Fu Ying; Qu Changzheng
2012-01-01
In this article,the unique continuation and persistence properties of solutions of the 2-component Degasperis-Procesi equations are discussed.It is shown that strong solutions of the 2-component Degasperis-Procesi equations,initially decaying exponentially together with its spacial derivative,must be identically equal to zero if they also decay exponentially at a later time.
Two-Mode Wave Solutions to the Degasperis-Procesi Equation
ZHANG Zheng-Di; BI Qin-Sheng
2008-01-01
@@ By introducing a new type of solutions, called the multiple-mode wave solutions which can be expressed in nonlinear superposition of single-mode waves with different speeds, we investigate the two-mode wave solutions in Degasperis-Procesi equation and two cases are derived.The explicit expressions for the two-mode waves as well as the existence conditions are presented.It is shown that the two-mode waves may be the nonlinear combinations of many types of single-mode waves, such as periodic waves, solitons, compactons, etc., and more complicated multiple-mode waves can be obtained if higher order or more single-mode waves are taken into consideration.It is pointed out that the two-mode wave solutions can be employed to display the typical mechanism of the interactions between different single-mode waves.
Classification of All Single Travelling Wave Solutions to Calogero-Degasperis-Focas Equation
无
2007-01-01
Under the travelling wave transformation, Calogero-Degasperis-Focas equation is reduced to an ordinary differential equation. Using a symmetry group of one parameter, this ODE is reduced to a second-order linear inho-mogeneous ODE. Furthermore, we apply the change of the variable and complete discrimination system for polynomial to solve the corresponding integrals and obtained the classification of all single travelling wave solutions to Calogero-Degasperis-Focas equation.
Multicomponent integrable wave equations: II. Soliton solutions
Degasperis, A [Dipartimento di Fisica, Universita di Roma ' La Sapienza' , and Istituto Nazionale di Fisica Nucleare, Sezione di Roma, Rome (Italy); Lombardo, S [School of Mathematics, University of Manchester, Alan Turing Building, Upper Brook Street, Manchester M13 9EP (United Kingdom)], E-mail: antonio.degasperis@roma1.infn.it, E-mail: sara.lombardo@manchester.ac.uk, E-mail: sara@few.vu.nl
2009-09-25
The Darboux-dressing transformations developed in Degasperis and Lombardo (2007 J. Phys. A: Math. Theor. 40 961-77) are here applied to construct soliton solutions for a class of boomeronic-type equations. The vacuum (i.e. vanishing) solution and the generic plane wave solution are both dressed to yield one-soliton solutions. The formulae are specialized to the particularly interesting case of the resonant interaction of three waves, a well-known model which is of boomeronic type. For this equation a novel solution which describes three locked dark pulses (simulton) is introduced.
Self-Similar Blowup Solutions to the 2-Component Degasperis-Procesi Shallow Water System
Yuen, Manwai
2010-01-01
In this article, we study the self-similar solutions of the 2-component Degasperis-Procesi water system:% [c]{c}% \\rho_{t}+k_{2}u\\rho_{x}+(k_{1}+k_{2})\\rho u_{x}=0 u_{t}-u_{xxt}+4uu_{x}-3u_{x}u_{xx}-uu_{xxx}+k_{3}\\rho\\rho_{x}=0. By the separation method, we can obtain a class of self-similar solutions,% [c]{c}% \\rho(t,x)=\\max(\\frac{f(\\eta)}{a(4t)^{(k_{1}+k_{2})/4}},\\text{}0),\\text{}u(t,x)=\\frac{\\overset{\\cdot}{a}(4t)}{a(4t)}x \\overset{\\cdot\\cdot}{a}(s)-\\frac{\\xi}{4a(s)^{\\kappa}}=0,\\text{}a(0)=a_{0}% \
A numerical scheme using multi-shockpeakons to compute solutions of the Degasperis-Procesi equation
Hakon A. Hoel
2007-07-01
Full Text Available We consider a numerical scheme for entropy weak solutions of the DP (Degasperis-Procesi equation $u_t - u_{xxt} + 4uu_x = 3u_{x}u_{xx}+ uu_{xxx}$. Multi-shockpeakons, functions of the form $$ u(x,t =sum_{i=1}^n(m_i(t -hbox{sign}(x-x_i(ts_i(te^{-|x-x_i(t|}, $$ are solutions of the DP equation with a special property; their evolution in time is described by a dynamical system of ODEs. This property makes multi-shockpeakons relatively easy to simulate numerically. We prove that if we are given a non-negative initial function $u_0 in L^1(mathbb{R}cap BV(mathbb{R}$ such that $u_{0} - u_{0,x}$ is a positive Radon measure, then one can construct a sequence of multi-shockpeakons which converges to the unique entropy weak solution in $mathbb{R}imes[0,T$ for any $T>0$. From this convergence result, we construct a multi-shockpeakon based numerical scheme for solving the DP equation.
Soliton solutions for Davydov solitons in α-helix proteins
Taghizadeh, N.; Zhou, Qin; Ekici, M.; Mirzazadeh, M.
2017-02-01
The propagation equation for describing Davydov solitons in α-helix proteins has been investigated analytically. There are seven integration tools to extract analytical soliton solutions. They are the Ricatti equation expansion approach, ansatz scheme, improved extended tanh-equation method, the extend exp(-Ψ(τ)) -expansion method, the extended Jacobi elliptic function expansion method, the extended trial equation method and the extended G ' / G - expansion method.
无
2005-01-01
By using the further extended tanh method [Phys. Lett. A 307 (2003) 269; Chaos, Solitons & Fractals 17(2003) 669] to the Broer-Kaup system with variable coefficients, abundant new soliton-like solutions and multi-soliton-like solutions are derived. Based on the derived multi-soliton-like solutions which contain arbitrary functions, some interesting multi-soliton structures are revealed.
Soliton-like solution in quantum electrodynamics
Skoromnik, O D; Keitel, C H
2016-01-01
A novel soliton-like solution in quantum electrodynamics is obtained via a self-consistent field method. By writing the Hamiltonian of quantum electrodynamics in the Coulomb gauge, we separate out a classical component in the density operator of the electron-positron field. Then, by modeling the state vector in analogy with the theory of superconductivity, we minimize the functional for the energy of the system. This results in the equations of the self-consistent field, where the solutions are associated with the collective excitation of the electron-positron field---the soliton-like solution. In addition, the canonical transformation of the variables allowed us to separate out the total momentum of the system and, consequently, to find the relativistic energy dispersion relation for the moving soliton.
Solitons in nonlocal nonlinear media: Exact solutions
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...
Soliton solutions of a generalized discrete KdV equation
Kanki, Masataka; Tokihiro, Tetsuji
2012-01-01
We investigate the multi-soliton solutions to the generalized discrete KdV equation. In some cases a soliton with smaller amplitude moves faster than that with larger amplitude unlike the soliton solutions of the KdV equation. This phenomenon is intuitively understood from its ultradiscrete limit, where the system turns to the box ball system with a carrier. KEYWORDS: soliton, integrable equation, nonlinear system, discrete KdV equation, cellular automaton
LIU Chun-Ping; LING Zhi
2005-01-01
By using the generally projective Riccati equation method, a series of doubly periodic solutions (Jacobi elliptic function solution) for a class of nonlinear partial differential equations are obtained in a unified way. When the module m → 1, these solutions exactly degenerate to the soliton solutions of the equations. Then we reveal the relationship between the soliton-like solutions obtained by other authors and these soliton solutions of the equations.
The Degasperis-Procesi equation as a non-metric Euler equation
Escher, Joachim
2009-01-01
In this paper we present a geometric interpretation of the periodic Degasperis-Procesi equation as the geodesic flow of a right invariant symmetric linear connection on the diffeomorphism group of the circle. We also show that for any evolution in the family of $b$-equations there is neither gain nor loss of the spatial regularity of solutions. This in turn allows us to view the Degasperis-Procesi and the Camassa-Holm equation as an ODE on the Fr\\'echet space of all smooth functions on the circle.
Darboux transformation of generalized coupled KdV soliton equation and its odd-soliton solutions
LIU Ping
2008-01-01
Based on the resulting Lax pairs of the generalized coupled KdV soliton equation,a new Darboux transformation with multi-parameters for the generalized coupled KdV soliton equation is derived with the help of a gauge transformation of the spectral problem.By using Darboux transformation,the generalized odd-soliton solutions of the generalized coupled KdV soliton equation are given and presented in determinant form.As an application,the first two cases are given.
Wazwaz, Abdul-Majid
2010-03-01
In this work, the generalized (2+1) and (3+1)-dimensional Calogero-Bogoyavlenskii-Schiff equations are studied. We employ the Cole-Hopf transformation and the Hirota bilinear method to derive multiple-soliton solutions and multiple singular soliton solutions for these equations. The necessary conditions for complete integrability of each equation are derived
Exact discrete soliton solutions of quintic discrete nonlinear Schr(o)dinger equation
Li Hua-Mei; Wu Feng-Min
2005-01-01
By using the extended hyperbolic function approach, we have studied a quintic discrete nonlinear Schrodinger equation and obtained new exact localized solutions, including the discrete bright soliton solution, dark soliton solution,alternating phase bright soliton solution and alternating phase dark soliton solution, if a special constraint is imposed on the coefficients of the equation.
