fibers. By taking the 3-CNLS equations as an example for the N-CNLS ones (N≥3), we derive the analytic mixed-type two- and three-soliton solutions in more general forms than those obtained in the previous studies with the Hirota method and symbolic computation. With the choice of parameters for those soliton solutions, soliton interactions and complexes are investigated through the asymptotic and graphic analysis. Soliton interactions and complexes with the bound dark solitons in a mode or two modes are observed, including that (i) the two bright solitons display the breatherlike structures while the two dark ones stay parallel, (ii) the two bright and dark solitons all stay parallel, and (iii) the states of the bound solitons change from the breatherlike structures to the parallel one even with the distance between those solitons smaller than that before the interaction with the regular one soliton. Asymptotic analysis is also used to investigate the elastic and inelastic interactions between the bound solitons and the regular one soliton. Furthermore, some discussions are extended to the N-CNLS equations (N>3). Our results might be helpful in such applications as the soliton switch, optical computing, and soliton amplification in the nonlinear optics.
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.
Rosenberger, Tessa; Lindner, John F.
We study the dynamics of mechanical arrays of bistable elements coupled one-way by wind. Unlike earlier hydromechanical unidirectional arrays, our aeromechanical one-way arrays are simpler, easier to study, and exhibit a broader range of phenomena. Soliton-like waves propagate in one direction at speeds proportional to wind speeds. Periodic boundaries enable solitons to annihilate in pairs in even arrays where adjacent elements are attracted to opposite stable states. Solitons propagate indefinitely in odd arrays where pairing is frustrated. Large noise spontaneously creates soliton- antisoliton pairs, as predicted by prior computer simulations. Soliton annihilation times increase quadratically with initial separations, as expected for random walk models of soliton collisions.
Dynamical behaviours and exact travelling wave solutions of ...
Indian Academy of Sciences (India)
Modified generalized Vakhnenko equation; cusped solitons; loop solitons; periodic cusp wave solutions; smooth periodic wave solutions; pseudopeakon solitons; ... Guangxi 541004, People's Republic of China; School of Mathematics and Statistics, Guizhou University of Finance and Economics, Guiyang, Guizhou 550025, ...
Existence and stability of the externally driven, damped nonlinear Schroedinger solitons
International Nuclear Information System (INIS)
Barashenkov, I.V.; Smirnov, Yu.S.
1997-01-01
The externally driven damped nonlinear Schroedinger (NLS) equation on the infinite line is studied. Existence and stability chart for its soliton solution is constructed on the plane of two control parameters, the forcing amplitude h and dissipation coefficient γ. For generic values of h and γ there are two coexisting solitons one of which (ψ + ) is always unstable. The bifurcation diagram of the second solution (ψ - ) depends on the dissipation coefficient: if γ cr , the ψ - is stable for small h and loses its stability via a Hopf bifurcation as h is increased; if γ>γ cr , the ψ - is stable for all h. There are no 'stability windows' in the unstable region. We show that the previously reported 'stability windows' occur only when the equation is considered on a finite (and small) spatial interval
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)
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
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)
Semiclassical geons as solitonic black hole remnants
Energy Technology Data Exchange (ETDEWEB)
Lobo, Francisco S.N. [Centro de Astronomia e Astrofísica da Universidade de Lisboa, Campo Grande, Ed. C8 1749-016 Lisboa (Portugal); Olmo, Gonzalo J.; Rubiera-Garcia, D., E-mail: flobo@cii.fc.ul.pt, E-mail: gonzalo.olmo@csic.es, E-mail: drubiera@fisica.ufpb.br2 [Departamento de Física Teórica and IFIC, Centro Mixto Universidad de Valencia - CSIC. Universidad de Valencia, Burjassot-46100, Valencia (Spain)
2013-07-01
We find that the end state of black hole evaporation could be represented by non-singular and without event horizon stable solitonic remnants with masses of the order the Planck scale and up to ∼ 16 units of charge. Though these objects are locally indistinguishable from spherically symmetric, massive electric (or magnetic) charges, they turn out to be sourceless geons containing a wormhole generated by the electromagnetic field. Our results are obtained by interpreting semiclassical corrections to Einstein's theory in the first-order (Palatini) formalism, which yields second-order equations and avoids the instabilities of the usual (metric) formulation of quadratic gravity. We also discuss the potential relevance of these solutions for primordial black holes and the dark matter problem.
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
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.)
Topological Solitons in Physics.
Parsa, Zohreh
1979-01-01
A broad definition of solitons and a discussion of their role in physics is given. Vortices and magnetic monopoles which are examples of topological solitons in two and three spatial dimensions are described in some detail. (BB)
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
Directory of Open Access Journals (Sweden)
Yakup YÄ±ldÄ±rÄ±m
Full Text Available In this study, we perform the extended Kudryashov method to nonlinear SchrÃ¶dinger equation (NLSE with spatio-temporal dispersion that arises in a propagation of light in nonlinear optical fibers, planar waveguides, BoseâEinstein condensate theory. Four types of nonlinearity â Kerr law, power law, parabolic law and dual-power law â are being considered for the model. By using this scheme, the topological, singular soliton and rational solutions are obtained. In addition, some graphical simulations of solutions are provided.It is demonstrated that the proposed algorithm is effective and can be handled for many other nonlinear complex differential equations. Keywords: Solitons, Nonlinear SchrÃ¶dinger equation with spatio-temporal dispersion, Extended Kudryashovâs method
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.
International Nuclear Information System (INIS)
Rajaraman, R.
1982-01-01
In recent years, a host of new non-perturbative results in relativistic quantum field theory have been obtained, based on classical soliton and instanton solutions. This book offers an elementary and unified introduction to these developments. Such solutions are derived for a variety of models and classified by topological indices. The methods are then developed for quantizing solitons to obtain quantum particles. Vacuum tunnelling, theta-vacua and the dilute-instanton-gas approximation are described in detail. Other instanton effects related to quark-quark forces, confinement, the U(1) problem and Borel summability are also discussed. The emphasis is on presenting the basic ideas in a simple pedagogical way. Technical tools like functional methods, Grassman integrals, homotopy classification, collective coordinates etc. are developed from the very outset. The presentation of this work is kept at a fairly simple level, and ideas are developed through illustrative examples. Techniques not covered in older field theory textbooks, such as functional integral methods, are presented in some detail to the necessary extent. These techniques are important in their own right. The book is mainly addressed to particle physicists and quantum field theorists. (Auth.)
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.
Quasi-one-dimensional spin-orbit- and Rabi-coupled bright dipolar Bose-Einstein-condensate solitons
Chiquillo, Emerson
2018-01-01
We study the formation of stable bright solitons in quasi-one-dimensional (quasi-1D) spin-orbit- (SO-) and Rabi-coupled two pseudospinor dipolar Bose-Einstein condensates (BECs) of 164Dy atoms in the presence of repulsive contact interactions. As a result of the combined attraction-repulsion effect of both interactions and the addition of SO and Rabi couplings, two kinds of ground states in the form of self-trapped bright solitons can be formed, a plane-wave soliton (PWS) and a stripe soliton (SS). These quasi-1D solitons cannot exist in a condensate with purely repulsive contact interactions and SO and Rabi couplings (no dipole). Neglecting the repulsive contact interactions, our findings also show the possibility of creating PWSs and SSs. When the strengths of the two interactions are close to each other, the SS develops an oscillatory instability indicating a possibility of a breather solution, eventually leading to its destruction. We also obtain a phase diagram showing regions where the solution is a PWS or SS.
Indian Academy of Sciences (India)
Abstract. As an introduction to the special issue on nonlinear waves, solitons and their signiﬁcance in physics are reviewed. The soliton is the ﬁrst universal concept in nonlinear science. Universality and ubiquity of the soliton concept are emphasized.
Solitons of axion-dilaton gravity
Bakas, Ioannis
1996-01-01
We use soliton techniques of the two-dimensional reduced beta-function equations to obtain non-trivial string backgrounds from flat space. These solutions are characterized by two integers (n, m) referring to the soliton numbers of the metric and axion-dilaton sectors respectively. We show that the Nappi-Witten universe associated with the SL(2) x SU(2) / SO(1, 1) x U(1) CFT coset arises as an (1, 1) soliton in this fashion for certain values of the moduli parameters, while for other values of the soliton moduli we arrive at the SL(2)/SO(1, 1) x SO(1, 1)^2 background. Ordinary 4-dim black-holes arise as 2-dim (2, 0) solitons, while the Euclidean worm-hole background is described as a (0, 2) soliton on flat space. The soliton transformations correspond to specific elements of the string Geroch group. These could be used as starting point for exploring the role of U-dualities in string compactifications to two dimensions.
International Nuclear Information System (INIS)
Serkin, Vladimir N; Belyaeva, T L
2001-01-01
The existence of the Lax representation for a model of soliton management under certain conditions is shown, which proves a complete integrability of the model. The exact analytic solutions are obtained for the problem of the optimal control of parameters of Schrodinger solitons in nonconservative systems with the group velocity dispersion, nonlinear refractive index, and gain (absorption coefficient) varying over the length. The examples demonstrating the non-trivial amplification dynamics of optical solitons, which are important from practical point of view, are considered. The exact analytic solutions are obtained for problems of the optimal amplification of solitons in optical fibres with monotonically decreasing dispersion and of Raman pumping of solitons in fibreoptic communication systems. (solitons)
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
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
Asymptotically flat, stable black hole solutions in Einstein-Yang-Mills-Chern-Simons theory.
Brihaye, Yves; Radu, Eugen; Tchrakian, D H
2011-02-18
We construct finite mass, asymptotically flat black hole solutions in d=5 Einstein-Yang-Mills-Chern-Simons theory. Our results indicate the existence of a second order phase transition between Reissner-Nordström solutions and the non-Abelian black holes which generically are thermodynamically preferred. Some of the non-Abelian configurations are also stable under linear, spherically symmetric perturbations.
International Nuclear Information System (INIS)
Yan Zhenya; Hang Chao
2009-01-01
We provide analytical three-dimensional bright multisoliton solutions to the (3+1)-dimensional Gross-Pitaevskii equation with time- and space-dependent potential, time-dependent nonlinearity, and gain or loss. The zigzag propagation trace and the breathing behavior of solitons are observed. Different shapes of bright solitons and fascinating interactions between two solitons can be achieved with different parameters. The obtained results may raise the possibility of relative experiments and potential applications.
Luo, Rui; Liang, Hanxiao; Lin, Qiang
2016-07-25
We show a new class of complex solitary wave that exists in a nonlinear optical cavity with appropriate dispersion characteristics. The cavity soliton consists of multiple soliton-like spectro-temporal components that exhibit distinctive colors but coincide in time and share a common phase, formed together via strong inter-soliton four-wave mixing and Cherenkov radiation. The multicolor cavity soliton shows intriguing spectral locking characteristics and remarkable capability of spectrum management to tailor soliton frequencies, which would be very useful for versatile generation and manipulation of multi-octave spanning phase-locked Kerr frequency combs, with great potential for applications in frequency metrology, optical frequency synthesis, and spectroscopy.
Peaked and Smooth Solitons for K*(4,1 Equation
Directory of Open Access Journals (Sweden)
Yongan Xie
2013-01-01
Full Text Available This paper is contributed to explore all possible single peak solutions for the K*(4,1 equation ut=uxu2+2α(uuxxx+2uxuxx. Our procedure shows that the K*(4,1 equation either has peakon, cuspon, and smooth soliton solutions when sitting on a nonzero constant pedestal limξ→±∞u=A≠0 or possesses compacton solutions only when limξ→±∞u=A=0. We present a new smooth soliton solution in an explicit form. Mathematical analysis and numeric graphs are provided for those soliton solutions of the K*(4,1 equation.
Solitons and rogue waves in spinor Bose-Einstein condensates
Li, Sitai; Prinari, Barbara; Biondini, Gino
2018-02-01
We present a general classification of one-soliton solutions as well as families of rogue-wave solutions for F =1 spinor Bose-Einstein condensates (BECs). These solutions are obtained from the inverse scattering transform for a focusing matrix nonlinear Schrödinger equation which models condensates in the case of attractive mean-field interactions and ferromagnetic spin-exchange interactions. In particular, we show that when no background is present, all one-soliton solutions are reducible via unitary transformations to a combination of oppositely polarized solitonic solutions of single-component BECs. On the other hand, we show that when a nonzero background is present, not all matrix one-soliton solutions are reducible to a simple combination of scalar solutions. Finally, by taking suitable limits of all the solutions on a nonzero background we also obtain three families of rogue-wave (i.e., rational) solutions.
Yue, Chen; Seadawy, Aly; Lu, Dianchen
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.
Directory of Open Access Journals (Sweden)
Chen Yue
2016-01-01
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.
Zhang, Xiaoen; Chen, Yong
2017-11-01
In this paper, a combination of stripe soliton and lump soliton is discussed to a reduced (3+1)-dimensional Jimbo-Miwa equation, in which such solution gives rise to two different excitation phenomena: fusion and fission. Particularly, a new combination of positive quadratic functions and hyperbolic functions is considered, and then a novel nonlinear phenomenon is explored. Via this method, a pair of resonance kink stripe solitons and rogue wave is studied. Rogue wave is triggered by the interaction between lump soliton and a pair of resonance kink stripe solitons. It is exciting that rogue wave must be attached to the stripe solitons from its appearing to disappearing. The whole progress is completely symmetry, the rogue wave starts itself from one stripe soliton and lose itself in another stripe soliton. The dynamic properties of the interaction between one stripe soliton and lump soliton, rogue wave are discussed by choosing appropriate parameters.
Radiation by solitons due to higher-order dispersion
DEFF Research Database (Denmark)
Karpman, V.I.
1993-01-01
We consider the Korteweg-de Vries (KdV) and nonlinear Schrodinger (NS) equations with higher-order derivative terms describing dispersive corrections. Conditions of existence of stationary and radiating solitons of the fifth-order KdV equation are obtained. An asymptotic time-dependent solution...... to the latter equation, describing the soliton radiation, is found. The radiation train may be in front as well as behind the soliton, depending on the sign of dispersion. The change rate of the soliton due to the radiation is calculated. A modification of the WKB method, that permits one to describe...... in a simple and general way the radiation of KdV and NS, as well as other types. of solitons, is developed. From the WKB approach it follows that the soliton radiation is a result of a tunneling transformation of the non-linearly self-trapped wave into the free-propagating radiation....
Electro-magnetic waves within a model for charged solitons
International Nuclear Information System (INIS)
Borisyuk, Dmitry; Faber, Manfried; Kobushkin, Alexander
2007-01-01
We analyse the model of topological fermions (MTF), where charged fermions are treated as soliton solutions of the field equations. In the region far from the sources we find plane waves solutions with the properties of electro-magnetic waves
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
Dynamics of coupled field solitons: A collective coordinate approach
Indian Academy of Sciences (India)
mensional space-time, with the main motivation of studying classical stability of soliton solutions using collective coordinate ... presented in some previous works [1,2] which where motivated by investigations intro- duced in [3,4], ... The collision of coupled field solitons leads to resonance structure depending on the energy ...
Interaction between "dissipative solitons" stabilized by aggregation in excitable kinetics
Mangioni, Sergio E.
2014-10-01
We consider that a population of individuals governed by the Nagumo model is characterized by predisposition towards aggregation. "Dissipative solitons" interacting are solutions for such system. We changed the possibility of extinction, predicted by Nagumo model, by a uniform background of low population's density and then we observed relevant effect on interaction between "solitons".
Liu, Wenjun; Yang, Chunyu; Liu, Mengli; Yu, Weitian; Zhang, Yujia; Lei, Ming
2017-10-01
The interactions of multiple solitons show different properties with two-soliton interactions. For the difficulty of deriving multiple soliton solutions, it is rare to study multiple soliton interactions analytically. In this paper, three-soliton interactions in inhomogeneous optical fibers, which are described by the variable coefficient Hirota equation, are investigated. Via the Hirota bilinear method and symbolic computation, analytic three-soliton solutions are obtained. According to the obtained solutions, properties and features of three-soliton interactions are discussed by changing the third-order dispersion (TOD) and other relevant coefficients, and some plentiful structure of three-soliton interactions are presented for the first time. The influences of TOD on the intensity and propagation distance of solitons are described, which can be used to realize the soliton control. Besides, the method that can achieve the phase reverse of solitons is suggested, and bound states of three solitons are observed, which have potential applications in the mode-locked fiber lasers. Furthermore, comparing to two-soliton interactions, a novel phenomenon of three-soliton interactions with a strong phase shift at x=0 is revealed, which is potentially useful for optical logic switches.
Blanco-Redondo, Andrea; Martijn, de Sterke C.; Sipe, J.E.; Krauss, Thomas F.; Eggleton, Benjamin J.; Husko, Chad
2016-01-01
Temporal optical solitons have been the subject of intense research due to their intriguing physics and applications in ultrafast optics and supercontinuum generation. Conventional bright optical solitons result from the interaction of anomalous group-velocity dispersion and self-phase modulation. Here we experimentally demonstrate a class of bright soliton arising purely from the interaction of negative fourth-order dispersion and self-phase modulation, which can occur even for normal group-velocity dispersion. We provide experimental and numerical evidence of shape-preserving propagation and flat temporal phase for the fundamental pure-quartic soliton and periodically modulated propagation for the higher-order pure-quartic solitons. We derive the approximate shape of the fundamental pure-quartic soliton and discover that is surprisingly Gaussian, exhibiting excellent agreement with our experimental observations. Our discovery, enabled by precise dispersion engineering, could find applications in communications, frequency combs and ultrafast lasers. PMID:26822758
Solitonic Josephson Thermal Transport
Guarcello, Claudio; Solinas, Paolo; Braggio, Alessandro; Giazotto, Francesco
2018-03-01
We explore the coherent thermal transport sustained by solitons through a long Josephson junction as a thermal gradient across the system is established. We observe that a soliton causes the heat current through the system to increase. Correspondingly, the junction warms up in conjunction with the soliton, with temperature peaks up to, e.g., approximately 56 mK for a realistic Nb-based proposed setup at a bath temperature Tbath=4.2 K . The thermal effects on the dynamics of the soliton are also discussed. Markedly, this system inherits the topological robustness of the solitons. In view of these results, the proposed device can effectively find an application as a superconducting thermal router in which the thermal transport can be locally mastered through solitonic excitations, whose positions can be externally controlled through a magnetic field and a bias current.
Higher-order-effects management of soliton interactions in the Hirota equation.
Wong, Pring; Liu, Wen-Jun; Huang, Long-Gang; Li, Yan-Qing; Pan, Nan; Lei, Ming
2015-03-01
The study of soliton interactions is of significance for improving pulse qualities in nonlinear optics. In this paper, interaction between two solitons, which is governed by the Hirota equation, is considered. Via use of the Hirota method, an analytic soliton solution is obtained. Then a two-period vibration phenomenon is observed. Moreover, turning points of the coefficients of higher-order terms, which are related with sudden delaying or leading, are found and analyzed. With different coefficient constraints, soliton interactions are discussed by different frequency separation with the split-step Fourier method, and characteristics of soliton interactions are exhibited. Through turning points, we get a pair of solitons which tend to be bound solitons but not exactly. Furthermore, we control a pair of solitons to emit at different emission angles. The stability of the two-period vibration is analyzed. Results in this paper may be helpful for the applications of optical self-routing, waveguiding, and faster switching.
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(...
Analytical Solitons for Langmuir Waves in Plasma Physics with Cubic Nonlinearity and Perturbations
Zhou, Qin; Mirzazadeh, M.
2016-09-01
We presented an analytical study on dynamics of solitons for Langmuir waves in plasma physics. The mathematical model is given by the perturbed nonlinear Schrödinger equation with full nonlinearity and Kerr law nonlinearity. There are three techniques of integrability were employed to extract exact solutions along with the integrability conditions. The topological 1-soliton solutions, singular 1-soliton solutions, and plane wave solution were reported by Ricatti equation expansion approach and then the bright 1-soliton solution, singular 1-soliton solution, periodic singular solutions, and plane wave solution were derived with the help of trial solution method. Finally, based on the G'/G-expansion scheme, we obtained the hyperbolic function travelling wave solution, trigonometric function travelling wave solution, and plane wave solution.
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
Collective Modes of a Soliton Train in a Fermi Superfluid.
Dutta, Shovan; Mueller, Erich J
2017-06-30
We characterize the collective modes of a soliton train in a quasi-one-dimensional Fermi superfluid, using a mean-field formalism. In addition to the expected Goldstone and Higgs modes, we find novel long-lived gapped modes associated with oscillations of the soliton cores. The soliton train has an instability that depends strongly on the interaction strength and the spacing of solitons. It can be stabilized by filling each soliton with an unpaired fermion, thus forming a commensurate Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) phase. We find that such a state is always dynamically stable, which paves the way for realizing long-lived FFLO states in experiments via phase imprinting.
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....
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
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
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.
Quasiperiodic Envelope Solitons
DEFF Research Database (Denmark)
Clausen, Carl A. Balslev; Kivshar, Yuri S.; Bang, Ole
1999-01-01
We analyze nonlinear wave propagation and cascaded self-focusing due to second-harmonic generation in Fibbonacci optical superlattices and introduce a novel concept of nonlinear physics. the quasiperiodic soliton, which describes spatially localized self-trapping of a quasiperiodic wave. We point...... out a link between the quasiperiodic soliton and partially incoherent spatial solitary waves recently generated experimentally....
Semirelativity and Kink Solitons
Nowak, Mariusz Karol
2014-01-01
It is hard to observe relativistic effects in everyday life. However, table experiments using a mechanical transmission line for solitons may be an efficient and simple way to show effects such as Lorentz contraction in a classroom. A kink soliton is a deformation of a lattice of several dozen or more pendulums placed on a wire and connected by a…
A Numerical Solution for Hirota-Satsuma Coupled KdV Equation
Directory of Open Access Journals (Sweden)
M. S. Ismail
2014-01-01
Full Text Available A Petrov-Galerkin method and product approximation technique are used to solve numerically the Hirota-Satsuma coupled Korteweg-de Vries equation, using cubic B-splines as test functions and a linear B-spline as trial functions. The implicit midpoint rule is used to advance the solution in time. Newton’s method is used to solve the block nonlinear pentadiagonal system we have obtained. The resulting schemes are of second order accuracy in both directions, space and time. The von Neumann stability analysis of the schemes shows that the two schemes are unconditionally stable. The single soliton solution and the conserved quantities are used to assess the accuracy and to show the robustness of the schemes. The interaction of two solitons, three solitons, and birth of solitons is also discussed.
Stationary and moving solitons in spin-orbit-coupled spin-1 Bose-Einstein condensates
Li, Yu-E.; Xue, Ju-Kui
2018-04-01
We investigate the matter-wave solitons in a spin-orbit-coupled spin-1 Bose-Einstein condensate using a multiscale perturbation method. Beginning with the one-dimensional spin-orbit-coupled threecomponent Gross-Pitaevskii equations, we derive a single nonlinear Schrödinger equation, which allows determination of the analytical soliton solutions of the system. Stationary and moving solitons in the system are derived. In particular, a parameter space for different existing soliton types is provided. It is shown that there exist only dark or bright solitons when the spin-orbit coupling is weak, with the solitons depending on the atomic interactions. However, when the spin-orbit coupling is strong, both dark and bright solitons exist, being determined by the Raman coupling. Our analytical solutions are confirmed by direct numerical simulations.
Soliton synchronization in the focusing nonlinear Schrödinger equation.
Sun, Yu-Hao
2016-05-01
The focusing nonlinear Schrödinger equation (NLSE) describes propagation of quasimonochromatic waves in weakly nonlinear media. The aim of this study is to determine conditions of soliton synchronization in the NLSE in terms of the solitons' position and phase parameters. For this purpose, the concept of asymptotic middle states of solitons in the NLSE is first introduced. With soliton solutions of the NLSE, it is shown that soliton synchronization can be achieved by synchronizing the asymptotic middle states of the solitons, and conditions of soliton synchronization in terms of the solitons' position and phase parameters are given. Although the interaction of the solitons is nonlinear, the conditions are linear equations. Then, aided with the synchronization conditions, simple initial conditions are presented for producing synchronized interaction of solitons without the need to obtain analytic expressions for the synchronized interaction of the solitons. The initial conditions are summations of fundamental solitons with no mutual overlap, so they might be convenient to implement in applicative contexts.
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
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...
Theory of nonlocal soliton interaction in nematic liquid crystals
DEFF Research Database (Denmark)
Rasmussen, Per Dalgaard; Bang, Ole; Krolikowski, Wieslaw
2005-01-01
We investigate interactions between spatial nonlocal bright solitons in nematic liquid crystals using an analytical “effective particle” approach as well as direct numerical simulations. The model predicts attraction of out-of-phase solitons and the existence of their stable bound state....... This nontrivial property is solely due to the nonlocal nature of the nonlinear response of the liquid crystals. We further predict and verify numerically the critical outwards angle and degree of nonlocality which determine the transition between attraction and repulsion of out-of-phase solitons....
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.
Chai, Jun; Tian, Bo; Sun, Wen-Rong; Liu, De-Yin
2018-01-01
Under investigation in this paper is the reduced Maxwell-Bloch equations with variable coefficients, which describe the propagation of the intense ultra-short optical pulses through an inhomogeneous two-level dielectric medium. Hirota method and symbolic computation are applied to solve such equations. By introducing the dependent variable transformations, we give the bilinear forms, vector one-, two- and N-soliton solutions in analytic forms. The types of the vector solitons are analyzed: Only the bright-single-hump solitons can be observed in q and r1 , the soliton in r2 is the bright-double-hump soliton, and there exist three types of solitons in r3 , including the dark-single-hump soliton, dark-double-hump soliton and dark-like-bright soliton, with q as the inhomogeneous electric field, r1 and r2 as the real and imaginary parts of the polarization of the two-level medium, and r3 as the population difference between the ground and excited states. Figures are presented to show the vector soliton solutions. Different types of the interactions between the vector two solitons are presented. In each component, only the overtaking elastic interaction can be observed.
Lin, Wei; Wang, Simin; Xu, Shanhui; Luo, Zhi-Chao; Yang, Zhongmin
2015-06-01
A combined analytical approach to classify soliton dynamics from dissipative soliton to dissipative soliton resonance (DSR) is developed based on the established laser models. The approach, derived from two compatible analytical solutions to the complex cubic-quintic Ginzburg-Landau equation (CQGLE), characterizes the pulse evolution process from both algebraic and physical points of view. The proposed theory is proved to be valid in real world laser oscillators according to numerical simulations, and potentially offers guideline on the design of DSR cavity configurations.
soliton dynamics in a modified Yakushevich model
Indian Academy of Sciences (India)
1Department of Physics, College of Engineering and Technology, Biju Patnaik University of Technology, Bhubaneswar 751 ... senting different bases and find two new in-phase solitonic solutions. We also discuss here the effect of ..... (29) and adoption of the procedure of linear perturbation anal- ysis [13-15] gives. ШШ =.
Solitons in Bose–Einstein condensates
Indian Academy of Sciences (India)
The solution (8) shows that both the density profile ρ(z) and the phase profile φ(z) travel with the same speed ... always travel with different speeds, contrary to the solitons of the repulsive GPE, where they travel with the ... tory using standing waves of laser light, load BEC atoms on such lattices, and also tune the interactions ...
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.)
Dabholkar, Atish
This thesis is divided into two chapters. Chapter I is about the dynamics of radiating axionic strings and the lower bound on the mass of the invisible axion. It has been suggested that, without inflation, the decay of axionic strings produced after the Peccei -Quinn phase transition is the primary source of cosmic relic axions. Knowing the density of these axions would then allow the derivation of a cosmological bound on the mass of the axion. In order to obtain a sharp bound it is essential to know the spectrum of the emitted axions and the detailed motion of a global string strongly coupled to the axionic field. To this end, following the analogy with Dirac's treatment of classical radiating electrons, self-consistent renormalized equations are obtained that describe the dynamics of a radiating global string interacting with its surrounding axionic field. The numerical formalism for evolving string trajectories using these equations is described, and is applied to the case of a circular loop. It is argued that for large wavelength oscillations of cosmic string loops, the motion is well approximated by the motion of a free Nambu-Goto string with appropriate renormalization. Consequently, a lower bound of 10 ^{-3} eV on the mass of the axion is obtained. Together with the recent upperbound of 4 times 10^{-4 } eV from the supernova SN1987a, it marginally rules out the invisible axion. Chapter II is about superstrings and solitons. It is shown that the quantum renormalization of the superstring tension vanishes to all orders in string perturbation theory. A low-energy analysis of macroscopic superstrings is presented and various analogies between these superstrings and solitons in supersymmetric theories are discussed. These include the existence of exact multi-string solutions of the low -energy supergravity super-Yang-Mills equations of motion and a Bogomol'nyi bound for the energy per unit length which is saturated by these solutions. Arguments are presented that
Dissipative solitons in pair-ion plasmas
Energy Technology Data Exchange (ETDEWEB)
Ghosh, Samiran, E-mail: sran-g@yahoo.com [Department of Applied Mathematics, University of Calcutta, 92, Acharya Prafulla Chandra Road, Kolkata 700 009 (India); Adak, Ashish, E-mail: ashish-adak@yahoo.com; Khan, Manoranjan, E-mail: mkhan.ju@gmail.com [Department of Instrumentation Science, Jadavpur University, Kolkata 700 032 (India)
2014-01-15
The effects of ion-neutral collisions on the dynamics of the nonlinear ion acoustic wave in pair-ion plasma are investigated. The standard perturbative approach leads to a Korteweg-de Vries equation with a linear damping term for the dynamics of the finite amplitude wave. The ion-neutral collision induced dissipation is responsible for the linear damping. The analytical solution and numerical simulation reveal that the nonlinear wave propagates in the form of a weakly dissipative compressive solitons. Furthermore, the width of the soliton is proportional to the amplitude of the wave for fixed soliton velocity. Results are discussed in the context of the fullerene pair-ion plasma experiment.
Bright and dark solitons in optical fibers with parabolic law nonlinearity
Directory of Open Access Journals (Sweden)
Milović Daniela
2013-01-01
Full Text Available This paper utilizes the ansatz method to obtain bright and dark 1-soliton solution to the nonlinear Schrodinger’s equation with parabolic law nonlinearity in birefringent fibers. There are a few Hamiltonian type perturbation terms taken into account. The exact soliton solution comes with baggages that are referred to as constraint conditions that must hold in order for these solitons to exist.
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.
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 $k=1$ .
Fuzzy Objects and Noncommutative Solitons
Kobayashi, Shinpei; Asakawa, Tsuguhiko
2015-01-01
The fuzzy disc is a disc-shaped region in a noncommutative plane, and is a fuzzy approximation of a commutative disc. We showed that one can introduce a concept of angles to the fuzzy disc, by using the phase operator and phase states known in quantum optics. We also constructed fan-shaped soliton solutions, which would be identified with D-branes, of a scalar field theory on the fuzzy disc and applied this concept to a theory of noncommutative gravity. This proceeding is based on our previous work.
Observation of Kuznetsov-Ma soliton dynamics in optical fibre
Kibler, B.; Fatome, J.; Finot, C.; Millot, G.; Genty, G.; Wetzel, B.; Akhmediev, N.; Dias, F.; Dudley, J. M.
2012-01-01
The nonlinear Schrödinger equation (NLSE) is a central model of nonlinear science, applying to hydrodynamics, plasma physics, molecular biology and optics. The NLSE admits only few elementary analytic solutions, but one in particular describing a localized soliton on a finite background is of intense current interest in the context of understanding the physics of extreme waves. However, although the first solution of this type was the Kuznetzov-Ma (KM) soliton derived in 1977, there have in fact been no quantitative experiments confirming its validity. We report here novel experiments in optical fibre that confirm the KM soliton theory, completing an important series of experiments that have now observed a complete family of soliton on background solutions to the NLSE. Our results also show that KM dynamics appear more universally than for the specific conditions originally considered, and can be interpreted as an analytic description of Fermi-Pasta-Ulam recurrence in NLSE propagation. PMID:22712052
DEFF Research Database (Denmark)
Krolikowski, Wieslaw; Bang, Ole; Wyller, John
2004-01-01
We investigate the propagation of partially coherent beams in spatially nonlocal nonlinear media with a logarithmic type of nonlinearity. We derive analytical formulas for the evolution of the beam parameters and conditions for the formation of nonlocal incoherent solitons....
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
Gap solitons in Rabi lattices.