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 invarian
Gravitational multi-soliton solutions on flat space
Chen, Yu
2015-01-01
It is well-known that, for even n, the n-soliton solution on the Minkowski seed, constructed using the inverse-scattering method (ISM) of Belinski and Zakharov (BZ), is the multi-Kerr-NUT solution. We show that, for odd n, the natural seed to use is the Euclidean space with two manifest translational symmetries, and the n-soliton solution is the accelerating multi-Kerr-NUT solution. We thus define the n-soliton solution on flat space for any positive integer n. It admits both Lorentzian and Euclidean sections. In the latter section, we find that a number say m of solitons can be eliminated in a non-trivial way, by appropriately fixing their corresponding so-called BZ parameters. The resulting solutions, which may split into separate classes, are collectively denoted as [n-m]-soliton solutions on flat space. We then carry out a systematic study of the n- and [n-m]-soliton solutions on flat space. This includes, in particular, an explicit presentation of their ISM construction, an analysis of their local geomet...
Brane Inflation, Solitons and Cosmological Solutions: I
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 generalized Kaup-Boussinesq equation: multiple soliton solutions
Wazwaz, Abdul-Majid
2015-10-01
In this work, we investigate the generalized two-field Kaup-Boussinesq (KB) equation. The KB equation possesses the cubic nonlinearity that distinguishes it from the Boussinesq equation that contains quadratic nonlinearity. We use the simplified form of Hirota's direct method to determine multiple soliton solutions and multiple singular soliton solutions for this equation. The study exhibits physical structures for a generalized water-wave model.
1-Soliton solutions of complex modified KdV equation with time-dependent coefficients
Kumar, H.; Chand, F.
2013-09-01
In this paper, we have obtained exact 1-soliton solutions of complex modified KdV equation with variable—coefficients using solitary wave ansatz. Restrictions on parameters of the soliton have been observed in course of the derivation of soliton solutions. Finally, a few numerical simulations of dark and bright solitons have been given.
The new soliton solutions via modified Hereman's simplified method
Pınar, Zehra
2017-02-01
It is well recognized that new types of exact travelling wave solutions to nonlinear partial differential equations can be obtained modifications of the methods which are in hand. In this study, the new ansatz which was proposed by Wazwaz is considered to get new soliton solutions modifying the methodology which is known as Hereman's simplified method.
Relationship Between Solitonic Solutions of Five-Dimensional Einstein Equations
Tomizawa, S; Mishima, T; Iguchi, Hideo; Mishima, Takashi; Tomizawa, Shinya
2006-01-01
We give the relation between the solutions generated by the inverse scattering method and the B\\"acklund transformation applied to the vacuum five-dimensional Einstein equations. In particular, we show that the two-solitonic solutions generated from an arbitrary diagonal seed by the B\\"acklund transformation are contained those generated from the same seed by the inverse scattering method.
The multi-soliton solutions of the CH-γ equation
2008-01-01
This paper solves the integrable CH-γequation for analytical multiple soliton solutions with the Darboux transformation method.Some properties of the soliton solutions are different from the CH equation.
Zhao, Chen; Gao, Yi-Tian; Lan, Zhong-Zhou; Yang, Jin-Wei
2016-09-01
In this article, a (3+1)-dimensional variable-coefficient breaking soliton equation is investigated. Based on the Bell polynomials and symbolic computation, the bilinear forms and Bäcklund transformation for the equation are derived. One-, two-, and three-soliton solutions are obtained via the Hirota method. N-soliton solutions are also constructed. Propagation characteristics and interaction behaviors of the solitons are discussed graphically: (i) solitonic direction and position depend on the sign of the wave numbers; (ii) shapes of the multisoliton interactions in the scaled space and time coordinates are affected by the variable coefficients; (iii) multisoliton interactions are elastic for that the velocity and amplitude of each soliton remain unchanged after each interaction except for a phase shift.
Exact traveling soliton solutions for the scalar Qiao equation
Abdoulkary, Saïdou; Aboubakar, Mahamoudou; Aboukar; Mohamadou, Alidou; Beda, Tibi
2015-01-01
We investigate exact traveling wave solutions of the scalar Qiao equation proposed by Li and Qiao (2010 J. Math. Phys. 51 042703) using the generalized auxiliary equation method. This equation is known to have bi-Hamiltonian structure and Lax pair, which imply integrability of the equation for a fixed value of k. Symmetries of the scalar Qiao equation and its solutions are also considered. The obtained solutions include kink and antikink solitons, bright and dark solitons, singular solutions and exponential solutions. This method could be used in further works to establish more entirely new solutions for other kinds of nonlinear evolution equations arising in physics. This work could be also relevant for numerical studies of the scalar Qiao equation.
Soliton-Like Solutions of Three Non-isospectral Equations
石教云; 宁同科; 张大军
2005-01-01
n-soliton-like solutions of three non-isospectral equations, the non-isospectral mKdV equation, the non-isospectral sine-Gordon equation and the non-isospeetral nonlinear Schroedinger equation were obtained by using the Hirota method.
One-soliton solutions from Laplace’s seed
S Chaudhuri; K C Das
2002-03-01
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 Ernst potential is also presented. It is found that the solutions do not reduce to the Euclidean form at spatial inﬁnity. However, in the static limit, Weyl solutions are obtained for half integral -values.
Wang Dengshan [CEMA and CIAS, Central Univ. of Finance and Economics, BJ (China); BNLCMP, Inst. of Physics, Chinese Academy of Sciences, BJ (China); Liu Yifang [School of Economics, Central Univ. of Finance and Economics, BJ (China)
2010-01-15
In this paper, with the aid of symbolic computation the bright soliton solutions of two variable-coefficient coupled nonlinear Schroedinger equations are obtained by Hirota's method. Some figures are plotted to illustrate the properties of the obtained solutions. The properties are meaningful for the investigation on the stability of soliton propagation in the optical soliton communications. (orig.)
Soliton and similarity solutions of N=2,4 supersymmetric equations
Delisle, Laurent
2012-01-01
We produce soliton and similarity solutions of supersymmetric extensions of Burgers, Korteweg-de Vries and modified KdV equations. We give new representations of the $\\tau$-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.
Soliton and Similarity Solutions of Ν = 2, 4 Supersymmetric Equations
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.
N-soliton solutions to the modified Boussinesq equation
LI Qiong; XIA Tie-cheng; CHEN Deng-yuan
2009-01-01
Searching for exact solutions to nonlinear evolution equations is a very important and interesting work in non-linear science. In this paper, the modified Boussinesq equation is derived from the modified Gel'fand-Dikii (mG-D) system. Furthermore, we study the modified Boussinesq equation by using the bilinear method and Wronskian technique, we obtain the N-soliton solutions to the above equation.
Limiting Behavior of Travelling Waves for the Modified Degasperis-Procesi Equation
Jiuli Yin
2014-01-01
Full Text Available Using an improved qualitative method which combines characteristics of several methods, we classify all travelling wave solutions of the modified Degasperis-Procesi equation in specified regions of the parametric space. Besides some popular exotic solutions including peaked waves, and looped and cusped waves, this equation also admits some very particular waves, such as fractal-like waves, double stumpons, double kinked waves, and butterfly-like waves. The last three types of solutions have not been reported in the literature. Furthermore, we give the limiting behavior of all periodic solutions as the parameters trend to some special values.
Solitonic generation of five-dimensional black ring solution
Iguchi, H; Iguchi, Hideo; Mishima, Takashi
2006-01-01
Using the solitonic solution-generating technique we rederived the one-rotational five-dimensional black ring solution found by Emparan and Reall. The seed solution is not the Minkowski metric, which is the seed of $S^2$-rotating black ring. The obtained solution has more parameters than the Emparan and Reall's $S^1$-rotating black ring. We found the conditions of parameters to reduce the solution to the $S^1$-rotating black ring. In addition we examined the relation between the expressions of the metric in the prolate-spheroidal coordinates and in the canonical coordinates.
Multi-soliton rational solutions for some nonlinear evolution equations
Osman Mohamed S.
2016-01-01
Full Text Available The Korteweg-de Vries equation (KdV and the (2+ 1-dimensional Nizhnik-Novikov-Veselov system (NNV are presented. Multi-soliton rational solutions of these equations are obtained via the generalized unified method. The analysis emphasizes the power of this method and its capability of handling completely (or partially integrable equations. Compared with Hirota’s method and the inverse scattering method, the proposed method gives more general exact multi-wave solutions without much additional effort. The results show that, by virtue of symbolic computation, the generalized unified method may provide us with a straightforward and effective mathematical tool for seeking multi-soliton rational solutions for solving many nonlinear evolution equations arising in different branches of sciences.
Symmetries and Exact Solutions of the Breaking Soliton Equation
陈美; 刘希强
2011-01-01
With the aid of the classical Lie group method and nonclassical Lie group method, we derive the classical Lie point symmetry and the nonclassical Lie point symmetry of （2＋1）-dimensional breaking soliton （BS） equation. Using the symmetries, we find six classical similarity reductions and two nonclassical similarity reductions of the BS equation. Varieties of exact solutions of the BS equation are obtained by solving the reduced equations.
Soliton-like solutions to the ordinary Schroedinger equation
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)
ZhangTiande; CaoQingjie; PriceG.W.; DjidjeliK.; TwizellE.H.
1999-01-01
Spatial soliton solutions of a class of generalized nonlinear Schrodinger equations in N-space are discussed analytically and numerically. This achieved using a traveling wavemethod to formulate one-soliton solution and the P-R method is employed to the numerlcal solutions and the interactions between the solirons for the generalized nonlinear systems in Z-pace.The results presented show that the soliton phenomena are characteristics associated with the nonlinearhies of the dynamical systems.