Chen, Zhaopin; Malomed, Boris A
2017-03-01
We introduce a two-component one-dimensional system, which is based on two nonlinear Schrödinger or Gross-Pitaevskii equations (GPEs) with spatially periodic modulation of linear coupling ("Rabi lattice") and self-repulsive nonlinearity. The system may be realized in a binary Bose-Einstein condensate, whose components are resonantly coupled by a standing optical wave, as well as in terms of the bimodal light propagation in periodically twisted waveguides. The system supports various types of gap solitons (GSs), which are constructed, and their stability is investigated, in the first two finite bandgaps of the underlying spectrum. These include on- and off-site-centered solitons (the GSs of the off-site type are additionally categorized as spatially even and odd ones), which may be symmetric or antisymmetric, with respect to the coupled components. The GSs are chiefly stable in the first finite bandgap and unstable in the second one. In addition to that, there are narrow regions near the right edge of the first bandgap, and in the second one, which feature intricate alternation of stability and instability. Unstable solitons evolve into robust breathers or spatially confined turbulent modes. On-site-centered GSs are also considered in a version of the system that is made asymmetric by the Zeeman effect, or by birefringence of the optical waveguide. A region of alternate stability is found in the latter case too. In the limit of strong asymmetry, GSs are obtained in a semianalytical approximation, which reduces two coupled GPEs to a single one with an effective lattice potential.
Chen, Zhaopin; Malomed, Boris A.
2017-03-01
We introduce a two-component one-dimensional system, which is based on two nonlinear Schrödinger or Gross-Pitaevskii equations (GPEs) with spatially periodic modulation of linear coupling ("Rabi lattice") and self-repulsive nonlinearity. The system may be realized in a binary Bose-Einstein condensate, whose components are resonantly coupled by a standing optical wave, as well as in terms of the bimodal light propagation in periodically twisted waveguides. The system supports various types of gap solitons (GSs), which are constructed, and their stability is investigated, in the first two finite bandgaps of the underlying spectrum. These include on- and off-site-centered solitons (the GSs of the off-site type are additionally categorized as spatially even and odd ones), which may be symmetric or antisymmetric, with respect to the coupled components. The GSs are chiefly stable in the first finite bandgap and unstable in the second one. In addition to that, there are narrow regions near the right edge of the first bandgap, and in the second one, which feature intricate alternation of stability and instability. Unstable solitons evolve into robust breathers or spatially confined turbulent modes. On-site-centered GSs are also considered in a version of the system that is made asymmetric by the Zeeman effect, or by birefringence of the optical waveguide. A region of alternate stability is found in the latter case too. In the limit of strong asymmetry, GSs are obtained in a semianalytical approximation, which reduces two coupled GPEs to a single one with an effective lattice potential.
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)
Stable branches of a solution for a fermion on domain wall
Energy Technology Data Exchange (ETDEWEB)
Gani, V. A. [National Research Nuclear University MEPhI, Department of Mathematics (Russian Federation); Ksenzov, V. G.; Kudryavtsev, A. E. [Institute for Theoretical and Experimental Physics (Russian Federation)
2011-05-15
The case when a fermion occupies an excited nonzero frequency level in the field of domain wall is discussed. It is demonstrated that a solution exists for the coupling constant in the limited interval 1 < g < g{sub max} Almost-Equal-To 1.65. It is shown that indeed there are different branches of stable solution for g in this interval. The first one corresponds to a fermion located on the domain wall (1 < g < 4{radical}2{pi}). The second branch, which belongs to the interval 4{radical}2{pi} {<=} g {<=} g{sub max}, describes a polarized fermion off the domain wall. The third branch with 1 < g < g{sub max} describes an excited antifermion in the field of the domain wall.
Breaking soliton equations and negative-order breaking soliton ...
Indian Academy of Sciences (India)
We develop breaking soliton equations and negative-order breaking soliton equations of typical and higher orders. The recursion operator of the KdV equation is used to derive these models.We establish the distinctdispersion relation for each equation. We use the simplified Hirota's method to obtain multiple soliton ...
Controllable Akhmediev breather and Kuznetsov-Ma soliton trains in PT-symmetric coupled waveguides.
Dai, Chaoqing; Wang, Yueyue; Zhang, Xiaofei
2014-12-01
The PT-symmetric and PT-antisymmetric Akhmediev breather (AB) and Kuznetsov-Ma (KM) soliton train solutions of a (2+1)-dimensional variable-coefficient coupled nonlinear Schrödinger equation in PT-symmetric coupled waveguides with gain and loss are derived via the Darboux transformation method. From these analytical solutions, we investigate the controllable behaviors of AB and KM soliton trains in a diffraction decreasing system with exponential profile. By adjusting the relation between the maximum Zm of effective propagation distance and the peak locations Zi of AB and KM soliton trains, we can control the restraint, maintenance and postpone excitations of AB and KM soliton trains.
Bistable dark solitons of a cubic-quintic Helmholtz equation
International Nuclear Information System (INIS)
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.
Li, Daojing; Shen, Deyuan; Li, Lei; Tang, Dingyuan; Su, Lei; Zhao, Luming
2018-03-01
Investigation of internal polarization dynamics of vector dissipative-soliton-resonance (DSR) pulses in a mode-locked fiber laser is presented. Stable vector DSR pulses are experimentally ob- served. Using a waveplate-analyzer configuration, we find that polarization is not uniform across a resonant dissipative soliton. Specifically, although the central plane wave of the resonant dissi- pative soliton acquires nearly a fixed polarization, the fronts feature polarization states that are different and spatially varying. This distinct polarizaiton distribution is maintained while the whole soliton structrue extends with varying gain conditions. Numerical simulation further confirms the experimental observations.
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.
Solute dispersion for stable density-driven flow in randomly heterogeneous porous media
Dell'Oca, Aronne; Riva, Monica; Carrera, Jesus; Guadagnini, Alberto
2018-01-01
We present a theoretical investigation on the processes underpinning the reduced longitudinal spreading documented in stable variable density flows, as opposed to constant density settings, within heterogeneous porous media. We do so by decomposing velocity and pressure in terms of stationary and dynamic components. The former corresponds to the solution of the constant density flow problem, while the latter accounts for the effects induced by density variability. We focus on a stable flow configuration and analyze the longitudinal spread of saltwater injected from the bottom of a column formed by a heterogeneous porous medium initially fully saturated by freshwater. We adopt a perturbation expansion approach and derive the equations satisfied by section-averaged concentrations and their ensemble mean values. These formulations are respectively characterized by a single realization and an ensemble dispersive flux, which we determine through appropriate closure equations. The latter are solved via semi-analytical and numerical approaches. Our formulations and associated results enable us to discriminate the relative impact on the density-driven solute displacement of (a) covariance of the permeability of the porous medium, (b) cross-covariance between permeability and concentration, which is in turn linked to the coupling of flow and transport problems, and (c) cross-covariance between the dynamic and stationary velocities.
Bipolar solitons of the focusing nonlinear Schrödinger equation
Energy Technology Data Exchange (ETDEWEB)
Liu, Zhongxuan, E-mail: 13237379393@163.com; Feng, Qi; Lin, Chengyou; Chen, Zhaoyang; Ding, Yingchun, E-mail: dingyc@mail.buct.edu.cn
2016-11-15
The focusing nonlinear Schrödinger equation (NLSE) is a universal model for studying solitary waves propagation in nonlinear media. The NLSE is especially important in understanding how solitons on a condensate background (SCB) appear from a small perturbation through modulation instability. We study theoretically the one- and two-soliton solutions of the NLSE in presence of a condensate by using the dressing method. It is found that a class of bipolar elliptically polarized solitons with the choice of specific parameters in the one- and two-soliton solutions. Collisions among these solitons are studied by qualitative analysis and graphical illustration. We also generalize the concept of the quasi-Akhmediev breather to the bipolar solitons and show how it can be used for wave profile compression down to the extremely short duration. Our results extend previous studies in this area of the SCB and play an important role in the theory of freak wave.
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.
Darwish, Mohamed Abdalla; Rzepka, Beata
2014-01-01
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.
Solitons in Bose-Einstein Condensates with Helicoidal Spin-Orbit Coupling
Kartashov, Yaroslav V.; Konotop, Vladimir V.
2017-05-01
We report on the existence and stability of freely moving solitons in a spatially inhomogeneous Bose-Einstein condensate with helicoidal spin-orbit (SO) coupling. In spite of the periodically varying parameters, the system allows for the existence of stable propagating solitons. Such states are found in the rotating frame, where the helicoidal SO coupling is reduced to a homogeneous one. In the absence of the Zeeman splitting, the coupled Gross-Pitaevskii equations describing localized states feature many properties of the integrable systems. In particular, four-parametric families of solitons can be obtained in the exact form. Such solitons interact elastically. Zeeman splitting still allows for the existence of two families of moving solitons, but makes collisions of solitons inelastic.
Impurity driven diffusion and destruction of solitons in quasi-1D Bose-Einstein condensates
Aycock, Lauren; Hurst, Hilary; Lu, Hsin-I.; Genkina, Dina; Spielman, Ian
2016-05-01
Current experimental research on solitons focuses on their collisions with each other and how dimensionality influences their stability and decay. Here, we investigate the effect of evenly distributed impurity atoms on soliton dynamics. We launch lone, long-lived solitons in highly elongated 87 Rb Bose-Einstein condensates (BECs) by phase imprinting and observe oscillations stable over many seconds. We compare these long-lived solitons to those launched in BECs containing a few percent of impurity-the same atomic species in a different Zeeman sublevel-controllably introduced just before evaporation to degeneracy. These impurities - evenly distributed throughout the condensate - dramatically decrease the soliton lifetime and enhance Brownian-like diffusion in the soliton's trajectory.
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)
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.
Noncommuting Momenta of Topological Solitons
Watanabe, Haruki; Murayama, Hitoshi
2014-05-01
We show that momentum operators of a topological soliton may not commute among themselves when the soliton is associated with the second cohomology H2 of the target space. The commutation relation is proportional to the winding number, taking a constant value within each topological sector. The noncommutativity makes it impossible to specify the momentum of a topological soliton, and induces a Magnus force.
Nonlinear compression of optical solitons
Indian Academy of Sciences (India)
pulse area can be conserved by the inclusion of gain (or loss) and phase modulation effects. Keywords. Optical solitons; bright and dark solitons; nonlinear compression; phase modulation; fibre amplification; loss. PACS Nos 42.81. Dp; 02.30 Jr; 04.30 Nk. 1. Introduction. The term soliton refers to special kinds of waves that ...
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.
Exact soliton of (2 + 1)-dimensional fractional Schrödinger equation
Rizvi, S. T. R.; Ali, K.; Bashir, S.; Younis, M.; Ashraf, R.; Ahmad, M. O.
2017-07-01
The nonlinear fractional Schrödinger equation is the basic equation of fractional quantum mechanics introduced by Nick Laskin in 2002. We apply three tools to solve this mathematical-physical model. First, we find the solitary wave solutions including the trigonometric traveling wave solutions, bell and kink shape solitons using the F-expansion and Improve F-expansion method. We also obtain the soliton solution, singular soliton solutions, rational function solution and elliptic integral function solutions, with the help of the extended trial equation method.
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.
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
Head on collision of multi-solitons in an electron-positron-ion plasma having superthermal electrons
Energy Technology Data Exchange (ETDEWEB)
Roy, Kaushik, E-mail: kaushikbolpur@rediffmail.com [Beluti M. K. M. High School, P.O. Beluti, Birbhum, West Bengal 731301 (India); Chatterjee, Prasanta, E-mail: prasantachatterjee1@rediffmail.com; Roychoudhury, Rajkumar [Department of Mathematics, Siksha Bhavana Visva Bharati, Santiniketan 731235 (India)
2014-10-15
The head-on collision and overtaking collision of four solitons in a plasma comprising superthermal electrons, cold ions, and Boltzmann distributed positrons are investigated using the extended Poincare-Lighthill-Kuo (PLK) together with Hirota's method. PLK method yields two separate Korteweg-de Vries (KdV) equations where solitons obtained from any KdV equation move along a direction opposite to that of solitons obtained from the other KdV equation, While Hirota's method gives multi-soliton solution for each KdV equation all of which move along the same direction where the fastest moving soliton eventually overtakes the other ones. We have considered here two soliton solutions obtained from Hirota's method. Phase shifts acquired by each soliton due to both head-on collision and overtaking collision are calculated analytically.
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
Teeka, Chat; Jalil, Muhammad Arif; Yupapin, Preecha P; Ali, Jalil
2010-12-01
We propose a novel system of the dynamic optical tweezers generated by a dark soliton in the fiber optic loop. A dark soliton known as an optical tweezer is amplified and tuned within the microring resonator system. The required tunable tweezers with different widths and powers can be controlled. The analysis of dark-bright soliton conversion using a dark soliton pulse propagating within a microring resonator system is analyzed. The dynamic behaviors of soliton conversion in add/drop filter is also analyzed. The control dark soliton is input into the system via the add port of the add/drop filter. The dynamic behavior of the dark-bright soliton conversion is observed. The required stable signal is obtained via a drop and throughput ports of the add/drop filter with some suitable parameters. In application, the trapped light/atom and transportation can be realized by using the proposed system.
Ricci solitons, Ricci flow and strongly coupled CFT in the Schwarzschild Unruh or Boulware vacua
Figueras, Pau; Lucietti, James; Wiseman, Toby
2011-11-01
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 AdS5/CFT4. 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(N2c) part of the CFT stress tensor, which interestingly is regular on both the future and past Schwarzschild horizons.
Ricci solitons, Ricci flow and strongly coupled CFT in the Schwarzschild Unruh or Boulware vacua
Energy Technology Data Exchange (ETDEWEB)
Figueras, Pau [DAMTP, Centre for Mathematical Sciences, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA (United Kingdom); Lucietti, James [School of Mathematics and Maxwell Institute for Mathematical Sciences, University of Edinburgh, King' s Buildings, Edinburgh EH9 3JZ (United Kingdom); Wiseman, Toby, E-mail: t.wiseman@imperial.ac.uk [Theoretical Physics Group, Blackett Laboratory, Imperial College, London SW7 2AZ (United Kingdom)
2011-11-07
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{sub 5}/CFT{sub 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{sup 2}{sub c}) part of the CFT stress tensor, which interestingly is regular on both the future and past Schwarzschild horizons. (paper)
Zhang, Guoqiang; Yan, Zhenya; Wen, Xiao-Yong
2018-03-01
We investigate three-wave resonant interactions through both the generalized Darboux transformation method and numerical simulations. Firstly, we derive a simple multi-dark-dark-dark-soliton formula through the generalized Darboux transformation. Secondly, we use the matrix analysis method to avoid the singularity of transformed potential functions and to find the general nonsingular breather solutions. Moreover, through a limit process, we deduce the general rogue wave solutions and give a classification by their dynamics including bright, dark, four-petals, and two-peaks rogue waves. Ever since the coexistence of dark soliton and rogue wave in non-zero background, their interactions naturally become a quite appealing topic. Based on the N-fold Darboux transformation, we can derive the explicit solutions to depict their interactions. Finally, by performing extensive numerical simulations we can predict whether these dark solitons and rogue waves are stable enough to propagate. These results can be available for several physical subjects such as fluid dynamics, nonlinear optics, solid state physics, and plasma physics.
Bonilla, L L; Carretero, M; Terragni, F; Birnir, B
2016-08-09
Angiogenesis is a multiscale process by which blood vessels grow from existing ones and carry oxygen to distant organs. Angiogenesis is essential for normal organ growth and wounded tissue repair but it may also be induced by tumours to amplify their own growth. Mathematical and computational models contribute to understanding angiogenesis and developing anti-angiogenic drugs, but most work only involves numerical simulations and analysis has lagged. A recent stochastic model of tumour-induced angiogenesis including blood vessel branching, elongation, and anastomosis captures some of its intrinsic multiscale structures, yet allows one to extract a deterministic integropartial differential description of the vessel tip density. Here we find that the latter advances chemotactically towards the tumour driven by a soliton (similar to the famous Korteweg-de Vries soliton) whose shape and velocity change slowly. Analysing these collective coordinates paves the way for controlling angiogenesis through the soliton, the engine that drives this process.
Klasifikasi Interaksi Gelombang Permukaan Bertipe Dua Soliton
sutimin, Sutimin; Rusgiyono, Agus
2001-01-01
Pada tulisan ini diselidiki, masalah klasifikasi interaksi gelombang bertipe dua soliton Kadomtsev-Petviashvilli (KP). Disini dianalisis berdasarkan parameter interaksi dua solusi soliton baik melalui harga eksak maupun proses pelimitan. Proses pelimitan ini dilakukan untuk mengetahui resonansi diantara dua soliton. Selanjutnya resonansi soliton ini dikaji untuk mendapatkan soliton yang baru.
Soliton equations solved by the boundary CFT
Saito, Satoru; Sato, Ryuichi
2003-01-01
Soliton equations are derived which characterize the boundary CFT a la Callan et al. Soliton fields of classical soliton equations are shown to appear as a neutral bound state of a pair of soliton fields of BCFT. One soliton amplitude under the influence of the boundary is calculated explicitly and is shown that it is frozen at the Dirichlet limit.
Direct soliton generation in microresonators.
Bao, Chengying; Xuan, Yi; Jaramillo-Villegas, Jose A; Leaird, Daniel E; Qi, Minghao; Weiner, Andrew M
2017-07-01
We investigate, numerically and experimentally, the effect of thermo-optical (TO) chaos on soliton generation dynamics in microresonators. Numerical simulations that include the thermal dynamics show that the generated solitons can either survive or annihilate when the pump laser is scanned from blue to red and then stop at a fixed wavelength; the outcome is stochastic and is strongly related to the number of solitons generated. The random fluctuations of the cavity resonance occurring under TO chaos are also found to trigger delayed spontaneous soliton generation after the laser scan ends, which could enable soliton excitation with slow laser tuning speed. Stochastic soliton annihilation/survival, as well as delayed spontaneous soliton generation, is observed experimentally in a silicon-nitride microresonator.
A potential new, stable state of the E-cadherin strand-swapped dimer in solution.
Schumann-Gillett, Alexandra; Mark, Alan E; Deplazes, Evelyne; O'Mara, Megan L
2018-01-01
E-cadherin is a transmembrane glycoprotein that facilitates inter-cellular adhesion in the epithelium. The ectodomain of the native structure is comprised of five repeated immunoglobulin-like domains. All E-cadherin crystal structures show the protein in one of three alternative conformations: a monomer, a strand-swapped trans homodimer and the so-called X-dimer, which is proposed to be a kinetic intermediate to forming the strand-swapped trans homodimer. However, previous studies have indicated that even once the trans strand-swapped dimer is formed, the complex is highly dynamic and the E-cadherin monomers may reorient relative to each other. Here, molecular dynamics simulations have been used to investigate the stability and conformational flexibility of the human E-cadherin trans strand-swapped dimer. In four independent, 100 ns simulations, the dimer moved away from the starting structure and converged to a previously unreported structure, which we call the Y-dimer. The Y-dimer was present for over 90% of the combined simulation time, suggesting that it represents a stable conformation of the E-cadherin dimer in solution. The Y-dimer conformation is stabilised by interactions present in both the trans strand-swapped dimer and X-dimer crystal structures, as well as additional interactions not found in any E-cadherin dimer crystal structures. The Y-dimer represents a previously unreported, stable conformation of the human E-cadherin trans strand-swapped dimer and suggests that the available crystal structures do not fully capture the conformations that the human E-cadherin trans homodimer adopts in solution.
National Research Council Canada - National Science Library
Rebbi, Claudio; Soliani, G
1984-01-01
... may find in the reprints on the mathematical theories of solitons useful ideas and inspirations, while the latter may find in this volume interesting and challenging applications of the concept of solitons in the domain of particle physics. We would like to express our gratitude to the many colleagues, in particular to Sidney Coleman, Neil Craigie, Roman Jackiw and Ed Witten, who have given us advice in the selection of the reprints. We are also thankful to Dr. Phua and World Scientific Publishing Co. for giving u...
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)
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.
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.
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
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
Self-trapped optical beams: Spatial solitons
Indian Academy of Sciences (India)
We present a brief overview of the basic concepts of the theory ofspatial optical solitons, including the soliton stability in non-Kerr media, the instability-induced soliton dynamics, and collision of solitary waves in nonintegrable nonlinear models.
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
Breather-to-soliton transformation rules in the hierarchy of nonlinear Schrödinger equations.
Chowdury, Amdad; Krolikowski, Wieslaw
2017-06-01
We study the exact first-order soliton and breather solutions of the integrable nonlinear Schrödinger equations hierarchy up to fifth order. We reveal the underlying physical mechanism which transforms a breather into a soliton. Furthermore, we show how the dynamics of the Akhmediev breathers which exist on a constant background as a result of modulation instability, is connected with solitons on a zero background. We also demonstrate that, while a first-order rogue wave can be directly transformed into a soliton, higher-order rogue wave solutions become rational two-soliton solutions with complex collisional structure on a background. Our results will have practical implications in supercontinuum generation, turbulence, and similar other complex nonlinear scenarios.
Yaşar, Emrullah; Yıldırım, Yakup; Zhou, Qin; Moshokoa, Seithuti P.; Ullah, Malik Zaka; Triki, Houria; Biswas, Anjan; Belic, Milivoj
2017-11-01
This paper obtains optical soliton solution to perturbed nonlinear Schrödinger's equation by modified simple equation method. There are four types of nonlinear fibers studied in this paper. They are Anti-cubic law, Quadratic-cubic law, Cubic-quintic-septic law and Triple-power law. Dark and singular soliton solutions are derived. Additional solutions such as singular periodic solutions also fall out of the integration scheme.
Soliton interaction as a possible model for extreme waves in shallow water
Peterson, P.; Soomere, T.; Engelbrecht, J.; van Groesen, Embrecht W.C.
2003-01-01
Interaction of two long-crested shallow water waves is analysed in the framework of the two-soliton solution of the Kadomtsev-Petviashvili equation. The wave system is decomposed into the incoming waves and the interaction soliton that represents the particularly high wave hump in the crossing area
Interaction of spatial photorefractive solitons
DEFF Research Database (Denmark)
Królikowski, W.; Denz, C.; Stepken, A.
1998-01-01
We present a review of our recent theoretical and experimental results on the interaction of two-dimensional solitary beams in photorefractive SBN crystals. We show that the collision of coherent solitons may result in energy exchange, fusion of the interacting solitons, the birth of a new solita...... that a soliton pair may experience both attractive and repulsive forces; depending on their mutual separation. We also show that strong attraction leads to periodic collision or helical motion of solitons depending on initial conditions.......We present a review of our recent theoretical and experimental results on the interaction of two-dimensional solitary beams in photorefractive SBN crystals. We show that the collision of coherent solitons may result in energy exchange, fusion of the interacting solitons, the birth of a new solitary...
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.
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
Many-body interaction in fast soliton collisions.
Peleg, Avner; Nguyen, Quan M; Glenn, Paul
2014-04-01
We study n-pulse interaction in fast collisions of N solitons of the cubic nonlinear Schrödinger (NLS) equation in the presence of generic weak nonlinear loss. We develop a generalized reduced model that yields the contribution of the n-pulse interaction to the amplitude shift for collisions in the presence of weak (2m+1)-order loss, for any n and m. We first employ the reduced model and numerical solution of the perturbed NLS equation to analyze soliton collisions in the presence of septic loss (m=3). Our calculations show that the three-pulse interaction gives the dominant contribution to the collision-induced amplitude shift already in a full-overlap four-soliton collision, and that the amplitude shift strongly depends on the initial soliton positions. We then extend these results for a generic weak nonlinear loss of the form G(|ψ|2)ψ, where ψ is the physical field and G is a Taylor polynomial of degree mc. Considering mc=3, as an example, we show that three-pulse interaction gives the dominant contribution to the amplitude shift in a six-soliton collision, despite the presence of low-order loss. Our study quantitatively demonstrates that n-pulse interaction with high n values plays a key role in fast collisions of NLS solitons in the presence of generic nonlinear loss. Moreover, the scalings of n-pulse interaction effects with n and m and the strong dependence on initial soliton positions lead to complex collision dynamics, which is very different from that observed in fast NLS soliton collisions in the presence of cubic loss.
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.
Directory of Open Access Journals (Sweden)
C. Adam
2016-03-01
Full Text Available 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.
Chiral solitons a review volume
1987-01-01
This review volume on topological and nontopological chiral solitons presents a global view on the current developments of this field in particle and nuclear physics. The book addresses problems in quantization, restoration of translational and rotational symmetry, and the field theoretical approach to solitons which are common problems in the field of solitons. Primarily aimed for graduate students and the novice in the field, the collected articless cover a broad spectrum of topics in formalism as well as phenomenology.
Capture and confinement of solitons in nonlinear integrable systems
International Nuclear Information System (INIS)
Mel'nikov, V.K.
1988-01-01
Some nonlinear integrable systems were found to have solutions describing solitons that come from infinity and then are captured into oscillatory regimes. These solutions were obtained by the inverse scattering method for the one-dimensional Schroedinger operator on a straight line. The obtained results are relevant to some problems of hydrodynamics, plasma physics, solid state physics, etc. 2 refs
Collisional Effect On Magnetosonic Solitons In A Dusty Plasma Slab ...
African Journals Online (AJOL)
An analytical investigation of collisional effect on magnetosonic solitons in a dusty plasma slab is presented. We have derived and presented solutions of nonlinear magetohydrodynamic equations for a warm dusty magnetoplasma. It is observed that, our work could be considered a general case for magnetosonic solutions ...
One-parameter family of solitons from minimal surfaces
Indian Academy of Sciences (India)
In this paper, we discuss a one parameter family of complex Born–Infeld 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.
One-parameter family of solitons from minimal surfaces
Indian Academy of Sciences (India)
Abstract. In this paper, we discuss a one parameter family of complex Born–Infeld 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 ...
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)
Ivashchuk, V D; Ernazarov, K K
2017-01-01
A ( n + 1)-dimensional gravitational model with cosmological constant and Gauss-Bonnet term is studied. The ansatz with diagonal cosmological metrics is adopted and solutions with exponential dependence of scale factors: a i ∼ exp ( v i t ), i = 1, …, n , are considered. The stability analysis of the solutions with non-static volume factor is presented. We show that the solutions with v 1 = v 2 = v 3 = H > 0 and small enough variation of the effective gravitational constant G are stable if certain restriction on ( v i ) is obeyed. New examples of stable exponential solutions with zero variation of G in dimensions D = 1 + m + 2 with m > 2 are presented. (paper)
Biological soliton in multicellular movement
Kuwayama, Hidekazu; Ishida, Shuji
2013-01-01
Solitons have been observed in various physical phenomena. Here, we show that the distinct characteristics of solitons are present in the mass cell movement of non-chemotactic mutants of the cellular slime mould Dictyostelium discoideum. During starvation, D. discoideum forms multicellular structures that differentiate into spore or stalk cells and, eventually, a fruiting body. Non-chemotactic mutant cells do not form multicellular structures; however, they do undergo mass cell movement in the form of a pulsatile soliton-like structure (SLS). We also found that SLS induction is mediated by adhesive cell-cell interactions. These observations provide novel insights into the mechanisms of biological solitons in multicellular movement. PMID:23893301
Bjoraker; Hosotani
2000-02-28
A continuum of new monopole and dyon solutions in the Einstein-Yang-Mills theory in asymptotically anti-de Sitter space are found. They are regular everywhere and specified by their mass and their non-Abelian electric and magnetic charges. A class of monopole solutions which have no node in non-Abelian magnetic fields is shown to be stable against spherically symmetric linear perturbations.
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
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
Djoufack, Z I; Tala-Tebue, E; Nguenang, J P; Kenfack-Jiotsa, A
2016-10-01
We report in this work, an analytical study of quantum soliton in 1D Heisenberg spin chains with Dzyaloshinsky-Moriya Interaction (DMI) and Next-Nearest-Neighbor Interactions (NNNI). By means of the time-dependent Hartree approximation and the semi-discrete multiple-scale method, the equation of motion for the single-boson wave function is reduced to the nonlinear Schrödinger equation. It comes from this present study that the spectrum of the frequencies increases, its periodicity changes, in the presence of NNNI. The antisymmetric feature of the DMI was probed from the dispersion curve while changing the sign of the parameter controlling it. Five regions were identified in the dispersion spectrum, when the NNNI are taken into account instead of three as in the opposite case. In each of these regions, the quantum model can exhibit quantum stationary localized and stable bright or dark soliton solutions. In each region, we could set up quantum localized n-boson Hartree states as well as the analytical expression of their energy level, respectively. The accuracy of the analytical studies is confirmed by the excellent agreement with the numerical calculations, and it certifies the stability of the stationary quantum localized solitons solutions exhibited in each region. In addition, we found that the intensity of the localization of quantum localized n-boson Hartree states increases when the NNNI are considered. We also realized that the intensity of Hartree n-boson states corresponding to quantum discrete soliton states depend on the wave vector.
Asymmetric spatial soliton dragging.
Blair, S; Wagner, K; McLeod, R
1994-12-01
A new low-latency, cascadable optical logic gate with gain, high contrast, and three-terminal input-output isolation is introduced. The interaction between two orthogonally polarized spatial solitons brought into coincidence at the boundary of a saturating nonlinear medium and propagating in different directions results in the phase-insensitive spatial dragging of a strong pump soliton by a weaker signal. As a result, the strong pump is transmitted through an aperture when the weak signal is not present, and it is dragged to the side by more than a beam width and blocked in the presence of the weak signal, thus implementing an inverter with gain. A multi-input, logically complete NOR gate also can be implemented in a cascaded system.
Vortices and ring solitons in Bose-Einstein condensates
International Nuclear Information System (INIS)
Carr, L. D.; Clark, Charles W.
2006-01-01
The form and stability properties of axisymmetric and spherically symmetric stationary states in two and three dimensions, respectively, are elucidated for Bose-Einstein condensates. These states include the ground state, central vortices, and radial excitations of both. The latter are called ring solitons in two dimensions and spherical shells in three. The nonlinear Schroedinger equation is taken as the fundamental model; both extended and harmonically trapped condensates are considered. It is found that the instability times of ring solitons can be long compared to experimental time scales, making them effectively stable over the lifetime of an experiment
Breaking soliton equations and negative-order breaking soliton ...
Indian Academy of Sciences (India)
2016-10-06
Oct 6, 2016 ... Abstract. We develop breaking soliton equations and negative-order breaking soliton equations of typical and higher orders. The recursion operator of the KdV equation is used to derive these models. We establish the distinct dispersion relation for each equation. We use the simplified Hirota's method to ...
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.
Solutions of the coupled Higgs field equations
Talukdar, Benoy; Ghosh, Swapan K.; Saha, Aparna; Pal, Debabrata
2013-07-01
By an appropriate choice for the phase of the complex nucleonic field and going over to the traveling coordinate, we reduce the coupled Higgs equations to the Hamiltonian form and treat the resulting equation using the dynamical system theory. We present a phase-space analysis of its stable points. The results of our study demonstrate that the equation can support both traveling- and standing-wave solutions. The traveling-wave solution appears in the form of a soliton and resides in the midst of doubly periodic standing-wave solutions.
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.
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.
Annular gap solitons in Kerr media with circular gratings
International Nuclear Information System (INIS)
Scheuer, Jacob; Malomed, Boris
2007-01-01
We introduce standing-light patterns trapped in a Bragg grating written along the radial direction in a self-focusing (SF) or self-defocusing (SDF) optical medium. Unlike previously studied axisymmetric settings that deal with the axial propagation, we consider the propagation of light in the radial directions (outward and inward), which may give rise to annular gap solitons (AGSs), supported by the circular grating. An estimate for the threshold of the modulational instability of the AGS against azimuthal perturbations in the SF medium is obtained analytically, and verified by direct simulations. In the SDF model, stable annular and dipole solitons are found in a numerical form, while multipole patterns and vortex rings are unstable. Similar solitons are possible in the Bose-Einstein condensate
Soliton nanoantennas in two-dimensional arrays of quantum dots
Gligorić, G.; Maluckov, A.; Hadžievski, Lj; Slepyan, G. Ya; Malomed, B. A.
2015-06-01
We consider two-dimensional (2D) arrays of self-organized semiconductor quantum dots (QDs) strongly interacting with electromagnetic field in the regime of Rabi oscillations. The QD array built of two-level states is modelled by two coupled systems of discrete nonlinear Schrödinger equations. Localized modes in the form of single-peaked fundamental and vortical stationary Rabi solitons and self-trapped breathers have been found. The results for the stability, mobility and radiative properties of the Rabi modes suggest a concept of a self-assembled 2D soliton-based nano-antenna, which is stable against imperfections In particular, we discuss the implementation of such a nano-antenna in the form of surface plasmon solitons in graphene, and illustrate possibilities to control their operation by means of optical tools.
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.
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.
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.
Gravitational field of Schwarzschild soliton
Directory of Open Access Journals (Sweden)
Musavvir Ali
2015-01-01
Full Text Available The aim of this paper is to study the gravitational field of Schwarzschild soliton. Use of characteristic of λ-tensor is given to determine the kinds of gravitational fields. Through the cases of two and three dimension for Schwarzschild soliton, the Gaussian curvature is expressed in terms of eigen values of the characteristic equation.