Soliton solutions for a quasilinear Schrodinger equation
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.
New multi-soliton solutions and travelling wave solutions of the dispersive long-wave equations
张解放; 郭冠平; 吴锋民
2002-01-01
Using the extended homogeneous balance method, the (1+1)-dimensional dispersive Iong-wave equations have been solved. Starting from the homogeneous balance method, we have obtained a nonlinear transformation for simplifying a dispersive long-wave equation into a linear partial differential equation. Usually, we can obtain only a type of soliton-like solution. In this paper, we have further found some new multi-soliton solutions and exact travelling solutions of the dispersive long-wave equations from the linear partial equation.
Instabilities of optical solitons and Hamiltonian singular solutions in a medium of finite extension
Assemat, E.; Picozzi, A.; Jauslin, H. R.; Sugny, D. [Laboratoire Interdisciplinaire Carnot de Bourgogne (ICB), UMR 5209 CNRS-Universite de Bourgogne, 9 Avenue A. Savary, Boite Postale 47 870, F-21078 Dijon Cedex (France)
2011-07-15
We analyze the role of soliton solutions and Hamiltonian singularities in the dynamics of counterpropagating waves in a medium of finite spatial extension. The soliton solution can become unstable due to the finite extension of the system. We show that the spatiotemporal dynamics then relaxes toward a Hamiltonian singular state of a nature different than that of the soliton state. This phenomenon can be explained through a geometrical analysis of the singularities of the stationary Hamiltonian system.
Soliton solutions of some nonlinear evolution equations with time-dependent coefficients
Hitender Kumar; Anand Malik; Fakir Chand
2013-02-01
In this paper, we obtain exact soliton solutions of the modified KdV equation, inho-mogeneous nonlinear Schrödinger equation and (, ) equation with variable coefficients using solitary wave ansatz. The constraint conditions among the time-dependent coefficients turn out as necessary conditions for the solitons to exist. Numerical simulations for dark and bright soliton solutions for the mKdV equation are also given.
XU Chang-Zhi
2006-01-01
Variable separation approach is introduced to solve the (2+1)-dimensional KdV equation. A series of variable separation solutions is derived with arbitrary functions in system. We present a new soliton excitation model (24). Based on this excitation, new soliton structures such as the multi-lump soliton and periodic soliton are revealed by selecting the arbitrary function appropriately.
Dynamical understanding of loop soliton solution for several nonlinear wave equations
Ji-bin LI
2007-01-01
It has been found that some nonlinear wave equations have one-loop soliton solutions. What is the dynamical behavior of the so-called one-loop soliton solution? To answer this question, the travelling wave solutions for four nonlinear wave equations are discussed. Exact explicit parametric representations of some special travelling wave solutions are given. The results of this paper show that a loop solution consists of three different breaking travelling wave solutions. It is not one real loop soliton travelling wave solution.
Cusp-like singular soliton solutions of Jaulent-Miodek equation using symbolic computation
Kavitha, L; Sathishkumar, P; Nathiyaa, T [Department of Physics, Periyar University, Salem 636 011 (India); Gopi, D [Department of Chemistry, Periyar University, Salem 636 011 (India)], E-mail: louiskavitha@yahoo.co.in
2009-03-15
In this paper, the sine-cosine method is employed to construct a series of exact solitary solutions to the celebrated Jaulent-Miodek equation. Solitons, anti-solitons and cusp-like singular solutions are obtained with the aid of symbolic computation.
N-Soliton Solutions of (2+1)-Dimensional Non-isospectral AKNS System
ZHANG Xiao-Xian; SUN Ye-Peng
2008-01-01
The bilinear form of the (2+1)-dimensional non-isospectral AKNS system is derived. Its N-soliton solutions are obtained by using the Hirota method. As a reduction, a (2+1)-dimensional non-isospectral Schrodinger equation and its N-soliton solutions are constructed.
Exact periodic wave and soliton solutions in two-component Bose-Einstein condensates
Li Hua-Mei
2007-01-01
We present several families of exact solutions to a system of coupled nonlinear Schr(o)dinger equations. The model describes a binary mixture of two Bose-Einstein condensates in a magnetic trap potential. Using a mapping deformation method, we find exact periodic wave and soliton solutions, including bright and dark soliton pairs.
Soliton Solutions of Coupled KdV System from Hirota's Bilinear Direct Method
ZHANG Chen-Jun; YANG Jian-Rong; ZHOU Jian-Hua; MAO Jie-Jian; YUE Rui-Hong
2008-01-01
With Hirota's bilinear direct method, we study the special coupled KdV system to obtain its new soliton solutions. Then we further discuss soliton evolution, corresponding structures, and interesting interactive phenomena in detail with plot. As a result, we find that after the interaction, the solitons make elastic collision and there are no exchanges of their physical quantities including energy, velocity and shape except the phase shift.
Sun, Yan; Tian, Bo; Zhen, Hui-Ling; Wu, Xiao-Yu; Xie, Xi-Yang
2016-07-01
Under investigation in this paper is a (3 + 1)-dimensional modified Korteweg-de Vries-Zakharov-Kuznetsov (KdV-ZK) equation, which describes the nonlinear behaviors of ion-acoustic waves in a magnetized plasma where the cooler ions are treated as a fluid with adiabatic pressure and the hot isothermal electrons are described by a Boltzmann distribution. With the Hirota method and symbolic computation, we obtain the one-, two- and three-soliton solutions for such an equation. We graphically study the solitons related with the coefficient of the cubic nonlinearity M. Amplitude of the one soliton increases with increasing M, but the width of one soliton keeps unchanged as M increases. The two solitons and three solitons are parallel, and the amplitudes of the solitons increase with increasing M, but the widths of the solitons are unchanged. It is shown that the interactions between the two solitons and among the three solitons are elastic.
Tian, Qing; Wu, Lei; Zhang, Jie-Fang; Malomed, Boris A; Mihalache, D; Liu, W M
2011-01-01
We put forward a generic transformation which helps to find exact soliton solutions of the nonlinear Schrödinger equation with a spatiotemporal modulation of the nonlinearity and external potentials. As an example, we construct exact solitons for the defocusing nonlinearity and harmonic potential. When the soliton's eigenvalue is fixed, the number of exact solutions is determined by energy levels of the linear harmonic oscillator. In addition to the stable fundamental solitons, stable higher-order modes, describing array of dark solitons nested in a finite-width background, are constructed too. We also show how to control the instability domain of the nonstationary solitons.
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
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.
CAO Li-Na; WANG Deng-Shan; CHEN Lan-Xin
2007-01-01
In this paper,by using symbolic and algebra computation,Chen and Wang's multiple Riccati equations rational expansion method was further extended.Many double soliton-like and other novel combined forms of exact solutions of the (2+1 )-dimensional Breaking soliton equation are derived by using the extended multiple Riccati equations expansion method.
A Bilinear B(a)cklund Transformation and Explicit Solutions for a (3+1)-Dimensional Soliton Equation
WU Jian-Ping
2008-01-01
@@ Considering the bilinear form of a (3+1)-dimensional soliton equation, we obtain a bilinear Backlund transformation for the equation.As an application, soliton solution and stationary rational solution for the (3+1)-dimensional soliton equation are presented.
On the Link between Umbilic Geodesics and Soliton Solutions of Nonlinear PDEs
1995-01-01
In this paper we describe a new class of soliton solutions, called umbilic solitons, for certain nonlinear integrable PDES. These umbilic solitons have the property that as the space variable x tends to infinity, the solution tends to a periodic wave, and as x tends to minus infinity, it tends to a phase shifted wave of the same shape. The equations admitting solutions in this new class include the Dym equation and equations in its hierarchy. The methods used to find and analyse these solutio...
Breathers and Soliton Solutions for a Generalization of the Nonlinear Schrödinger Equation
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.
New multiple-soliton (kink) solutions for the high-order Boussinesq-Burgers equation
Guo, Peng; Wu, Xiang; Wang, Liangbi
2016-07-01
The homogeneous balance method is extended to find more new solutions of nonlinear evolution equations. As illustrative examples, many new multiple-soliton (kink) solutions of the high-order Boussinesq-Burgers equation are constructed. It is shown that the homogeneous balance method may provide us with a straightforward and effective mathematic tool for generating new multiple-soliton (kink) solutions of nonlinear evolution equations.
Soliton-like solutions to the generalized Burgers-Huxley equation with variable coefficients
Triki, Houria; Wazwaz, Abdul-Majid
2013-12-01
In this paper, we consider the generalized Burgers-Huxley equation with arbitrary power of nonlinearity and timedependent coefficients. We analyze the traveling wave problem and explicitly find new soliton-like solutions for this extended equation by using the ansatz of Zhao et al. [X. Zhao, D. Tang, L. Wang, Phys. Lett. A 346 (2005) 288-291]. We also employ the solitary wave ansatz method to derive the exact bright and dark soliton solutions for the considered evolution equation. The physical parameters in the soliton solutions are obtained as function of the time-dependent model coefficients. The conditions of existence of solitons are presented. As a result, rich exact travelling wave solutions, which contain new soliton-like solutions, bell-shaped solitons and kink-shaped solitons for the generalized Burgers-Huxley equation with time-dependent coefficients, are obtained. The methods employed here can also be used to solve a large class of nonlinear evolution equations with variable coefficients.
Lin, Ji; Ren, Bo; Li, Hua-mei; Li, Yi-Shen
2008-03-01
Two Darboux transformations of the (1+1) -dimensional Wu-Zhang (WZ) equation and the two-component Camassa-Holm (2CH) system with the reciprocal transformation are obtained. One-loop and two-loop soliton solutions and multisoliton(like) solutions of the 2CH system are obtained by using the Darboux transformations and selecting different seed solutions of the corresponding equations. The bidirectional soliton solutions of the (1+1) -dimensional WZ equation are also obtained. The interactions of two-soliton head-on and overtaking collisions for the WZ equation and the evolution of the two-soliton(-like) solutions for the 2CH system are studied.
Inversion of the linearized Korteweg-de Vries equation at the multi-soliton solutions
Haragus-Courcelle, M
1998-01-01
Uniform estimates for the decay structure of the $n$-soliton solution of the Korteweg-deVries equation are obtained. The KdV equation, linearized at the $n$-soliton solution is investigated in a class $\\WW$ consisting of sums of travelling waves plus an exponentially decaying residual term. An analog of the kernel of the time-independent equation is proposed, leading to solvability conditions on the inhomogeneous term. Estimates on the inversion of the linearized KdV equation at the $n$-soliton are obtained.
Stability of solitonic solutions of Super KdV equations under Susy breaking conditions
Restuccia, A
2012-01-01
A supersymmetric breaking procedure for N=1 Super KdV, preserving the positivity of the hamiltonian as well as the existence of solitonic solutions, is implemented. The resulting integrable system is shown to have nice stability properties.
New multi-soliton solutions for generalized Burgers-Huxley equation
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.
Cusp solitons and cusp-like singular solutions for nonlinear equations
Qiao Zhijun [Department of Mathematics, University of Texas Pan-American, 1201 West University Drive, Edinburg, TX 78539 (United States) and Institute of Mathematics, Fudan University, Shanghai 200433 (China)]. E-mail: qiao@utpa.edu; Qiao, Xin Brian [Memorial High School, 101E Hackberry, McAllen TX 78501 (United States)
2005-07-01
This paper gives two new families of nonlinear partial differential equations (PDEs). One has cusp soliton solution while the other possesses the cusp-like singular traveling wave solution. A typical integrable system: Harry-Dym (HD) equation is able to be contained in both families and has cusp soliton solution as well as cusp-like singular traveling wave solution. We prove that the cusp solution of the HD equation is not stable and the cusp-like solution is not included in the parametric solutions of the HD equati0008.
New Method for Finding a Series of Exact Solutions to Generalized Breaking Soliton Equation
BAI Cheng-Lin; GUO Jun; ZHAO Hong
2005-01-01
In this paper, a new generalized extended tanh-function method is presented for constructing soliton-like,period-form solutions of nonlinear evolution equations (NEEs). This method is more powerful than the extended tanhfunction method [Phys. Lett. A 277 (2000) 212] and the modified extended tanh-function method [Phys. Lett. A 285 (2001) 355]. Abundant new families of the exact solutions of Bogoyavlenskii's generalized breaking soliton equation are obtained by using this method and symbolic computation system Maple.
New Method for Finding a Series of Exact Solutions to Generalized Breaking Soliton Equation
BAICheng-Lin; GUOJun; ZHAOHong
2005-01-01
In this paper, a new generalized extended tanh-function method is presented for constructing soliton-like,period-form solutions of nonlinear evolution equations (NEEs). This method is more powerful than the extended tanhfunction method [Phys. Left. A 277 (2000) 212] and the modified extended tanh-function method [Phys. Left. A 285 (2001) 355]. Abundant new families of the exact solutions of Bogoyavlenskii's generalized breaking soliton equation are obtained by using this method and symbolic computation system Maple.
Explicit Soliton and Periodic Solutions to Three-Wave System with Quadratic and Cubic Nonlinearities
LIN Ji; ZHAO Li-Na; LI Hua-Mei
2011-01-01
Lie group theoretical method and the equation of the Jacobi elliptic function are used to study the three wave system that couples two fundamental frequency (FF) and a single second harmonic (SH) one by competing x(2)(quadratic) and x(3) (cubic) nonlinearities and birefringence.This system shares some of the nice properties of soliton system.On the phase-locked condition, we obtain large families of analytical solutions as the soliton, kink and periodic solutions of this system.
Guo, Bang-Xing; Gao, Zhan-Jie; Lin, Ji
2016-12-01
The consistent tanh expansion (CTE) method is applied to the (2+1)-dimensional Boussinesq equation which describes the propagation of ultrashort pulse in quadratic nonlinear medium. The interaction solutions are explicitly given, such as the bright soliton-periodic wave interaction solution, variational amplitude periodic wave solution, and kink-periodic wave interaction solution. We also obtain the bright soliton solution, kind bright soliton solution, double well dark soliton solution and kink-bright soliton interaction solution by using Painlevé truncated expansion method. And we investigate interactive properties of solitons and periodic waves. Supported by the National Natural Science Foundation of Zhejiang Province under Grant No. LZ15A050001 and the National Natural Science Foundation of China under Grant No. 11675164
Soliton Solution of SU(3) Gauge Fields at Finite Temperature
WANG Dian-Fu; SONG He-Shan
2005-01-01
@@ Starting from a soliton model of SU(3) gauge fields, we investigate the behaviour of the model at finite temperature. it is found that colour confinement at zero temperature can be melted away under high temperatures.
Ouyang Shi-Gen; Guo Qi; Lan Sheng; Wu Li-Jun
2007-01-01
The fundamental and second order strongly nonlocal solitons of the nonlocal nonlinear Schr(o)dinger equation for several types of nonlocal responses are calculated by Ritz's variational method.For a specific type of nonlocal response, the solutions of the strongly nonlocal solitons with the same beam width but difierent degrees of nonlocality are identical except for an amplitude factor.For a nonlocal case where the nonlocal response function decays in direct proportion to the ruth power of the distance near the source point,the power and the phase constant of the strongly nonlocal soliton are in inverse proportion to the(m+2)th power of its beam width.
Finite-Length Soliton Solutions of the Local Homogeneous Nonlinear Schrödinger Equation
Caparelli, E C; Mizrahi, S S
1998-01-01
We found a new kind of soliton solutions for the 5-parameter family of the potential-free Stenflo-Sabatier-Doebner-Goldin nonlinear modifications of the Schrödinger equation. In contradistinction to the "usual'' solitons like are nonanalytical functions with continuous first derivatives, which are different from zero only inside some finite regions of space. The simplest one-dimensional example is the function which is equal to identically equal to zero for |x-kt|>\\pi/(2g). The FLS exist even in the case of a weak nonlinearity, whereas the ``usual'' solitons exist provided the nonlinearity parameters surpass some critical values.
Lump and lump-soliton solutions to the (2+1) -dimensional Ito equation
Yang, Jin-Yun; Ma, Wen-Xiu; Qin, Zhenyun
2017-06-01
Based on the Hirota bilinear form of the (2+1) -dimensional Ito equation, one class of lump solutions and two classes of interaction solutions between lumps and line solitons are generated through analysis and symbolic computations with Maple. Analyticity is naturally guaranteed for the presented lump and interaction solutions, and the interaction solutions reduce to lumps (or line solitons) while the hyperbolic-cosine (or the quadratic function) disappears. Three-dimensional plots and contour plots are made for two specific examples of the resulting interaction solutions.
Soliton solutions for a variable-coefficient Korteweg-de Vries equation in fluids and plasmas
Jiang, Yan; Tian, Bo; Liu, Wen-Jun; Sun, Kun; Qu, Qi-Xing
2010-11-01
In this paper, we investigate a variable-coefficient Korteweg-de Vries (vc-KdV) equation, which can be used to describe the propagation of nonlinear waves in fluids, plasmas and other fields. Through the rational transformation and Hirota method, new soliton solutions to the vc-KdV equation are derived. On the basis of those soliton solutions, three types of collisions are obtained: overtaking collision between two unidirectional solitons, head-on collision between two bidirectional ones and collision between moving and stationary solitons. These collisions are proved to be elastic through asymptotic analysis, and figures are plotted which show that they are indeed elastic except for a phase shift.
New Multiple Soliton-like Solutions to (3+1)-Dimensional Burgers Equation with Variable Coefficients
CHEN Huai-Tang; ZHANG Hong-Qing
2004-01-01
A new generalized tanh function method is used for constructing exact travelling wave solutions of nonlinear partial differential equations in a unified way. The main idea of this method is to take full advantage of the Riccati equation, which has more new solutions. More new multiple soliton-like solutions are obtained for the (3+ 1 )-dimensional Burgers equation with variable coefficients.
Asymptotic Behavior of Soliton Solutions with a Double Spectral Parameter for Principal Chiral Field
SONG Quan-Fu; ZHOU Zi-Xiang
2005-01-01
The soliton solutions with a double spectral parameter for the principal chiral field are derived by Darboux transformation. The asymptotic behavior of the solutions as time tends to infinity is obtained and the speeds of the peaks in the asymptotic solutions are not constants.
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
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 ...
张解放; 吴锋民
2002-01-01
We study an approach to constructing multiple soliton solutions of the (3+1)-dimensional nonlinear evolution equation. We take the (3+1)-dimensional Jimbo-Miwa (JM) equation as an example. Using the extended homogeneous balance method, one can find a Backlund transformation to decompose the (3+1)-dimensional JM equation into a linear partial differential equation and two bilinear partial differential equations. Starting from these linear and bilinear partial differential equations, some multiple soliton solutions for the (3+1)-dimensional JM equation are obtained by introducing a class of formal solutions.