Multi-soliton energy transport in anharmonic lattices
DEFF Research Database (Denmark)
Ostrovskaya, Elena A A.; Mingaleev, Serge F.; Kivshar, Yuri S S.
2001-01-01
We demonstrate the existence of dynamically stable multihump solitary waves in polaron-type models describing interaction of envelope and lattice excitations. In comparison with the earlier theory of multihump optical solitons (see Phys. Rev. Lett. 83 (1999) 296), our analysis reveals a novel...... physical mechanism for the formation of stable multihump solitary waves in nonintegrable multi-component nonlinear models. (C) 2001 Elsevier Science B.V. All rights reserved....
Breather soliton dynamics in microresonators
Yu, Mengjie; Jang, Jae K.; Okawachi, Yoshitomo; Griffith, Austin G.; Luke, Kevin; Miller, Steven A.; Ji, Xingchen; Lipson, Michal; Gaeta, Alexander L.
2017-01-01
The generation of temporal cavity solitons in microresonators results in coherent low-noise optical frequency combs that are critical for applications in spectroscopy, astronomy, navigation or telecommunications. Breather solitons also form an important part of many different classes of nonlinear wave systems, manifesting themselves as a localized temporal structure that exhibits oscillatory behaviour. To date, the dynamics of breather solitons in microresonators remains largely unexplored, and its experimental characterization is challenging. Here we demonstrate the excitation of breather solitons in two different microresonator platforms based on silicon nitride and on silicon. We investigate the dependence of the breathing frequency on pump detuning and observe the transition from period-1 to period-2 oscillation. Our study constitutes a significant contribution to understanding the soliton dynamics within the larger context of nonlinear science. PMID:28232720
Soliton mobility in disordered lattices.
Sun, Zhi-Yuan; Fishman, Shmuel; Soffer, Avy
2015-10-01
We investigate soliton mobility in the disordered Ablowitz-Ladik (AL) model and the standard nonlinear Schrödinger (NLS) lattice with the help of an effective potential generalizing the Peierls-Nabarro potential. This potential results from a deviation from integrability, which is due to randomness for the AL model, and both randomness and lattice discreteness for the NLS lattice. The statistical properties of such a potential are analyzed, and it is shown how the soliton mobility is affected by its size. The usefulness of this effective potential in studying soliton dynamics is demonstrated numerically. Furthermore, we propose two ways to enhance soliton transport in the presence of disorder: one is to use specific realizations of randomness, and the other is to consider a specific soliton pair.
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.
Slunyaev, A V; Pelinovsky, E N
2016-11-18
The role of multiple soliton and breather interactions in the formation of very high waves is disclosed within the framework of the integrable modified Korteweg-de Vries (MKdV) equation. Optimal conditions for the focusing of many solitons are formulated explicitly. Namely, trains of ordered solitons with alternate polarities evolve to huge strongly localized transient waves. The focused wave amplitude is exactly the sum of the focusing soliton heights; the maximum wave inherits the polarity of the fastest soliton in the train. The focusing of several solitary waves or/and breathers may naturally occur in a soliton gas and will lead to rogue-wave-type dynamics; hence, it represents a new nonlinear mechanism of rogue wave generation. The discovered scenario depends crucially on the soliton polarities (phases), and is not taken into account by existing kinetic theories. The performance of the soliton mechanism of rogue wave generation is shown for the example of the focusing MKdV equation, when solitons possess "frozen" phases (certain polarities), though the approach is efficient in some other integrable systems which admit soliton and breather solutions.
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.
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.
Scaling behaviour of the effective chiral action and stability of the chiral soliton
International Nuclear Information System (INIS)
Reinhardt, H.
1986-12-01
The effective chiral action is evaluated within a novel improved heat-kernel expansion, which includes gradients of the chiral field in a non-perturbative way. The exact scaling behaviour of the effective action of a localized chiral field with respect to changing its spatial size is found. From this it is proved that the radiatively induced derivative terms cannot absolutely stabilize the chiral soliton against collapsing. The collapsing of the soliton is, however, accompanied by a vanishing of the baryon charge. It is argued that the effective chiral action constrained to a fixed baryon number may still admit stable soliton configurations. (orig.)
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
Variational methods in nonlinear field equations solitary waves, hylomorphic solitons and vortices
Benci, Vieri
2014-01-01
The book analyzes the existence of solitons, namely of finite energy solutions of field equations which exhibit stability properties. The book is divided in two parts. In the first part, the authors give an abstract definition of solitary wave and soliton and we develop an abstract existence theory for hylomorphic solitons, namely for those solitons which minimize the energy for a given charge. In the second part, the authors apply this theory to prove the existence of hylomorphic solitons for some classes of field equations (nonlinear Klein-Gordon-Maxwell equations, nonlinear Schrödinger-Maxwell equations, nonlinear beam equation,..). The abstract theory is sufficiently flexible to be applied to other situations, like the existence of vortices. The books is addressed to Mathematicians and Physicists.
Scalar-vector soliton fiber laser mode-locked by nonlinear polarization rotation.
Wu, Zhichao; Liu, Deming; Fu, Songnian; Li, Lei; Tang, Ming; Zhao, Luming
2016-08-08
We report a passively mode-locked fiber laser by nonlinear polarization rotation (NPR), where both vector and scalar soliton can co-exist within the laser cavity. The mode-locked pulse evolves as a vector soliton in the strong birefringent segment and is transformed into a regular scalar soliton after the polarizer within the laser cavity. The existence of solutions in a polarization-dependent cavity comprising a periodic combination of two distinct nonlinear waves is first demonstrated and likely to be applicable to various other nonlinear systems. For very large local birefringence, our laser approaches the operation regime of vector soliton lasers, while it approaches scalar soliton fiber lasers under the condition of very small birefringence.
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.
Carroll, RW
1991-01-01
When soliton theory, based on water waves, plasmas, fiber optics etc., was developing in the 1960-1970 era it seemed that perhaps KdV (and a few other equations) were really rather special in the set of all interesting partial differential equations. As it turns out, although integrable systems are still special, the mathematical interaction of integrable systems theory with virtually all branches of mathematics (and with many currently developing areas of theoretical physics) illustrates the importance of this area. This book concentrates on developing the theme of the tau function. KdV and K
Wang, Pan; Bao, Chengying; Fu, Bo; Xiao, Xiaosheng; Grelu, Philippe; Yang, Changxi
2016-05-15
We report on the experimental observation of stable single solitons and soliton molecules in a 2-μm thulium-holmium-doped fiber laser mode-locked through the nonlinear polarization evolution technique within an anomalously dispersive cavity. Single 0.65 nJ solitons feature a 7.3 nm spectral FWHM and 540 fs temporal duration, yielding a time-bandwidth product close to the Fourier-transform limitation. Under the same pumping power of 740 mW, stable out-of-phase twin-soliton molecules, featuring a temporal separation of 2.5 ps between the two ∼700 fs pulses, are generated in a deterministic way, while the central wavelength of the soliton molecules can be tuned from 1920 to 1940 nm. Finally, we present strong experimental evidence of vibrating soliton molecules.
Noise induced creation and annihilation of solitons in dispersion managed fiber oscillators
Teamir, Tesfay G.; Ilday, F. Ömer
2017-01-01
Optical solitons and their interaction with other solitons or with dispersive wave shed by solitons under perturbation constitute a versatile experimental and theoretical platform for studying the nature of complex dynamics occurring in laser cavities [1-3] in addition to common physical principles in terms with a range of other nonlinear, non-equilibrium, coupled systems outside of optics. A soliton is energy localization of dissipative structures of electric field which evolves from noise in laser cavities. It is stationary solution of nonlinear Schrödinger equation that balances the effects of chromatic dispersion with nonlinearity during propagation in a medium. Strong pumping in soliton regime drives a laser system in to a multi pulsing self-organized system. Such a system in fiber medium is ubiquitous and always attracts research interest. Multi-soliton pulses or soliton bunches generated from different systems through a long range interaction due to acoustic waves generated from electrostriction and its perturbation induced refractive index change of the medium by a propagating pulse on the next pulse in the neighborhood. A short range interaction can occur as a result of pulses overlapping, acoustoptic interaction or it can occur when dispersive waves at the tail of pulses interact with a back ground field or with solitons near to its.
Observation of Coexisting Dissipative Solitons in a Mode-Locked Fiber Laser.
Bao, Chengying; Chang, Wonkeun; Yang, Changxi; Akhmediev, Nail; Cundiff, Steven T
2015-12-18
We show, experimentally and numerically, that a mode-locked fiber laser can operate in a regime where two dissipative soliton solutions coexist and the laser will periodically switch between the solutions. The two dissipative solitons differ in their pulse energy and spectrum. The switching can be controlled by an external perturbation and triggered even when switching does not occur spontaneously. Numerical simulations unveil the importance of the double-minima loss spectrum and nonlinear gain to the switching dynamics.
Tanh-type and sech-type solitons for some space-time fractional PDE models
Guner, Ozkan; Bekir, Ahmet; Korkmaz, Alper
2017-02-01
Tanh-type and sech-type soliton solutions are constructed for the fractional modified KdV-Zakharov-Kuznetsov equation and the fractional generalized Duffing equation. Both equations are reduced to ordinary differential equations by using compatible fractional complex transforms. Suitable powers of tanh and sech ansatzs including unknown free parameters are applied to both equations. After determining the powers, these parameters are determined using computer algebra. The obtained soliton solutions are depicted for particular cases for various values of derivative order.
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
Directory of Open Access Journals (Sweden)
Dianchen Lu
Full Text Available In this article, we study one of the most popular models in nature and also industrial which is the van der Waals normal form for the fluidized granular matter. Understanding of static and dynamic property for these kinds of the models is very important in many aspects of industrial from pharmaceuticals to civil engineering and also some basic physical phenomena like those studied in geophysics. This model explains the phase separation phenomenon. We apply six different methods for this model to obtained the traveling and solitary wave solutions. We make the comparison between obtained solutions with each of them and also with obtained solutions with different methods. Keywords: The van der Waals normal form for fluidized granular matter, Modified simple equation method, The improved mapping approach and variable separation method, Traveling wave solutions, Solitary wave solutions, Mathematical physics
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)
Solitons in ideal optical fibers: a numerical development
Directory of Open Access Journals (Sweden)
Eliandro Rodrigues Cirilo
2010-03-01
Full Text Available This work developed a numerical procedure for a system of partial differential equations (PDEs describing the propagation of solitons in ideal optical fibers. The validation of the procedure was implemented from the numerical comparison between the known analytical solutions of the PDEs system and those obtained by using the numerical procedure developed. It was discovered that the procedure, based on the finite difference method and relaxation Gauss-Seidel method, was adequate in describing the propagation of soliton waves in ideals optical fibers.
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)
Quantized Solitons in the Extended Skyrme-Faddeev Model
Directory of Open Access Journals (Sweden)
L. A. Ferreira
2011-01-01
Full Text Available The construction of axially symmetric soliton solutions with non-zero Hopf topological charges according to a theory known as the extended Skyrme-Faddeev model, was performed in [1]. In this paper we show how masses of glueballs are predicted within this model.
Solitons, compactons and undular bores in Benjamin–Bona ...
Indian Academy of Sciences (India)
2017-01-04
Jan 4, 2017 ... 3Department of Physics, Bidhannagar College, EB-2, Sector-1, Salt Lake, Kolkata 700 064, India. ∗. Corresponding ... found to support soliton and compacton/anticompacton solutions depending on whether the dispersive term is linear or nonlinear. ... variety of ingenuous mathematical techniques includ-.
Dynamics of coupled field solitons: A collective coordinate approach
Indian Academy of Sciences (India)
In this paper we consider a class of systems of two coupled real scalar fields in bidimensional space-time, with the main motivation of studying classical stability of soliton solutions using collective coordinate approach. First, we present the class of systems of the collective coordinate equations which are derived using the ...
Solitons, compactons and undular bores in Benjamin–Bona ...
Indian Academy of Sciences (India)
Benjamin–Bona–Mahony-like equations; travelling wave solutions; solitons; compactons; dissipation; undular bores; shock waves. ... 731 235, India; Department of Physics, Abhedananda College, Sainthia 731 234, India; Department of Physics, Bidhannagar College, EB-2, Sector-1, Salt Lake, Kolkata 700 064, India ...
Optical solitons with DWDM technology and four-wave mixing
Ekici, Mehmet; Zhou, Qin; Sonmezoglu, Abdullah; Moshokoa, Seithuti P.; Ullah, Malik Zaka; Biswas, Anjan; Belic, Milivoj
2017-07-01
This paper obtains bright and singular optical soliton solutions to DWDM system in presence of four-wave mixing. The extended trial function scheme is adopted. The two types of nonlinear media studied are Kerr law and parabolic law. There are other types of waves that appears as a byproduct to this scheme.
Solitons, compactons and undular bores in Benjamin–Bona ...
Indian Academy of Sciences (India)
We examine the effect of dissipation on travelling waves in nonlinear dispersive systems modelled by Benjamin–Bona–Mahony (BBM)-like equations. In the absence of dissipation, the BBM-like equations are found to support soliton and compacton/anticompacton solutions depending on whether the dispersive term islinear ...
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.
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.
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.
Asymptotic Stability of High-dimensional Zakharov-Kuznetsov Solitons
Côte, Raphaël; Muñoz, Claudio; Pilod, Didier; Simpson, Gideon
2016-05-01
We prove that solitons (or solitary waves) of the Zakharov-Kuznetsov (ZK) equation, a physically relevant high dimensional generalization of the Korteweg-de Vries (KdV) equation appearing in Plasma Physics, and having mixed KdV and nonlinear Schrödinger (NLS) dynamics, are strongly asymptotically stable in the energy space. We also prove that the sum of well-arranged solitons is stable in the same space. Orbital stability of ZK solitons is well-known since the work of de Bouard [Proc R Soc Edinburgh 126:89-112, 1996]. Our proofs follow the ideas of Martel [SIAM J Math Anal 157:759-781, 2006] and Martel and Merle [Math Ann 341:391-427, 2008], applied for generalized KdV equations in one dimension. In particular, we extend to the high dimensional case several monotonicity properties for suitable half-portions of mass and energy; we also prove a new Liouville type property that characterizes ZK solitons, and a key Virial identity for the linear and nonlinear part of the ZK dynamics, obtained independently of the mixed KdV-NLS dynamics. This last Virial identity relies on a simple sign condition which is numerically tested for the two and three dimensional cases with no additional spectral assumptions required. Possible extensions to higher dimensions and different nonlinearities could be obtained after a suitable local well-posedness theory in the energy space, and the verification of a corresponding sign condition.
Breathing pulses in the damped-soliton model for nerves
Fongang Achu, G.; Moukam Kakmeni, F. M.; Dikande, A. M.
2018-01-01
Unlike the Hodgkin-Huxley picture in which the nerve impulse results from ion exchanges across the cell membrane through ion-gate channels, in the so-called soliton model the impulse is seen as an electromechanical process related to thermodynamical phenomena accompanying the generation of the action potential. In this work, account is taken of the effects of damping on the nerve impulse propagation, within the framework of the soliton model. Applying the reductive perturbation expansion on the resulting KdV-Burgers equation, a damped nonlinear Schrödinger equation is derived and shown to admit breathing-type solitary wave solutions. Under specific constraints, these breathing pulse solitons become self-trapped structures in which the damping is balanced by nonlinearity such that the pulse amplitude remains unchanged even in the presence of damping.
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
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.
Lu, Dianchen; Seadawy, Aly R.; Khater, Mostafa M. A.
In this article, we study one of the most popular models in nature and also industrial which is the van der Waals normal form for the fluidized granular matter. Understanding of static and dynamic property for these kinds of the models is very important in many aspects of industrial from pharmaceuticals to civil engineering and also some basic physical phenomena like those studied in geophysics. This model explains the phase separation phenomenon. We apply six different methods for this model to obtained the traveling and solitary wave solutions. We make the comparison between obtained solutions with each of them and also with obtained solutions with different methods.
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
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
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.