Soliton-like Solutions and Electron Transfer in DNA.
Lakhno, V D
2000-06-01
We consider various mechanisms of long-range electron transfer in DNAwhich enable us to explain recent controversial experiments. We show thatcontinuous super-exchange theory can explain the values of electron rateconstants in short fragments of DNA. The soliton-type electron transfer inlong segments of DNA is also dealt with.
Soliton-like Solutions and Electron Transfer in DNA
Lakhno, V.D.
2000-01-01
We consider various mechanisms of long-range electron transfer in DNAwhich enable us to explain recent controversial experiments. We show thatcontinuous super-exchange theory can explain the values of electron rateconstants in short fragments of DNA. The soliton-type electron transfer inlong segments of DNA is also dealt with.
Abundant soliton solutions for the coupled Schrödinger-Boussinesq system via an analytical method
Manafian, Jalil; Aghdaei, Mehdi Fazli
2016-04-01
In this paper, the improved tan(Φ(ξ)/2)-expansion method is proposed to find the exact soliton solutions of the coupled Schrödinger-Boussinesq (SB) system. The exact particular solutions are of five types: hyperbolic function solution (exact soliton wave solution), trigonometric function solution (exact periodic wave solution), rational exponential solution (exact singular kink-type wave solution), logarithmic solution and rational solution (exact singular cupson wave solution). We obtained the further solutions comparing with other methods. The results demonstrate that the new tan(Φ(ξ)/2)-expansion method is more efficient than the Ansatz method applied by Bilige et al. (2013). Recently this method was developed for searching the exact travelling-wave solutions of nonlinear partial differential equations. Abundant exact travelling-wave solutions including solitons, kink, periodic and rational solutions have been found. These solutions might play an important role in Laser and plasma. It is shown that this method, with the help of symbolic computation, provides a straightforward and powerful mathematical tool for solving the nonlinear problems.
Some Remarks on Similarity and Soliton Solutions of Nonlinear Klein-Gordon Equation
Tajiri, Masayoshi
1984-11-01
The three-dimensional nonlinear Klein-Gordon [, Higgs field and Yang-Milles] (3D-KG [, H and YM]) equation is first reduced to the 2D nonlinear Schrödinger (2D-NLS) and 2D-KG [, H and YM] equations, and secondly to the 1D-NLS and 1D-KG [, H and YM] equations by similarity transformations. It is shown that similar type soliton solutions of the 3D-KG, H and YM equations, which have singularity on a plane in (x, y, z, t) space, are obtained by substituting the soliton solutions of the 1D-NLS or 1D-KG (or H) equation into the similarity transformations. The soliton solutions of the YM equation are also investigated.
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.
Bell Polynomial Approach and N-Soliton Solutions for a Coupled KdV-mKdV System
覃翌; 高以天; 于鑫; 蒙高庆
2012-01-01
In fluid dynamics, plasma physics and nonlinear optics, Korteweg-de Vries （KdV）-type equations are used to describe certain phenomena. In this paper, a coupled KdV-modified KdV system is investigated. Based on the Bell polynomials and symbolic computation, the bilinear form of such system is derived, and its analytic N-soliton solutions are constructed through the Hirota method. Two types of multi-soliton interactions are found, one with the reverse of solitonic shapes, and the other, without. Both the two types can be considered elastic. For a pair of solutions to such system, u and v, with the number of solitons N even, the soliton shapes of u stay unvaried while those of v reverse after the interaction; with N odd, the soliton shapes of both u and v keep unchanged after the interaction.
ZHAO Xue-Qin; SUN Wei-Kun; ZHI Hong-Yan; CAO Nan-Bin; SHEN Ya-Liang
2008-01-01
In this paper, by means of double elliptic equation expansion approach, the novel double nonlinear wave solutions of the (2+1)-dimensional break soliton equation are obtained. These double nonlinear wave solutions contain the double Jacobi elliptic function-like solutions, the double solitary wave-like solutions, and so on. The method is also powerful to some other nonlinear wave equations in (2+1) dimensions.
Soliton solutions of the two-dimensional KdV-Burgers equation by homotopy perturbation method
Molabahrami, A. [Department of Mathematics, Ilam University, PO Box 69315516, Ilam (Iran, Islamic Republic of)], E-mail: a_m_bahrami@yahoo.com; Khani, F. [Department of Mathematics, Ilam University, PO Box 69315516, Ilam (Iran, Islamic Republic of); Bakhtar Institute of Higher Education, PO Box 696, Ilam (Iran, Islamic Republic of)], E-mail: farzad_khani59@yahoo.com; Hamedi-Nezhad, S. [Bakhtar Institute of Higher Education, PO Box 696, Ilam (Iran, Islamic Republic of)
2007-10-29
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.
Solitonic generation of vacuum solutions in five-dimensional General Relativity
Iguchi, H; Iguchi, Hideo; Mishima, Takashi
2006-01-01
We describe a solitonic solution-generating technique for the five-dimensional General Relativity. Reducing the five-dimensional problem to the four-dimensional one, we can systematically obtain single-rotational axially symmetric vacuum solutions. Applying the technique for a simple seed solution, we have previously obtained the series of stationary solutions which includes $S^2$-rotating black ring. We analyze the qualitative features of these solutions, e.g., conical singularities, closed timelike curves, and spacetime curvatures. We investigate the rod structures of seed and solitonic solutions. We examine the relation between the expressions of the metric in the prolate-spheroidal coordinates and in the C-metric coordinates.
A simple method to construct soliton-like solution of the general KdV equation with external force
JiefangZHANG; FengminWU
2000-01-01
A simple and direct method is described to construct the soliton-like solution for the general KdV equation with external force. Crucial to the method is the assumption that the solution chosen is a special truncated expansion.
LIHua-Mei; LINJi; XUYou-Sheng
2005-01-01
In this paper, we extend the hyperbolic function approach for constructing the exact solutions of nonlinear differential-difference equation (NDDE) in a unified way. Applying the extended approach and with the aid of Maple,we have studied the discrete complex Ginzburg-Landau equation (dCGLE). As a result, we find a set of exact solutions which include bright and dark soliton solutions.
FAN Eh-Gui
2001-01-01
An explicit N-fold Darboux transformation for a coupled of derivative nonlinear Schrodinger equations is constructed with the help of a gauge transformation of spectral problems. As a reduction, the Darboux transformation for well-known Gerdjikov-Ivanov equation is further obtained, from which a general form of N-soliton solutions for Gerdjikov-Ivanov equation is given.``
Construction of N-soliton solutions for a new integrable equation by Darboux transformation
Bai, Shuting; Zhaqilao
2016-10-01
In this paper, the relationship between a new integrable equation and well-known KdV equation is established by a set of transformation. With the help of Darboux transformation of KdV equation and the set of transformation, parametric representations of multi-soliton solutions for the new integrable equation are obtained, and their figures are plotted.
Coupled Modified Korteweg-de Vries Lattice in (2+1) Dimensions and Soliton Solutions
无
2006-01-01
The coupled semi-discrete modified Korteweg-de Vries equation in (2+1)-dimensions is proposed. It is shown that it can be decomposed into two (1+1)-dimensional differential-difference equations belonging to mKdV lattice hierarchy by considering a discrete isospectral problem. A Darboux transformation is set up for the resulting (2+1)- dimensional lattice soliton equation with the help of gauge transformations of Lax pairs. As an illustration by example,the soliton solutions of the mKdV lattice equation in (2+1)-dimensions are explicitly given.
Verhoeven, C; Musette, M [Dienst Theoretische Natuurkunde, Vrije Universiteit Brussel, Pleinlaan 2, B-1050 Brussels (Belgium)
2003-02-28
In this letter, we analyse two bidirectional sixth-order partial differential equations, which are reductions in (1 + 1) dimensions of equations belonging to the KP hierarchy. They have fourth-order and fifth-order Lax pairs, respectively. We derive their Baecklund transformations and, from the nonlinear superposition formula, we can build their soliton solutions like a Grammian. The interesting dynamics of these solitons is that they may describe not only the overtaking collision but also the head-on collision of solitary waves of different type and shape. (letter to the editor)
Ahmet Bekir; Özkan Güner
2013-08-01
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 model. These solutions may be useful and desirable for explaining some nonlinear physical phenomena in genuinely nonlinear dynamical systems.
Shubina, Maria
2016-09-01
In this paper, we investigate the one-dimensional parabolic-parabolic Patlak-Keller-Segel model of chemotaxis. For the case when the diffusion coefficient of chemical substance is equal to two, in terms of travelling wave variables the reduced system appears integrable and allows the analytical solution. We obtain the exact soliton solutions, one of which is exactly the one-soliton solution of the Korteweg-de Vries equation.
Soliton solutions to a few fractional nonlinear evolution equations in shallow water wave dynamics
Mirzazadeh, Mohammad; Ekici, Mehmet; Sonmezoglu, Abdullah; Ortakaya, Sami; Eslami, Mostafa; Biswas, Anjan
2016-05-01
This paper studies a few nonlinear evolution equations that appear with fractional temporal evolution and fractional spatial derivatives. These are Benjamin-Bona-Mahoney equation, dispersive long wave equation and Nizhnik-Novikov-Veselov equation. The extended Jacobi's elliptic function expansion method is implemented to obtain soliton and other periodic singular solutions to these equations. In the limiting case, when the modulus of ellipticity approaches zero or unity, these doubly periodic functions approach solitary waves or shock waves or periodic singular solutions emerge.