Directory of Open Access Journals (Sweden)
Harun Or-Roshid
2017-06-01
Full Text Available A direct rational exponential scheme is proposed to construct exact multi-soliton solutions and its fission, fusion phenomena after interaction of the solitons has been discussed. We have considered the Burgers and Sharma–Tasso–Olver equation as two concrete examples to show the fission and fusion of the solitary wave and the solitons, respectively. We improve different structured multi-soliton solutions with possible conditions for fission and fusion of the Burgers and the Sharma–Tasso–Olver equations arises in plasma physics and in ocean dynamics. The amplitude and velocity relations between solitons and/or solitary waves before and after interactions are given and a possible condition for fission and fusion is proposed. Furthermore, three-dimensional plots of the wave solutions are given to visualize the dynamics of the model.
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.
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.
Solitons, compactons and undular bores in Benjamin-Bona-Mahony-like systems
Saha, Aparna; Talukdar, B.; Das, Umapada; Chatterjee, Supriya
2017-02-01
We examine the effect of dissipation on travelling waves in nonlinear dispersive systems modelled by Benjamin-Bona-Mahony (BBM)-like equations. In the absence of dissipation, the BBM-like equations are found to support soliton and compacton /anticompacton solutions depending on whether the dispersive term is linear or nonlinear. We study the influence of increasing nonlinearity of the medium on the soliton and compacton dynamics. The dissipative effect is found to convert the solitons either to undular bores or to shock-like waves depending on the degree of nonlinearity of the equations. The anticompacton solutions are also transformed to undular bores by the effect of dissipation. But the compactons tend to vanish due to viscous effects. The local oscillatory structures behind the bores and /or shock-like waves in the case of solitons and anticompactons are found to depend sensitively both on the coefficient of viscosity and solution of the unperturbed problem.
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...
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-Jon...
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
Stable Covalent Organic Frameworks for Exceptional Mercury Removal from Aqueous Solutions.
Huang, Ning; Zhai, Lipeng; Xu, Hong; Jiang, Donglin
2017-02-15
The pre-designable porous structures found in covalent organic frameworks (COFs) render them attractive as a molecular platform for addressing environmental issues such as removal of toxic heavy metal ions from water. However, a rational structural design of COFs in this aspect has not been explored. Here we report the rational design of stable COFs for Hg(II) removal through elaborate structural design and control over skeleton, pore size, and pore walls. The resulting framework is stable under strong acid and base conditions, possesses high surface area, has large mesopores, and contains dense sulfide functional termini on the pore walls. These structural features work together in removing Hg(II) from water and achieve a benchmark system that combines capacity, efficiency, effectivity, applicability, selectivity, and reusability. These results suggest that COFs offer a powerful platform for tailor-made structural design to cope with various types of pollution.
Liu, Lei; Tian, Bo; Xie, Xi-Yang; Guan, Yue-Yang
2017-01-01
Studied in this paper are the vector bright solitons of the coupled higher-order nonlinear Schrödinger system, which describes the simultaneous propagation of two ultrashort pulses in the birefringent or two-mode fiber. With the help of auxiliary functions, we obtain the bilinear forms and construct the vector bright one- and two-soliton solutions via the Hirota method and symbolic computation. Two types of vector solitons are derived. Single-hump, double-hump, and flat-top solitons are displayed. Elastic and inelastic interactions between the Type-I solitons, between the Type-II solitons, and between the two combined types of the solitons are revealed, respectively. Especially, from the interaction between a Type-I soliton and a Type-II soliton, we see that the Type-II soliton exhibits the oscillation periodically before such an interaction and becomes the double-hump soliton after the interaction, which is different from the previously reported.
Feng, Linrun; Tang, Wei; Zhao, Jiaqing; Yang, Ruozhang; Hu, Wei; Li, Qiaofeng; Wang, Ruolin; Guo, Xiaojun
2016-02-01
With its excellent mechanical flexibility, low-cost and low-temperature processing, the solution processed organic field-effect transistor (OFET) is a promising platform technology for developing ubiquitous sensor applications in digital health, environment monitoring and Internet of Things. However, a contradiction between achieving low voltage operation and having stable performance severely hinder the technology to become commercially viable. This work shows that, by reducing the sub-gap density of states (DOS) at the channel for low operation voltage and using a proper low-k non-polar polymer dielectric layer, such an issue can be addressed. Stable electrical properties after either being placed for weeks or continuously prolonged bias stressing for hours in ambient air are achieved for all solution processed unencapsulated OFETs with the channel being exposed to the ambient air for analyte detection. The fabricated device presents a steep subthreshold swing less than 100 mV/decade, and an ON/OFF ratio of 106 at a voltage swing of 3 V. The low voltage and stable operation allows the sensor made of the OFET to be incorporated into a battery-powered electronic system for continuously reliable sensing of ammonia vapor in ambient air with very small power consumption of about 50 nW.
Moslem, W. M.; Rezk, S.; Abdelsalam, U. M.; El-Labany, S. K.
2018-04-01
This paper introduces an investigation of shocklike soliton or small amplitude Double Layers (DLs) in a collisionless plasma, consisting of positive and negative ions, nonthermal electrons, as well as solar wind streaming protons and electrons. Gardner equation is derived and its shocklike soliton solution is obtained. The model is employed to recognize a possible nonlinear wave at Venus ionosphere. The results indicate that the number densities and velocities of the streaming particles play crucial role to determine the polarity and characteristic features (amplitude and width) of the shocklike soliton waves. An electron streaming speed modifies a negative shocklike wave profile, while an ion streaming speed modulates a positive shocklike wave characteristic.
A two-dimensional soliton system of vortex and Q-ball
Loginov, A. Yu.
2018-02-01
The (2 + 1)-dimensional gauge model describing two complex scalar fields that interact through a common Abelian gauge field is considered. It is shown that the model has a soliton solution that describes a system consisting of a vortex and a Q-ball. This two-dimensional system is electrically neutral, nevertheless it possesses a nonzero electric field. Moreover, the soliton system has a quantized magnetic flux and a nonzero angular momentum. Properties of this vortex-Q-ball system are investigated by analytical and numerical methods. It is found that the system combines properties of topological and nontopological solitons.
Soliton fission and fusion: Burgers equation and Sharma-Tasso-Olver equation
International Nuclear Information System (INIS)
Wang Song; Tang Xiaoyan; Lou Senyue
2004-01-01
Fission and fusion phenomena can happen for solitons (sometimes solitary waves may be more accurate) which have been recently discovered both theoretically and experimentally. In this paper, taking the Burgers equation and the Sharma-Tasso-Olver equation as two concrete examples to show the fission and fusion of the solitary wave and the soliton solutions respectively which are studied by means of the Hirota's direct method and the Baecklund transformation. Furthermore, the amplitude and velocity relations between solitons and/or solitary waves before and after interactions are given and a possible general condition for fission and/or fusion is proposed
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.
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
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.
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
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.
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
All-solution processed polymer light-emitting diodes with air stable metal-oxide electrodes
de Bruyn, P.; Moet, D. J. D.; Blom, P. W. M.
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
Analytical theory of dark nonlocal solitons
DEFF Research Database (Denmark)
Kong, Qian; Wang, Qi; Bang, Ole
2010-01-01
We investigate properties of dark solitons in nonlocal materials with an arbitrary degree of nonlocality. We employ the variational technique and describe dark solitons, for the first time to our knowledge, in the whole range of degree of nonlocality....
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.
Dissipative dynamics of matter-wave solitons in a nonlinear optical lattice
International Nuclear Information System (INIS)
Abdullaev, F. Kh.; Tomio, Lauro; Gammal, A.; Luz, H. L. F. da
2007-01-01
Dynamics and stability of solitons in two-dimensional (2D) Bose-Einstein condensates (BEC), with one-dimensional (1D) conservative plus dissipative nonlinear optical lattices, are investigated. In the case of focusing media (with attractive atomic systems), the collapse of the wave packet is arrested by the dissipative periodic nonlinearity. The adiabatic variation of the background scattering length leads to metastable matter-wave solitons. When the atom feeding mechanism is used, a dissipative soliton can exist in focusing 2D media with 1D periodic nonlinearity. In the defocusing media (repulsive BEC case) with harmonic trap in one direction and nonlinear optical lattice in the other direction, the stable soliton can exist. Variational approach simulations are confirmed by full numerical results for the 2D Gross-Pitaevskii equation
Scaling properties of pure-quartic solitons
DEFF Research Database (Denmark)
Blanco-Redondo, Andrea; Lo, Chih Wei; Stefani, Alessio
2017-01-01
We demonstrate, by experiments and analytical developments, that the recently discovered pure-quartic solitons significantly outperform conventional solitons for high-energy ultrafast pulses. This is due to the favorable scaling of their energy and their Kelly sidebands.......We demonstrate, by experiments and analytical developments, that the recently discovered pure-quartic solitons significantly outperform conventional solitons for high-energy ultrafast pulses. This is due to the favorable scaling of their energy and their Kelly sidebands....
Li, Min; Xu, Tao
2015-03-01
Via the Nth Darboux transformation, a chain of nonsingular localized-wave solutions is derived for a nonlocal nonlinear Schrödinger equation with the self-induced parity-time (PT) -symmetric potential. It is found that the Nth iterated solution in general exhibits a variety of elastic interactions among 2N solitons on a continuous-wave background and each interacting soliton could be the dark or antidark type. The interactions with an arbitrary odd number of solitons can also be obtained under different degenerate conditions. With N=1 and 2, the two-soliton and four-soliton interactions and their various degenerate cases are discussed in the asymptotic analysis. Numerical simulations are performed to support the analytical results, and the stability analysis indicates that the PT-symmetry breaking can also destroy the stability of the soliton interactions.
Fully stable cosmological solutions with a non-singular classical bounce
Ijjas, Anna; Steinhardt, Paul J.
2017-01-01
We recently showed how it is possible to use a cubic Galileon action to construct classical cosmological solutions that enter a contracting null energy condition (NEC) violating phase, bounce at finite values of the scale factor and exit into an expanding NEC-satisfying phase without encountering any singularities or pathologies. A drawback of these examples is that singular behavior is encountered at some time either just before or just after the NEC-violating phase. In this Letter, we show that it is possible to circumvent this problem by extending our method to actions that include the next order L4 Galileon interaction. Using this approach, we construct non-singular classical bouncing cosmological solutions that are non-pathological for all times.
Gramoll, K. C.; Dillard, D. A.; Brinson, H. F.
1989-01-01
In response to the tremendous growth in the development of advanced materials, such as fiber-reinforced plastic (FRP) composite materials, a new numerical method is developed to analyze and predict the time-dependent properties of these materials. Basic concepts in viscoelasticity, laminated composites, and previous viscoelastic numerical methods are presented. A stable numerical method, called the nonlinear differential equation method (NDEM), is developed to calculate the in-plane stresses and strains over any time period for a general laminate constructed from nonlinear viscoelastic orthotropic plies. The method is implemented in an in-plane stress analysis computer program, called VCAP, to demonstrate its usefulness and to verify its accuracy. A number of actual experimental test results performed on Kevlar/epoxy composite laminates are compared to predictions calculated from the numerical method.
Spatiotemporal solitons in quadratic nonlinear media
Indian Academy of Sciences (India)
Optical solitons are localized electromagnetic waves that propagate stably in nonlinear me- dia with group-velocity dispersion (GVD) and/or diffraction. Temporal solitons in single- mode optical fibers are the prototypical optical solitons; these were predicted theoretically in 1973 [1] and first observed experimentally in 1980 ...
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 bunching in annular Josephson junctions
DEFF Research Database (Denmark)
Vernik, I.V; Lazarides, Nickos; Sørensen, Mads Peter
1996-01-01
By studying soliton (fluxon) motion in long annular Josephson junctions it is possible to avoid the influence of the boundaries and soliton-soliton collisions present in linear junctions. A new experimental design consisting of a niobium coil placed on top of an annular junction has been used...
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.
Formation of multiple dark photovoltaic spatial solitons
Indian Academy of Sciences (India)
Photorefractive effect; photovoltaic soliton splitting; multiple dark solitons; beam propagation method. PACS No. 42.65.Jx. 1. Introduction. In the last two decades, photorefractive spatial solitons have attracted much interest due to their potential applications such as all-optical beam switching and routing, optical inter-.
Scattering of waves by Langmuir solitons
Energy Technology Data Exchange (ETDEWEB)
Mendonca, J.T. (Instituto Superior Tecnico, Lisbon (Portugal). Centro de Electrodinamica)
1983-08-01
Scattering of electromagnetic and electrostatic waves by one-dimensional Langmuir solitons in a uniform and isotropic plasma is studied analytically using a perturbation method. Mode conversion via scattering by solitons is also considered. The results are also relevant for the case of ion-acoustic solitons.
Observation of Peregrine solitons in a multicomponent plasma with negative ions.
Bailung, H; Sharma, S K; Nakamura, Y
2011-12-16
The experimental observation of Peregrine solitons in a multicomponent plasma with the critical concentration of negative ions is reported. A slowly amplitude modulated perturbation undergoes self-modulation and gives rise to a high amplitude localized pulse. The measured amplitude of the Peregrine soliton is 3 times the nearby carrier wave amplitude, which agrees with the theory. The numerical solution of the nonlinear Schrödinger equation is compared with the experimental results. © 2011 American Physical Society
Symmetry Reductions of A Nonisospectral Lax Pair for A (2+1)-Dimensional Breaking Soliton System
Lv, Na; Niu, Datian; Yuan, Xuegang; Qiu, Xudong
2016-08-01
In this paper, we use the classical Lie group method to seek the symmetry algebras of the nonisospectral Lax pair for a (2 + 1)-dimensional breaking soliton system by considering the spectral parameter as an additional field. Based on the obtained symmetries, four reduced (1 + 1)-dimensional equations with their new Lax pairs are presented. After studying one of the reduced Lax pairs, we obtain an explicit solution of the breaking soliton system by a Darboux transformation.
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 ...
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).
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
Localized dark solitons and vortices in defocusing media with spatially inhomogeneous nonlinearity
Zeng, Jianhua; Malomed, Boris A.
2017-05-01
Recent studies have demonstrated that defocusing cubic nonlinearity with local strength growing from the center to the periphery faster than rD, in space of dimension D with radial coordinate r , supports a vast variety of robust bright solitons. In the framework of the same model, but with a weaker spatial-growth rate ˜rα with α ≤D , we test here the possibility to create stable localized continuous waves (LCWs) in one-dimensional (1D) and 2D geometries, localized dark solitons (LDSs) in one dimension, and localized dark vortices (LDVs) in two dimensions, which are all realized as loosely confined states with a divergent norm. Asymptotic tails of the solutions, which determine the divergence of the norm, are constructed in a universal analytical form by means of the Thomas-Fermi approximation (TFA). Global approximations for the LCWs, LDSs, and LDVs are constructed on the basis of interpolations between analytical approximations available far from (TFA) and close to the center. In particular, the interpolations for the 1D LDS, as well as for the 2D LDVs, are based on a deformed-tanh expression, which is suggested by the usual 1D dark-soliton solution. The analytical interpolations produce very accurate results, in comparison with numerical findings, for the 1D and 2D LCWs, 1D LDSs, and 2D LDVs with vorticity S =1 . In addition to the 1D fundamental LDSs with the single notch and 2D vortices with S =1 , higher-order LDSs with multiple notches are found too, as well as double LDVs, with S =2 . Stability regions for the modes under consideration are identified by means of systematic simulations, the LCWs being completely stable in one and two dimensions, as they are ground states in the corresponding settings. Basic evolution scenarios are identified for those vortices that are unstable. The settings considered in this work may be implemented in nonlinear optics and in Bose-Einstein condensates.