Singular solitons and other solutions to a couple of nonlinear wave equations
Mustafa Inc; Esma Uluta(s); Anjan Biswas
2013-01-01
This paper addresses the extended (G′/G)-expansion method and applies it to a couple of nonlinear wave equations.These equations are modified the Benjamin-Bona-Mahoney equation and the Boussinesq equation.This extended method reveals several solutions to these equations.Additionally,the singular soliton solutions are revealed,for these two equations,with the aid of the ansatz method.
A Unified and Explicit Construction of N-Soliton Solutions for the Nonlinear Schrfdinger Equation
FAN En-Gui
2001-01-01
An explicit N-fold Darboux transformation with multiparameters for nonlinear Schrodinger equation is constructed with the help of its Lax pairs and a reduction technique. According to this Darboux transformation, the solutions of the nonlinear Schrfdinger equation are reduced to solving a linear algebraic system, from which a unified and explicit formulation of N-soliton solutions with multiparameters for the nonlinear Schrfdinger equation is given.``
Liu, Lei; Tian, Bo; Sun, Wen-Rong; Zhen, Hui-Ling; Shan, Wen-Rui
2016-10-01
Studied in this paper are the bright-dark vector soliton solutions for a generalized coupled Hirota system which describes the propagation for the high-intensity ultrashort pulses in the optical glass fiber. Beyond the existing bilinear forms, using an auxiliary function, we obtain the improved bilinear forms and bright-dark soliton solutions under two integrable constraints through the Hirota method and symbolic computation. With the help the analytic and graphic analysis, we study the soliton properties including the amplitudes, velocities and phase shifts, and show that the interactions for the bright-dark two solitons are elastic. For the bright-dark one soliton, parametric conditions that the dark component is "black" or "gray" are obtained. For the bright-dark two solitons, we find that the bright component is affected by the dark component background parameters during such an interaction, while the dark component is not affected by the bright component background parameters. Velocities for the bright-dark two solitons are inversely proportional to the higher-order effect parameter, but amplitudes and phase shifts are independent of it. Besides, the bound-state bright-dark two solitons are also presented.
Takahashi, Daisuke A
2015-01-01
The matrix-generalized Bogoliubov-de Gennes systems are recently considered by the present author [arXiv:1509.04242], and the time-dependent and self-consistent multi-soliton solutions are constructed based on the ansatz method. In this paper, restricting the problem to the static case, we exhaustively determine the self-consistent solutions using the inverse scattering theory. Solving the gap equation, we rigorously prove that the self-consistent potential must be reflectionless. As a supplementary topic, we elucidate the relation between the stationary self-consistent potentials and the soliton solutions in the matrix nonlinear Schr\\"odinger equation. The asymptotic formulae of multi-soliton solutions for sufficiently isolated solitons are also presented.
Some topics on Ricci solitons and self-similar solutions to mean curvature flow
Futaki, Akito
2012-01-01
In this survey article, we discuss some topics on self-similar solutions to the Ricci flow and the mean curvature flow. Self-similar solutions to the Ricci flow are known as Ricci solitons. In the first part of this paper we discuss a lower diameter bound for compact manifolds with shrinking Ricci solitons. Such a bound can be obtained from an eigenvalue estimate for a twisted Laplacian, called the Witten-Laplacian. In the second part we discuss self-similar solutions to the mean curvature flow on cone manifolds. Many results have been obtained for solutions in $\\bfR^n$ or $\\bfC^n$. We see that many of them extend to cone manifolds, and in particular results on $\\bfC^n$ for special Lagrangians and self-shrinkers can be extended to toric Calabi-Yau cones. We also see that a similar lower diameter bound can be obtained for self-shrinkers to the mean curvature flow as in the case of shrinking Ricci solitons.
Singular and non-topological soliton solutions for nonlinear fractional differential equations
Ozkan Guner
2015-01-01
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.
Inverse Scattering Method and Soliton Solution Family for String Effective Action
GAO Ya-Jun
2009-01-01
A modified Hauser-Ernst-type linear system is established and used to develop an inverse scattering method for solving the motion equations of the string effective action describing the coupled gravity, dilaton and Kalb-Ramond fields. The reduction procedures in this inverse scattering method are found to be fairly simple, which makes the proposed inverse scattering method applied fine and effective. As an application, a concrete family of soliton solutions for the considered theory is obtained.
Soliton solution and interaction property for a coupled modified Korteweg-de Vries (mKdV) system
Yang Jian-Rong; Mao Jie-Jian
2008-01-01
Hirota's bilinear direct method is applied to constructing soliton solutions to a special coupled modified Korteweg de Vries (mKdV) system. Some physical properties such as the spatiotemporal evolution, waveform structure, interactive phenomena of solitons are discussed, especially in the two-soliton case. It is found that different interactive behaviours of solitary waves take place under different parameter conditions of overtaking collision in this system. It is verified that the elastic interaction phenomena exist in this (11)-dimensionai integrable coupled model.
Soliton solutions and gauge equivalence for the problem of Zakharov-Shabat and its generalizations
Vaklev, Y.
1996-03-01
In a paper by Takhtadjan and Faddeev [Hamiltonian approach to the soliton theory (in Russian) (Nauka, Moskov, 1986)] the N-soliton solutions, related to the nonlinear Schrödinger equation (NSE), are given. A generalization of this approach allows us to apply it not only to the NSE, but to the whole hierarchy of the Zakharov-Shabat problem, to the quadratic bundle problem, and to the ones gauge equivalent to them [where one can find, for example, the Heisenberg ferromagnet equation, the relativistic Mikhailov model (which, in appropriate reduction, is equivalent to the massive Thirring model), the derivative nonlinear Schrödinger equation (which is equivalent to the derivative Landau-Lifshitz equation), etc.]. We have used an appropriate reduction, giving us interesting, from a physical point of view, results. Thus we manage to obtain the soliton solutions for the whole hierarchy of the quadratic bundle problem (free and under reduction) and for the ones gauge equivalent to it. This result was first announced in previous articles by Vaklev, but here we manage to solve the determinants given there and to present the searched result as simple fractions of products of numerical differences.
Wang, Yao; Chen, Mei-Dan; Li, Xian; Li, Biao
2017-05-01
Through Hirota bilinear transformation and symbolic computation with Maple, a class of lump solutions, rationally localised in all directions in the space, to a reduced generalised (3+1)-dimensional shallow water wave (SWW) equation are prensented. The resulting lump solutions all contain six parameters, two of which are free due to the translation invariance of the SWW equation and the other four of which must satisfy a nonzero determinant condition guaranteeing analyticity and rational localisation of the solutions. Then we derived the interaction solutions for lump solutions and one stripe soliton and the result shows that the particular lump solutions with specific values of the involved parameters will be drowned or swallowed by the stripe soliton. Furthermore, we extend this method to a more general combination of positive quadratic function and hyperbolic functions. Especially, it is interesting that a rogue wave is found to be aroused by the interaction between lump solutions and a pair of resonance stripe solitons. By choosing the values of the parameters, the dynamic properties of lump solutions, interaction solutions for lump solutions and one stripe soliton and interaction solutions for lump solutions and a pair of resonance solitons, are shown by dynamic graphs.
Constructing Soliton and Kink Solutions of PDE Models in Transport and Biology
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.
The soliton Kdv equation and its solution%孤立子Kdv方程及其解
司瑞芳
2012-01-01
通过对孤立子浅水波Kdv方程应用行波法、截断法、广田法等几种解法进行求解,比较了在各种解法下Kdv方程解的异同,同时对各种解法进行了比较。%The article solves the solutions of soliton shallow water wave Kdv equation by traveling wave method,truncation method and Hirota method,and compares the similarities and differences of all these three kinds solutions and the varieties to Kdv equation.
Soliton solution for nonlinear partial differential equations by cosine-function method
Ali, A.H.A. [Mathematics Department, Faculty of Science, Menoufia University, Shebein El-Koom (Egypt); Soliman, A.A. [Department of Mathematics, Faculty of Education (AL-Arish), Suez Canal University, AL-Arish 45111 (Egypt)], E-mail: asoliman_99@yahoo.com; Raslan, K.R. [Mathematics Department, Faculty of Science, Al-Azhar University, Nasr-City, Cairo (Egypt)
2007-08-20
In this Letter, we established a traveling wave solution by using Cosine-function algorithm for nonlinear partial differential equations. The method is used to obtain the exact solutions for five different types of nonlinear partial differential equations such as, general equal width wave equation (GEWE), general regularized long wave equation (GRLW), general Korteweg-de Vries equation (GKdV), general improved Korteweg-de Vries equation (GIKdV), and Coupled equal width wave equations (CEWE), which are the important soliton equations.
New Multiple Soliton-like Solutions to （3＋1）-Dimensional Burgers Equation with Variable Coefficients
CHENHuai-Tang; ZHANGHong-Qing
2004-01-01
A new generalized tanh function method is used for constructing exact travelling wave solutions of nonlinear partial differential equations in a unified way. The main idea of this method is to take full advantage of the Riccati equation, which has more new solutions. More new multiple soliton-like solutions are obtained for the (3+1)-dimensional Burgers equation with variable coefficients.