Scholl, Martha A.; Shanley, James B.; Murphy, Sheila F.; Willenbring, Jane K; Occhi, Marcie; González, Grizelle
2015-01-01
The prospect of changing climate has led to uncertainty about the resilience of forested mountain watersheds in the tropics. In watersheds where frequent, high rainfall provides ample runoff, we often lack understanding of how the system will respond under conditions of decreased rainfall or drought. Factors that govern water supply, such as recharge rates and groundwater storage capacity, may be poorly quantified. This paper describes 8-year data sets of water stable isotope composition (δ2H and δ18O) of precipitation (4 sites) and a stream (1 site), and four contemporaneous stream sample sets of solute chemistry and isotopes, used to investigate watershed response to precipitation inputs in the 1780-ha Río Mameyes basin in the Luquillo Mountains of northeastern Puerto Rico. Extreme δ2H and δ18O values from low-pressure storm systems and the deuterium excess (d-excess) were useful tracers of watershed response in this tropical system. A hydrograph separation experiment performed in June 2011 yielded different but complementary information from stable isotope and solute chemistry data. The hydrograph separation results indicated that 36% of the storm rain that reached the soil surface left the watershed in a very short time as runoff. Weathering-derived solutes indicated near-stream groundwater was displaced into the stream at the beginning of the event, followed by significant dilution. The more biologically active solutes exhibited a net flushing behavior. The d-excess analysis suggested that streamflow typically has a recent rainfall component (∼25%) with transit time less than the sampling resolution of 7 days, and a more well-mixed groundwater component (∼75%). The contemporaneous stream sample sets showed an overall increase in dissolved solute concentrations with decreasing elevation that may be related to groundwater inputs, different geology, and slope position. A considerable amount of water from rain events runs off as quickflow and bypasses
Mato-Iglesias, Marta; Balogh, Edina; Platas-Iglesias, Carlos; Tóth, Eva; de Blas, Andrés; Rodríguez Blas, Teresa
2006-12-07
We report an experimental and theoretical study of the stability and solution structure of lanthanide complexes with two novel ligands containing pyridine units and phosphonate pendant arms on either ethane-1,2-diamine (L2) or cyclohexane-1,2-diamine (L3) backbones. Potentiometric studies have been carried out to determine the protonation constants of the ligands and the stability constants of the complexes with Gd(III) and the endogenous metal ions Zn(II) and Cu(II). While the stability constant of the GdL2 complex is too high to be determined by direct pH-potentiometric titrations, the cyclohexyl derivative GdL3 has a lower and assessable stability (log K(GdL3)=17.62). Due to the presence of the phosphonate groups, various protonated species can be detected up to pH approximately 8 for both ligands and all metal ions studied. The molecular clusters [Ln(L)(H2O)](3-).19H2O (Ln=La, Nd, Ho or Lu; L=L2 or L3) were characterized by theoretical calculations at the HF level. Our calculations provide two minimum energy geometries where the ligand adopts different conformations: twist-wrap (tw), in which the ligand wraps around the metal ion by twisting the pyridyl units relative to each other, and twist-fold (tf), where the slight twisting of the pyridyl units is accompanied by an overall folding of the two pyridine units towards one of the phosphonate groups. The relative free energies of the tw and tf conformations of [Ln(L)(H2O)]3- (L=L2, L3) complexes calculated in aqueous solution (C-PCM) by using the B3LYP model indicate that the tw form is the most stable one along the whole lanthanide series for the complexes of L3, while for those of L2 only the Gd(III) complex is more stable in the tf conformation by ca. 0.5 kcal mol-1. 1H NMR studies of the Eu(III) complex of L3 show the initial formation of the tf complex in aqueous solution, which slowly converts to the thermodynamically stable tw form. The structures calculated for the Nd(III) complexes are in reasonably
Dynamics of soliton cascades in fiber amplifiers.
Arteaga-Sierra, F R; Antikainen, A; Agrawal, Govind P
2016-11-15
We study numerically the formation of cascading solitons when femtosecond optical pulses are launched into a fiber amplifier with less energy than required to form a soliton of equal duration. As the pulse is amplified, cascaded fundamental solitons are created at different distances, without soliton fission, as each fundamental soliton moves outside the gain bandwidth through the Raman-induced spectral shifts. As a result, each input pulse creates multiple, temporally separated, ultrashort pulses of different wavelengths at the amplifier output. The number of pulses depends not only on the total gain of the amplifier but also on the width of the input pulse.
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.
International Nuclear Information System (INIS)
Sanchez-Arriaga, G.; Lefebvre, E.
2011-01-01
The dynamics of two-dimensional s-polarized solitary waves is investigated with the aid of particle-in-cell (PIC) simulations. Instead of the usual excitation of the waves with a laser pulse, the PIC code was directly initialized with the numerical solutions from the fluid plasma model. This technique allows the analysis of different scenarios including the theoretical problems of the solitary wave stability and their collision as well as features already measured during laser-plasma experiments such as the emission of electromagnetic bursts when the waves reach the plasma-vacuum interface, or their expansion on the ion time scale, usually named post-soliton evolution. Waves with a single density depression are stable whereas multihump solutions decay to several waves. Contrary to solitons, two waves always interact through a force that depends on their relative phases, their amplitudes, and the distance between them. On the other hand, the radiation pattern at the plasma-vacuum interface was characterized, and the evolution of the diameter of different waves was computed and compared with the ''snow plow'' model.
TOPICAL REVIEW: Solitons in the Higgs phase: the moduli matrix approach
Eto, Minoru; Isozumi, Youichi; Nitta, Muneto; Ohashi, Keisuke; Sakai, Norisuke
2006-06-01
We review our recent work on solitons in the Higgs phase. We use U(NC) gauge theory with NF Higgs scalar fields in the fundamental representation, which can be extended to possess eight supercharges. We propose the moduli matrix as a fundamental tool to exhaust all BPS solutions, and to characterize all possible moduli parameters. Moduli spaces of domain walls (kinks) and vortices, which are the only elementary solitons in the Higgs phase, are found in terms of the moduli matrix. Stable monopoles and instantons can exist in the Higgs phase if they are attached by vortices to form composite solitons. The moduli spaces of these composite solitons are also worked out in terms of the moduli matrix. Webs of walls can also be formed with characteristic difference between Abelian and non-Abelian gauge theories. Instanton-vortex systems, monopole-vortex-wall systems, and webs of walls in Abelian gauge theories are found to admit negative energy objects with the instanton charge (called intersectons), the monopole charge (called boojums) and the Hitchin charge, respectively. We characterize the total moduli space of these elementary as well as composite solitons. In particular the total moduli space of walls is given by the complex Grassmann manifold SU(NF)/[SU(NC) × SU(NF - NC) × U(1)] and is decomposed into various topological sectors corresponding to boundary condition specified by particular vacua. The moduli space of k vortices is also completely determined and is reformulated as the half ADHM construction. Effective Lagrangians are constructed on walls and vortices in a compact form. We also present several new results on interactions of various solitons, such as monopoles, vortices and walls. Review parts contain our works on domain walls (Isozumi Y et al 2004 Phys. Rev. Lett. 93 161601 (Preprint hep-th/0404198), Isozumi Y et al 2004 Phys. Rev. D 70 125014 (Preprint hep-th/0405194), Eto M et al 2005 Phys. Rev. D 71 125006 (Preprint hep-th/0412024), Eto M et al 2005
Towards visible soliton microcomb generation.
Lee, Seung Hoon; Oh, Dong Yoon; Yang, Qi-Fan; Shen, Boqiang; Wang, Heming; Yang, Ki Youl; Lai, Yu-Hung; Yi, Xu; Li, Xinbai; Vahala, Kerry
2017-11-03
Frequency combs have applications that extend from the ultra-violet into the mid-infrared bands. Microcombs, a miniature and often semiconductor-chip-based device, can potentially access most of these applications, but are currently more limited in spectral reach. Here, we demonstrate mode-locked silica microcombs with emission near the edge of the visible spectrum. By using both geometrical and mode-hybridization dispersion control, devices are engineered for soliton generation while also maintaining optical Q factors as high as 80 million. Electronics-bandwidth-compatible (20 GHz) soliton mode locking is achieved with low pumping powers (parametric oscillation threshold powers as low as 5.4 mW). These are the shortest wavelength soliton microcombs demonstrated to date and could be used in miniature optical clocks. The results should also extend to visible and potentially ultra-violet bands.
Quark structure of chiral solitons
Energy Technology Data Exchange (ETDEWEB)
Dmitri Diakonov
2004-05-01
There is a prejudice that the chiral soliton model of baryons is something orthogonal to the good old constituent quark models. In fact, it is the opposite: the spontaneous chiral symmetry breaking in strong interactions explains the appearance of massive constituent quarks of small size thus justifying the constituent quark models, in the first place. Chiral symmetry ensures that constituent quarks interact very strongly with the pseudoscalar fields. The ''chiral soliton'' is another word for the chiral field binding constituent quarks. We show how the old SU(6) quark wave functions follow from the ''soliton'', however, with computable relativistic corrections and additional quark-antiquark pairs. We also find the 5-quark wave function of the exotic baryon Theta+.
Soliton formation in electron-temperature-gradient-driven magnetoplasma
M Yaqub, KHAN; Javed, IQBAL
2018-02-01
Electron-temperature-gradient (ETG)-driven solitons are studied in a plasma. We derive the linear dispersion relation and an admitted solitary wave solution Korteweg–de Vries-type equation (KdV) for the ETG mode in the nonlinear regime by using the Braginskii model and a transformation. It is found that the ETG mode supports only rarefactive solitons. It is also observed that the ratio of electron-to-ion temperature τ ={T}{{e}}/{T}{{i}}, the ratio of gradient scale lengths {η }{{e}}={L}n/{L}T, and the magnetic field B affect both the amplitude and width of a soliton. It is found that the soliton profile changes with variation in these parameters. We apply the homotopy perturbation method to the derived KdV equation. It is found this method is computationally attractive and the results are very impressive. This work may be useful to study the low electrostatic modes in inhomogeneous electron–ion plasma with density and ETG gradients. For illustration, the model has been applied to tokamak plasma.
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
Scattering in Soliton Models and the Bosonic Exchange description
Coriano', Claudio; Parwani, Rajesh R.; Yamagishi, Hidenaga; Zahed, Ismail
1992-01-01
We argue that the description of meson-nucleon dynamics based on the boson-exchange approach, is compatible with the description of the nucleon as a soliton in the nonrelativistic limit. Our arguments are based on an analysis of the meson-soliton form factor and the exact meson-soliton and soliton-soliton scattering amplitudes in the Sine-Gordon model.
Alsulami, Abdullah; Griffin, Jonathan; Alqurashi, Rania; Yi, Hunan; Iraqi, Ahmed; Lidzey, David; Buckley, Alastair
2016-03-25
Low-temperature solution-processable vanadium oxide (V₂O x ) thin films have been employed as hole extraction layers (HELs) in polymer bulk heterojunction solar cells. V₂O x films were fabricated in air by spin-coating vanadium(V) oxytriisopropoxide (s-V₂O x ) at room temperature without the need for further thermal annealing. The deposited vanadium(V) oxytriisopropoxide film undergoes hydrolysis in air, converting to V₂O x with optical and electronic properties comparable to vacuum-deposited V₂O₅. When s-V₂O x thin films were annealed in air at temperatures of 100 °C and 200 °C, OPV devices showed similar results with good thermal stability and better light transparency. Annealing at 300 °C and 400 °C resulted in a power conversion efficiency (PCE) of 5% with a decrement approximately 15% lower than that of unannealed films; this is due to the relative decrease in the shunt resistance (R sh ) and an increase in the series resistance (R s ) related to changes in the oxidation state of vanadium.
Li, Baozeng; Wang, Qing; Wang, Yingmin; Li, Chunyan; Qiang, Jianbing; Ji, Chunjun; Dong, Chuang
2012-02-01
Copper is a good corrosion resisting element, but due to its immiscibility with Fe, it is only used as a minor-alloying element in stainless steels. In this work, we introduced a double-cluster structure model [CuNi12][NiFe12] m for stable solid solutions in Cu-containing Fe-Ni corrosion-resistant invar alloys. Our model takes into account all of the enthalpies between the element pairs by assuming Fe-Ni and Ni-Cu nearest neighbors and by avoiding Fe-Cu ones, so that the ideally stabilized structures are described by mixing two cuboctahedral clusters in the fcc lattice, NiFe12 and CuNi12. Two alloy series were designed by varying the relative proportions of the two clusters and the Cu contents. It was proved that the alloys with Cu contents below those prescribed by this model could easily be solutionized and water-quenched to a monolithic fcc solid solution, and resultant alloys possessed good corrosion-resisting properties in 3.5 wt pct NaCl solution.
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.)
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)
Wang, Deng-Shan; Liu, Jiang; Wang, Lizhen
2018-03-01
In this paper, we investigate matter-wave solitons in hybrid atomic-molecular Bose-Einstein condensates with tunable interactions and external potentials. Three types of time-modulated harmonic potentials are considered and, for each of them, two groups of exact non-autonomous matter-wave soliton solutions of the coupled Gross-Pitaevskii equation are presented. Novel nonlinear structures of these non-autonomous matter-wave solitons are analyzed by displaying their density distributions. It is shown that the time-modulated nonlinearities and external potentials can support exact non-autonomous atomic-molecular matter-wave solitons.
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.
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...
On the complete integrability of an equation having solitons but not known to have a Lax pair
Directory of Open Access Journals (Sweden)
A. Roychowdhury
1986-01-01
Full Text Available It is usually assumed that a system having N-soliton solutions is completely integrable. Here we have analyzed a set of equations occuring in case of capillary gravity waves. Though the system under discussion has N-soliton solutions, it has yet to be shown that the system is completely integrable. No Lax pair is known for the system. Here we show that the system is not completely integrable in the sense of Ablowitz et al.
Head-on collision of ion-acoustic solitons in an ultracold neutral plasma
El-Tantawy, S. A.; Moslem, W. M.; Sabry, R.; El-Labany, S. K.; El-Metwally, M.; Schlickeiser, R.
2014-03-01
Properties of ion acoustic solitons head-on collision in an ultracold neutral plasma composed of ion fluid and non-Maxwellian electron distributions are investigated. For this purpose, the extended Poincare-Lighthill-Kuo (PLK) method is employed to derive coupled Kortweg-de Vries (KdV) equations describing the system. The nonlinear evolution equations for the colliding solitons and corresponding phase shifts are investigated both analytically and numerically. It is found that the polarity of the colliding solitons strongly depends on the type of the non-Maxwellian distribution (via nonthermal or superthermal electron distributions). Especially the phase shift due to solitons collision is strongly influenced by the non-Maxwellian distribution. A new critical nonthermal parameter β c , characterizing the nonthermal electron distribution, and which is not present for superthermal particle distributions, allows the existence of double polarity of the solitons. The phase shift increases below β c for compressive solitons, but it decreases above β c for rarefactive soliton. For superthermal distribution the phase shift increases rapidly for low spectral index κ, whereas for higher values of κ, the phase shift decreases smoothly and becomes nearly stable for κ>10. Around β c and small values of κ, the deviation from the Maxwellian state is strongest, and therefore the phase shift has unexpected behavior due to the presence of more energetic electrons that are represented by the non-Maxwellian distributions. The nonlinear structure, as reported here, could be useful for controlling the solitons that may be created in future ultracold neutral plasma experiments.
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
DEFF Research Database (Denmark)
Olsen, M.; Smith, H.; Scott, Alwyn 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...
Soliton dynamics in directional couplers
Valkering, T.P.; Hoekstra, Hugo; de Boer, Pieter-Tjerk
1998-01-01
The evolution of an initial condition consisting of one soliton(like) pulse in one channel and no signal in the other channel of the coupler is investigated. We focus upon the energy transfer (switching) between the two channels as function of the energy of the signal. For decreasing energy the
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
The Zakharov system and its soliton solutions
Guo, Boling; Kong, Linghai; Zhang, Jingjun
2016-01-01
This book focuses on the theory of the Zakharov system in the context of plasma physics. It has been over 40 years since the system was first derived by V. E. Zakharov – and in the course of those decades, many innovative achievements with major impacts on other research fields have been made. The book represents a first attempt to highlight the mathematical theories that are most important to researchers, including the existence and unique problems, blow-up, low regularity, large time behavior and the singular limit. Rather than attempting to examine every aspect of the Zakharov system in detail, it provides an effective road map to help readers access the frontier of studies on this system. .
One-soliton solutions from Laplace's seed
Indian Academy of Sciences (India)
Author Affiliations. S Chaudhuri1 2 K C Das3. Department of Physics, Gushkara Mahavidyalaya, Gushkara, Burdwan 713 128, India; Chaudhuri Lane, R. K. Palli, Badamtala, Burdwan 713 101, India; Department of Physics, Katwa College, Katwa, Burdwan 713 130, India ...
International Nuclear Information System (INIS)
Mayteevarunyoo, Thawatchai; Malomed, Boris A.; Krairiksh, Monai
2007-01-01
In a basic physical model where two-dimensional (2D) matter-wave solitons may be stable, namely, the Gross-Pitaevskii equation with the self-attractive nonlinearity and quasi-one-dimensional (1D) optical-lattice (OL) potential, we test robustness of the solitons against periodic time modulation of the OL strength. Stability diagrams for the 2D solitons are presented in the plane of the modulation depth and frequency. Basic features of the diagrams are explained with the help of the variational approximation for the stationary counterpart of the model. In the Bose-Einstein condensate of 7 Li atoms, the stable 2D solitons may contain the number of atoms in the range of 10 4 -10 5 , relevant values of the OL strength and modulation frequency being, respectively < or approx. 5 recoil energies and < or approx. 10 kHZ. Head-on collisions between stable 2D solitons moving in the unconfined direction are studied in detail too, for velocities up to ∼5 cm/s. A border between quasi-elastic collisions and merger of the solitons into a single localized state is identified. In some cases, the soliton produced by the merger is stable against collapse, which was not observed before in the static OL potential either
Johnson, C.A.; Grimes, D.J.; Rye, R.O.
2000-01-01
Stable isotope methods have been used to identify the mechanisms responsible for cyanide consumption at three heap-leach operations that process Carlin-type gold ores in Nevada, U.S.A. The reagent cyanide had ??15N values ranging from -5 to -2??? and ??13C values from -60 to -35???. The wide ??13C range reflects the use by different suppliers of isotopically distinct natural-gas feedstocks and indicates that isotopes may be useful in environmental studies where there is a need to trace cyanide sources. In heap-leach circuits displaying from 5 to 98% consumption of cyanide, barren-solution and pregnant-solution cyanide were isotopically indistinguishable. The similarity is inconsistent with cyanide loss predominantly by HCN offgassing (a process that in laboratory experiments caused substantial isotopic changes), but it is consistent with cyanide retention within the heaps as solids, a process that caused minimal isotopic changes in laboratory simulations, or with cyanide oxidation, which also appears to cause minimal changes. In many pregnant solutions cyanide was carried entirely as metal complexes, which is consistent with ferrocyanides having precipitated or cyanocomplexes having been adsorbed within the heaps. It is inferred that gaseous cyanide emissions from operations of this type are less important than has generally been thought and that the dissolution or desorption kinetics of solid species is an important control on cyanide elution when the spent heaps undergo rinsing. Nitrate, nitrite and ammonium had ??15N values of 1-16???. The data reflect isotopic fractionation during ammonia offgassing or denitrification of nitrate - particularly in reclaim ponds - but do not indicate the extent to which nitrate is derived from cyanide or from explosive residues. ?? The Institution of Mining and Metallurgy 2000.
Dai, Chao-Qing; Fan, Yan; Wang, Yue-Yue; Zheng, Jun
2018-02-01
The (3 + 1)-dimensional generalized coupled nonlinear Schrödinger equation with electric and magnetic nonlinearities of Kerr type and self-steepening effects is studied, and bright and dark soliton solutions are derived. Based on these analytical solutions, dynamical behaviors of bright and dark solitons are discussed. The amplitudes, widths and velocities of bright and dark solitons are all constants determined by the self-steepening effect parameters SE, SH. The phase chirp of a bright soliton diminishes in the pulse front of y-direction, however, it increases in the pulse back edge of y-direction. On the contrary, the phase chirp of a dark soliton increases in the pulse front of y-direction, however, it diminishes in the pulse back edge of y-direction. The phase chirps of a bright and dark soliton both shift along positive y -axis as time goes on. Moreover, the stability of the solutions is discussed.
Perez-Torres, R.; Belyaeva, T. L.; Hernandez-Tenorio, C.; Kovachev, L. M.; Serkin, V. N.
2010-10-01
The discovery of stimulated Raman self-scattering (SRSS) effect of femtosecond optical solitons is acknowledged to be among the most notable achievements of nonlinear fiber optics. This effect is also often called intrapulse stimulated Raman scattering (ISRS), or soliton self-frequency shift (SSFS), thereby emphasizing the unusual regime of stimulated Raman scattering, when the spectrum of a high-power ultrashort laser pulse proves to be so broad that it covers the band of Raman resonances of the medium. The soliton-like wave packets with continuously shifted spectrum traveling not only in the ordinary space and time, but also in the spectral space, are known as colored femtosecond solitons. Colored solitons play an important role in the soliton supercontinuum generation. The most interesting features of colored optical solitons are connected with the possibility of their tunneling in the spectral domain through a potential barrier-like spectral inhomogeneity of group velocity dispersion (GVD), including the forbidden band of positive GVD. This effect is known as soliton spectral tunneling effect (SST). In this Report, we consider the influence of the soliton binding energy on dynamics of the SST effect assuming that the amplitude and duration of the tunneling soliton vary in time when the soliton spectrum approaches a forbidden GVD barrier. We show that soliton self-compressing effect has dramatic impact on the SST through forbidden spectral region of positive GVD.
Interactions of Soliton Waves for a Generalized Discrete KdV Equation
Zhou, Tong; Zhu, Zuo-Nong
2017-07-01
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. Supported by the National Natural Science Foundation of China under Grant Nos. 11501353, 11271254, 11428102, and 11671255, also supported by the Ministry of Economy and Competitiveness of Spain under contracts MTM2012-37070 and MTM2016-80276-P (AEI/FEDER, EU)
Siminos, E; Sánchez-Arriaga, G; Saxena, V; Kourakis, I
2014-12-01
We investigate the dynamics of localized solutions of the relativistic cold-fluid plasma model in the small but finite amplitude limit, for slightly overcritical plasma density. Adopting a multiple scale analysis, we derive a perturbed nonlinear Schrödinger equation that describes the evolution of the envelope of circularly polarized electromagnetic field. Retaining terms up to fifth order in the small perturbation parameter, we derive a self-consistent framework for the description of the plasma response in the presence of localized electromagnetic field. The formalism is applied to standing electromagnetic soliton interactions and the results are validated by simulations of the full cold-fluid model. To lowest order, a cubic nonlinear Schrödinger equation with a focusing nonlinearity is recovered. Classical quasiparticle theory is used to obtain analytical estimates for the collision time and minimum distance of approach between solitons. For larger soliton amplitudes the inclusion of the fifth-order terms is essential for a qualitatively correct description of soliton interactions. The defocusing quintic nonlinearity leads to inelastic soliton collisions, while bound states of solitons do not persist under perturbations in the initial phase or amplitude.
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.
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
Solitons and quasi-periodic behaviors in an inhomogeneous optical fiber
Yang, Jin-Wei; Gao, Yi-Tian; Su, Chuan-Qi; Zuo, Da-Wei; Feng, Yu-Jie
2017-01-01
In this paper, a fifth-order variable-coefficient nonlinear Schrödinger equation for the attosecond pulses in an inhomogeneous optical fiber is studied. With the aid of auxiliary functions, we obtain the variable-coefficient Hirota bilinear equations and corresponding integrable constraints. Under those constraints, we obtain the Lax pair, conservation laws, one-, two- and three-soliton solutions via the Hirota method and symbolic computation. Soliton structures and interactions are discussed: (1) For the one soliton, we discuss the influence of the group velocity dispersion term α(x) and fifth-order dispersion term δ(x) on the velocities and structures of the solitons, where x is the normalized propagation along the fiber, and derive a constraint contributing to the stationary soliton; (2) For the two solitons, we analyze the interactions between them with different values of α(x) and δ(x), and derive the quasi-periodic formulae for three cases of the bound states: When α(x) and δ(x) are the linear functions of x, quasi-periodic attraction and repulsion lead to the redistribution of the energy of the two solitons, and ratios among the quasi-periods are derived; When α(x) and δ(x) are the quadratic functions of x, the ratios among them are also obtained; When α(x) and δ(x) are the periodic functions of x, bi-periodic phenomena are obtained; (3) For the three solitons, including the parabolic, cubic, periodic and stationary structures, interactions among them with different values of the α(x) and δ(x) are presented.
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.
Directory of Open Access Journals (Sweden)
Mahmoud M. Khader
2018-02-01
Full Text Available We report on the synthesis and testing of active and stable nano-catalysts for methane oxidation. The nano-catalyst was palladium/ceria supported on alumina prepared via a one-step solution-combustion synthesis (SCS method. As confirmed by X-ray photoelectron spectroscopy (XPS and high-resolution transmission electron microscopy (HTEM, SCS preparative methodology resulted in segregating both Pd and Ce on the surface of the Al2O3 support. Furthermore, HTEM showed that bigger Pd particles (5 nm and more were surrounded by CeO2, resembling a core shell structure, while smaller Pd particles (1 nm and less were not associated with CeO2. The intimate Pd-CeO2 attachment resulted in insertion of Pd ions into the ceria lattice, and associated with the reduction of Ce4+ into Ce3+ ions; consequently, the formation of oxygen vacancies. XPS showed also that Pd had three oxidation states corresponding to Pd0, Pd2+ due to PdO, and highly ionized Pd ions (Pd(2+x+ which might originate from the insertion of Pd ions into the ceria lattice. The formation of intrinsic Ce3+ ions, highly ionized (Pd2+ species inserted into the lattice of CeO2 Pd ions (Pd(2+x+ and oxygen vacancies is suggested to play a major role in the unique catalytic activity. The results indicated that the Pd-SCS nano-catalysts were exceptionally more active and stable than conventional catalysts. Under similar reaction conditions, the methane combustion rate over the SCS catalyst was ~18 times greater than that of conventional catalysts. Full methane conversions over the SCS catalysts occurred at around 400 °C but were not shown at all with conventional catalysts. In addition, contrary to the conventional catalysts, the SCS catalysts exhibited superior activity with no sign of deactivation in the temperature range between ~400 and 800 °C.
Dark soliton pair of ultracold Fermi gases for a generalized Gross-Pitaevskii equation model.
Wang, Ying; Zhou, Yu; Zhou, Shuyu; Zhang, Yongsheng
2016-07-01
We present the theoretical investigation of dark soliton pair solutions for one-dimensional as well as three-dimensional generalized Gross-Pitaevskii equation (GGPE) which models the ultracold Fermi gas during Bardeen-Cooper-Schrieffer-Bose-Einstein condensates crossover. Without introducing any integrability constraint and via the self-similar approach, the three-dimensional solution of GGPE is derived based on the one-dimensional dark soliton pair solution, which is obtained through a modified F-expansion method combined with a coupled modulus-phase transformation technique. We discovered the oscillatory behavior of the dark soliton pair from the theoretical results obtained for the three-dimensional case. The calculated period agrees very well with the corresponding reported experimental result [Weller et al., Phys. Rev. Lett. 101, 130401 (2008)PRLTAO0031-900710.1103/PhysRevLett.101.130401], demonstrating the applicability of the theoretical treatment presented in this work.
Non-linear dynamics in biological microtubules: solitons and dissipation-free energy transfer
Mavromatos, Nick E.
2017-08-01
I review some recent developments concerning soliton solutions in biological microtubules and their significance in transferring energy without dissipation. I discuss various types of soliton solutions, as well as ‘spikes’, of the associated non-linear Lagrange equations describing the dynamics of a ‘pseudo-spin non-linear σ-model’ that models the dynamics of a microtubule system with dipole-dipole interactions. These results will hopefully contribute to a better understanding of the functional properties of microtubules, including the motor protein dynamics and the information transfer processes. With regards to the latter we also speculate on the use of microtubules as ‘logical’ gates. Our considerations are classical, but the soliton solutions may have a microscopic quantum origin, which we briefly touch upon.
Longitudinal soliton tunneling in optical fiber.
Marest, T; Braud, F; Conforti, M; Wabnitz, S; Mussot, A; Kudlinski, A
2017-06-15
We report the observation of the longitudinal soliton tunneling effect in axially varying optical fibers. A fundamental soliton, initially propagating in the anomalous dispersion region of a fiber, can pass through a normal dispersion barrier without being substantially affected. We perform experimental studies by means of spectral and temporal characterizations that show the evidence of the longitudinal soliton tunneling process. Our results are well supported by numerical simulations using the generalized nonlinear Schrödinger equation.
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
Electrical solitons theory, design, and applications
Ricketts, David S
2010-01-01
The dominant medium for soliton propagation in electronics, nonlinear transmission line (NLTL) has found wide application as a testbed for nonlinear dynamics and KdV phenomena as well as for practical applications in ultra-sharp pulse/edge generation and novel nonlinear communication schemes in electronics. While many texts exist covering solitons in general, there is as yet no source that provides a comprehensive treatment of the soliton in the electrical domain.Drawing on the award winning research of Carnegie Mellon's David S. Ricketts, Electrical Solitons Theory, Design, and Applications i
Leibovich, S.; Randall, J. D.
1979-01-01
The paper considers a modified Korteweg-de Vries equation that permits wave amplification or damping. A 'terminal similarity' solution is identified for large times in amplified systems. Numerical results are given which confirm that the terminal similarity solution is a valid local approximation for mu t sufficiently large and positive, even though the approximation is not uniformly valid in space.
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
Indian Academy of Sciences (India)
(1) A localized wave propagates without change of its properties (shape, velocity etc.),. (2) Localized waves are stable against mutual collisions and retain their identities. The first is a solitary wave condition known in hydrodynamics since the 19th century. The second means that the wave has the property of a particle.
Soliton-like defects in nematic liquid crystal thin layers
Energy Technology Data Exchange (ETDEWEB)
Chuvyrov, A. N.; Krekhov, A. P.; Lebedev, Yu. A., E-mail: lebedev@anrb.ru; Timirov, Yu. I. [Russian Academy of Sciences, Institute of Molecule and Crystal Physics, Ufa Research Center (Russian Federation)
2016-11-15
The nonsingular soliton-like defects in plane nematic liquid crystal (NLC) layers and spherical NLC drops are experimentally detected and studied when the interaction of NLC molecules with a bounding surface is varied. The dynamics and the annihilation of nonsingular defects of opposite signs on a plane surface are investigated. Periodic transformations of the soliton-like defects in NLC drops in an electric field are detected. The theory of elasticity is used to show that the surface energy taken into account in the total free energy of NLC in the case of weak anchoring leads to the possibility of nonsingular solutions of a director equilibrium equation. The calculated pictures of director distribution in a plane NLC layer and in a spherical NLC drop characterized by weak surface anchoring agree well with the results of polarized light optical observations.
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
Bifurcations and new exact travelling wave solutions for the ...
Indian Academy of Sciences (India)
Bidirectional wave equations; dynamical system method; phase portrait; dark soliton solution; bright soliton solution; periodic travelling wave solution. ... HK), Kunming, 650106, People's Republic of China; College of Statistics and Mathematics, Yunnan University of Finance and Economics, Kunming, 650221, People's ...
An efficient algorithm for computation of solitary wave solutions to ...
Indian Academy of Sciences (India)
2017-09-08
Sep 8, 2017 ... Nonlinear mathematical problems and their solutions attain much attention in solitary waves. In soliton theory, an efficient tool to attain various types of soliton solutions is the exp ( − φ ( ζ ) ) -expansion technique. This article is devoted to find exact travelling wave solutions of Drinfeld–Sokolov equation via a ...
The Evolutionary Properties on Solitary Solutions of Nonlinear Evolution Equations
Directory of Open Access Journals (Sweden)
Wenxia Chen
2017-01-01
Full Text Available The evolution process of four class soliton solutions is investigated by basic calculus theory. For any given x, we describe the special curvature evolution following time t for the curve of soliton solution and also study the fluctuation of solution curve.
Solitary wave solutions to nonlinear evolution equations in ...
Indian Academy of Sciences (India)
This paper obtains solitons as well as other solutions to a few nonlinear evolution equations that appear in various areas of mathematical physics. The two analytical integrators that are applied to extract solutions are tan–cot method and functional variable approaches. The soliton solutions can be used in the further study of ...
An efficient algorithm for computation of solitary wave solutions to ...
Indian Academy of Sciences (India)
KAMRAN AYUB
2017-09-08
Sep 8, 2017 ... Abstract. Nonlinear mathematical problems and their solutions attain much attention in solitary waves. In soliton theory, an efficient tool to attain various types of soliton solutions is the exp(−ϕ(ζ))-expansion technique. This article is devoted to find exact travelling wave solutions of Drinfeld–Sokolov equation ...
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.
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.
Single Peak Soliton and Periodic Cusp Wave of the Generalized Schrodinger-Boussinesq Equations
Qiao, Li-Jing; Tang, Sheng-Qiang; Zhao, Hai-Xia
2015-06-01
In this paper, we study peakon, cuspon, smooth soliton and periodic cusp wave of the generalized Schrödinger-Boussinesq equations. Based on the method of dynamical systems, the generalized Schrödinger-Boussinesq equations are shown to have new the parametric representations of peakon, cuspon, smooth soliton and periodic cusp wave solutions. Under different parametric conditions, various sufficient conditions to guarantee the existence of the above solutions are given. Supported by National Natural Science Foundation of China under Grant Nos. 11361017, 11161013 and Natural Science Foundation of Guangxi under Grant Nos. 2012GXNSFAA053003, 2013GXNSFAA019010, and Program for Innovative Research Team of Guilin University of Electronic Technology