Classically Isospinning Hopf Solitons
Battye, Richard A
2013-01-01
We perform full 3-dimensional numerical relaxations of isospinning Hopf solitons with Hopf charge up to 8 in the Skyrme-Faddeev model with mass terms included. We explicitly allow the soliton solution to deform and to break the symmetries of the static configuration. It turns out that the model with its rich spectrum of soliton solutions, often of similiar energy, allows for transmutations, formation of new solution types and the rearrangement of the spectrum of minimal-energy solitons in a given topological sector when isospin is added. We observe that the shape of isospinning Hopf solitons can differ qualitatively from that of the static solution. In particular the solution type of the lowest energy soliton can change. Our numerical results are of relevance for the quantization of the classical soliton solutions.
ZHOU Zhen-Jiang; LI Zhi-Bin
2003-01-01
An explicit N-fold Darboux transformation for evolution equations determined by general 2×2 AKNS system is constructed. By using the Darboux transformation, the solutions of the evolution equations are reduced to solving alinear algebraic system, from which a unified and explicit formulation of 2N-soliton solutions for the evolution equation are given. Furthermore, a reduction technique for MKdV equation is presented, and an N-fold Darboux transformation of MKdV hierarchy is constructed through the reduction technique. A Maple package which can entirely automatically output the exact N-soliton solutions of the MKdV equation is developed.
BAICheng-Lin; LIUXi-Qiang; ZHAOHong
2004-01-01
We study an approach to constructing multiple soliton solutions of the (3+1)-dimensional nonlinear evolution equation. We take the (3+1)-dimensional potential- YTSF equation as an example. Using the extended homogeneous balance method, one can find a Backlund transformation to decompose the (3+1)-dimensional potential-YTSF equation into a set of partial differential equations. Starting from these partial differential equations, some multiple soliton solutions for the (3+1)-dimensional potential-YTSF equation are obtained by introducing a class of formal solutions.
Bai Cheng-Lin
2004-01-01
@@ We develop an approach to construct multiple soliton solutions of the (3+1)-dimensional nonlinear evolution equation. We take the (3+1)-dimensional Nizhnik-Novikov-Veselov (NNV) equation as an example. Using the extended homogeneous balance method, one can find a Backlünd transformation to decompose the (3+1)-dimensional NNV into a set of partial differential equations. Starting from these partial differential equations, some multiple soliton solutions for the (3+1)-dimensional NNV equation are obtained by introducing a class of formal solutions.
ZHANG Li-Hua; LIU Xi-Qiang; BAI Cheng-Lin
2006-01-01
In this paper, the generalized tanh function method is extended to (2+1)-dimensional canonical generalized KP (CGKP) equation with variable coefficients. Taking advantage of the Riccati equation, many explicit exact solutions,which contain multiple soliton-like and periodic solutions, are obtained for the (2+1)-dimensional CGKP equation with variable coefficients.
Wei Yi-Huan
2011-01-01
This paper points out that equations (18a) and (18b) in Ref. [7] [Gao Y J 2008 Chin. Phys. B 17 3574] only possess the solutions M = ±ρ(～γ)ε. So, there does not exist the so-called soliton solution family for the Einstein-Maxwell theory with multiple Abelian gauge fields shown in Ref. [7].
Soliton solution for the Landau-Lifshitz equation of a one-dimensional bicomponent magnonic crystal.
Giridharan, D; Sabareesan, P; Daniel, M
2016-09-01
We investigate nonlinear localized magnetic excitations in a one-dimensional bicomponent magnonic crystal under a periodic magnetic field of spatially varying strength. The governing Landau-Lifshitz equation is transformed into a variable coefficient nonlinear Schrödinger (VCNLS) equation using stereographic projection. In general, the VCNLS equation is nonintegrable and by using Painlevé analysis, we obtain necessary conditions for the VCNLS equation to pass the Weiss-Tabor-Carnevale Painlevé test. A sufficient integrability condition is obtained by further exploring a transformation, which can map the VCNLS equation into the well-known standard nonlinear Schrödinger equation. The transformation builds a systematic connection between the solution of the standard nonlinear Schrödinger equation and VCNLS equation. The results show that the excitation of magnetization in the form of a soliton exists on the oscillatory background with a structure similar to the form of spin Bloch waves. Such a solution exists only when certain conditions on the coefficient of the VCNLS equation are satisfied. To corroborate the analytical results, we performed the numerical simulation by solving the governing VCNLS equation with integrability conditions using the split step Fourier method and the result agrees well with analytical results, and it suggests a way to control the dynamics of magnetization in the form of solitons by an appropriate spatial modulation of the nonlinearity coefficient in the governing VCNLS equation, which depends on the ferromagnetic materials which form the bicomponent magnonic crystal.
Nonholonomic jet deformations, exact solutions for modified Ricci soliton and Einstein equations
Rajpoot, Subhash; Vacaru, Sergiu I.
Let g be a pseudo-Riemannian metric of arbitrary signature on a manifold V with conventional n + n-dimensional splitting, n ≥ 2, determined by a nonholonomic (nonintegrable) distribution 𝒩 defining a generalized (nonlinear) connection and associated nonholonomic frame structures. We work with an adapted linear metric compatible connection D ̂ and its nonzero torsion 𝒯 ̂, both completely determined by g. Our first goal is to prove that there are certain generalized frame and/or jet transforms and prolongations with (g,V) → (g ̂,V ̂) into explicit classes of solutions of some generalized Einstein equations R ̂ic = Λg ̂, Λ = const, encoding various types of (nonholonomic) Ricci soliton configurations and/or jet variables and symmetries. The second goal is to solve additional constraint equations for zero torsion, 𝒯 ̂ = 0, on generalized solutions constructed in explicit forms with jet variables and extract Levi-Civita configurations. This allows us to find generic off-diagonal exact solutions depending on all space time coordinates on V via generating and integration functions and various classes of constant jet parameters and associated symmetries. Our third goal is to study how such generalized metrics and connections can be related by the so-called “half-conformal” and/or jet deformations of certain subclasses of solutions with one, or two, Killing symmetries. Finally, we present some examples of exact solutions constructed as nonholonomic jet prolongations of the Kerr metrics, with possible Ricci soliton deformations, and characterized by nonholonomic jet structures and generalized connections.
Annihilation Solitons and Chaotic Solitons for the (2+1)-Dimensional Breaking Soliton System
无
2007-01-01
By means of an improved mapping method and a variable separation method, a scries of variable separation solutions (including solitary wave solutions, periodic wave solutions and rational function solutions) to the (2+1)-dimensional breaking soliton system is derived. Based on the derived solitary wave excitation, we obtain some special annihilation solitons and chaotic solitons in this short note.
陈怀堂; 张鸿庆
2003-01-01
A new generalized Jacobi elliptic function method is used to construct the exact travelling wave solutions of nonlinear partial differential equations (PDEs) in a unified way. The main idea of this method is to take full advantage of the elliptic equation which has more new solutions. More new doubly periodic and multiple soliton solutions are obtained for the generalized (3+1)-dimensional Kronig-Penny (KP) equation with variable coefficients. This method can be applied to other equations with variable coefficients.
Wen, Xiao-Yong; Yan, Zhenya
2017-02-01
The novel generalized perturbation (n, M)-fold Darboux transformations (DTs) are reported for the (2 + 1)-dimensional Kadomtsev-Petviashvili (KP) equation and its extension by using the Taylor expansion of the Darboux matrix. The generalized perturbation (1 , N - 1) -fold DTs are used to find their higher-order rational solitons and rogue wave solutions in terms of determinants. The dynamics behaviors of these rogue waves are discussed in detail for different parameters and time, which display the interesting RW and soliton structures including the triangle, pentagon, heptagon profiles, etc. Moreover, we find that a new phenomenon that the parameter (a) can control the wave structures of the KP equation from the higher-order rogue waves (a ≠ 0) into higher-order rational solitons (a = 0) in (x, t)-space with y = const . These results may predict the corresponding dynamical phenomena in the models of fluid mechanics and other physically relevant systems.
Comment on "Defocusing complex short-pulse equation and its multi-dark-soliton solution"
Youssoufa, Saliou; Kuetche, Victor K.; Kofane, Timoleon C.
2017-08-01
In their recent paper, Feng et al. [Phys. Rev. E 93, 052227 (2016), 10.1103/PhysRevE.93.052227] proposed a complex short-pulse equation of both focusing and defocusing types. They studied in detail the defocusing case and derived its multi-dark-soliton solutions. Nonetheless, from a physical viewpoint in order to better and deeply understand their genuine implications, we find it useful to provide a real and proper background for the derivation of the previous evolution system while showing that the expression of the nonlinear electric polarization the above authors used in their scheme is not suitable for getting the defocusing complex short-pulse equation.
XU Peng-Bo; GAO Yi-Tian; YU Xin; WANG Lei; LIN Guo-Dong
2011-01-01
This paper is to investigate the extended (2+1)-dimensional Konopelchenko-Dubrovsky equations, which can be applied to describing certain phenomena in the stratified shear flow, the internal and shallow-water waves,plasmas and other fields. Painlevé analysis is passed through via symbolic computation. Bilinear-form equations are constructed and soliton solutions are derived. Soliton solutions and interactions are illustrated. Bilinear-form B(a)cklund transformation and a type of solutions are obtained.
Gagnon, Ludovick
2016-01-01
The qualitative properties of the particle trajectories of the $N$-solitons solution of the KdV equation are recovered from the first order velocity field by the introduction of the stream function. Numerical simulations show an accurate depth dependance of the particles trajectories for solitary waves. Failure of the free surface kinematic boundary condition for the first order type velocity field is highlighted.
Two-component generalizations of the periodic Camassa-Holm and Degasperis-Procesi equations
Escher, Joachim; Lenells, Jonatan
2010-01-01
We use geometric methods to study two natural two-component generalizations of the periodic Camassa-Holm and Degasperis-Procesi equations. We show that these generalizations can be regarded as geodesic equations on the semidirect product of the diffeomorphism group of the circle $\\Diff(S^1)$ with some space of sufficiently smooth functions on the circle. Our goals are to understand the geometric properties of these two-component systems and to prove local well-posedness in various function spaces. Furthermore, we perform some explicit curvature calculations for the two-component Camassa-Holm equation, giving explicit examples of large subspaces of positive curvature.
Multi-soliton solution, rational solution of the Boussinesq-Burgers equations
Abdel Rady, A. S.; Osman, E. S.; Khalfallah, Mohammed
2010-05-01
In this paper we consider the Boussinesq-Burgers equations and establish the transformation which turns the Boussinesq-Burgers equations into the single nonlinear partial differential equation, then we obtain an auto-Bäcklund transformation and abundant new exact solutions, including the multi-solitary wave solution and the rational series solutions. Besides the new trigonometric function periodic solutions are obtained by using the generalized tan h method.
Abdel-Gawad, H. I.; Tantawy, M.
2017-06-01
The aim of this paper is to study the collision between the long surface water waves. This is done by considering the coupled KdV equations with the relevant constrains on the variable coefficients. The extended rational traveling wave solutions are obtained. Various solutions of solitary waves, via soliton, periodic, elliptic and two-soliton solutions has also found. The waveguide properties of the characterizing two-soliton are shown to be a graded-index with reflection component and transmission with periodic distributions in long-distance communication. Here the linear refractive index and transmission are been shown to evolute towards solitonic waves enable to confirm data transverse by restricting expansion in low-cost telecommunications systems.
Abdel-Gawad, H. I.; Tantawy, M.
2017-02-01
The aim of this paper is to study the collision between the long surface water waves. This is done by considering the coupled KdV equations with the relevant constrains on the variable coefficients. The extended rational traveling wave solutions are obtained. Various solutions of solitary waves, via soliton, periodic, elliptic and two-soliton solutions has also found. The waveguide properties of the characterizing two-soliton are shown to be a graded-index with reflection component and transmission with periodic distributions in long-distance communication. Here the linear refractive index and transmission are been shown to evolute towards solitonic waves enable to confirm data transverse by restricting expansion in low-cost telecommunications systems.
Chen, Mei-Dan; Li, Xian; Wang, Yao; Li, Biao
2017-06-01
With symbolic computation, some lump solutions are presented to a (3+1)-dimensional nonlinear evolution equation by searching the positive quadratic function from the Hirota bilinear form of equation. The quadratic function contains six free parameters, four of which satisfy two determinant conditions guaranteeing analyticity and rational localization of the solutions, while the others are free. Then, by combining positive quadratic function with exponential function, the interaction solutions between lump solutions and the stripe solitons are presented on the basis of some conditions. Furthermore, we extend this method to obtain more general solutions by combining of positive quadratic function and hyperbolic cosine function. Thus the interaction solutions between lump solutions and a pair of resonance stripe solitons are derived and asymptotic property of the interaction solutions are analyzed under some specific conditions. Finally, the dynamic properties of these solutions are shown in figures by choosing the values of the parameters. Supported by National Natural Science Foundation of China under Grant Nos. 11271211, 11275072, and 11435005, Ningbo Natural Science Foundation under Grant No. 2015A610159 and the Opening Project of Zhejiang Provincial Top Key Discipline of Physics Sciences in Ningbo University under Grant No. xkzw11502 and K.C. Wong Magna Fund in Ningbo University
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.
Paulo E G Assis; Andreas Fring
2010-06-01
We investigate whether the recently proposed $\\mathcal{PT}$-symmetric extensions of generalized Korteweg–de Vries equations admit genuine soliton solutions besides compacton 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 be found. 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 addition to compactons and are integrable.
Spectral boundary conditions and solitonic solutions in a classical Sellmeier dielectric
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.)
Abdel-Gawad, H. I.; Tantawy, M.
2017-02-01
Very recently, multi-solitary long waves for the homogeneous Boussinesq-Burgers equations (BBEs) were studied. Here its found that the time dependent coefficients (BBEs), shows multi-graded-index solitons waves, which are graded refractive index profile and can offer a new route for high-power lasers and transmission. They should increase data rates in low-cost telecommunications systems. Further, that (BBEs) show long periodic solitons waves in communications and television antennas.
CHENYong; WANGQi; LIBiao
2004-01-01
We generalize the algebraic method presented by Fan [J.Phys. A: Math. Gen. 36 (2003) 7009)] to uniformly construct a series of soliton-like solutions and double-like periodic solutions for nonlinear partial differential equations (NPDE). As an application of the method, we choose a (2+1)-dimensional asymmetric Nizhnik Novikov Vesselov equation and successfully construct new and more general solutions including a series of nontraveling wave and coefficient functions'soliton-like solutions, double-like periodic and trigonometric-like function solutions.
CHEN Yong; WANG Qi; LI Biao
2004-01-01
We generalize the algebraic method presented by Fan [J. Phys. A: Math. Gen. 36 (2003) 7009)] to uniformly construct a series of soliton-like solutions and double-like periodic solutions for nonlinear partial differential equations(NPDE). As an application of the method, we choose a (2+1)-dimensional asymmetric Nizhnik-Novikov-Vesselov equation and successfully construct new and more general solutions including a series of nontraveling wave and coefficient functions' soliton-like solutions, double-like periodic and trigonometric-like function solutions.
Shen, Yu-Jia; Gao, Yi-Tian; Yu, Xin
2013-09-01
With symbolic computation, the generalized variable-coefficient Drinfeld-Sokolov-Satsuma-Hirota (gvcDSSH) system in fluids and plasmas is investigated. Under the constraint conditions on variable coefficients obtained via the Painlevé test, the binary Bell polynomials are applied to the gvcDSSH system for its bilinear forms and multi-soliton solutions. With the different damping, dispersive and dissipative coefficients given, the multi-soliton solutions of the gvcDSSH system are illustrated and discussed. (i) The interactions between/among the solitons are elastic; (ii) the damping coefficient can only affect the amplitude of one field, while it has no effect on the other; (iii) the velocity and characteristic line for each soliton can be affected by the dispersive and dissipative coefficients.
Taylor, J. R.
2005-08-01
1. Optical solitons in fibres: theoretical review A. Hasegawa; 2. Solitons in optical fibres: an experimental account L. F. Mollenauer; 3. All-optical long-distance soliton-based transmission systems K. Smith and L. F. Mollenauer; 4. Nonlinear propagation effects in optical fibres: numerical studies K. J. Blow and N. J. Doran; 5. Soliton-soliton interactions C. Desem and P. L. Chu; 6. Soliton amplification in erbium-doped fibre amplifiers and its application to soliton communication M. Nakazawa; 7. Nonlinear transformation of laser radiation and generation of Raman solitons in optical fibres E. M. Dianov, A. B. Grudinin, A. M. Prokhorov and V. N. Serkin; 8. Generation and compression of femtosecond solitons in optical fibers P. V. Mamyshev; 9. Optical fibre solitons in the presence of higher order dispersion and birefringence C. R. Menyuk and Ping-Kong A. Wai; 10. Dark optical solitons A. M. Weiner; 11. Soliton Raman effects J. R. Taylor; Bibliography; Index.
Huai-Dong CAO
2006-01-01
Ricci solitons are natural generalizations of Einstein metrics on one hand, and are special solutions of the Ricci flow of Hamilton on the other hand. In this paper we survey some of the recent developments on Ricci solitons and the role they play in the singularity study of the Ricci flow.
Wang, Pan [State Key Laboratory of Information Photonics and Optical Communications, Beijing University of Posts and Telecommunications, Beijing 100876 (China); School of Science, Beijing University of Posts and Telecommunications, P.O. Box 122, Beijing 100876 (China); Tian, Bo, E-mail: tian.bupt@yahoo.com.cn [State Key Laboratory of Information Photonics and Optical Communications, Beijing University of Posts and Telecommunications, Beijing 100876 (China); School of Science, Beijing University of Posts and Telecommunications, P.O. Box 122, Beijing 100876 (China); Jiang, Yan; Wang, Yu-Feng [State Key Laboratory of Information Photonics and Optical Communications, Beijing University of Posts and Telecommunications, Beijing 100876 (China); School of Science, Beijing University of Posts and Telecommunications, P.O. Box 122, Beijing 100876 (China)
2013-02-15
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.
Ankiewicz, Adrian
2016-07-01
Analysis of short-pulse propagation in positive dispersion media, e.g., in optical fibers and in shallow water, requires assorted high-order derivative terms. We present an infinite-order "dark" hierarchy of equations, starting from the basic defocusing nonlinear Schrödinger equation. We present generalized soliton solutions, plane-wave solutions, and periodic solutions of all orders. We find that "even"-order equations in the set affect phase and "stretching factors" in the solutions, while "odd"-order equations affect the velocities. Hence odd-order equation solutions can be real functions, while even-order equation solutions are complex. There are various applications in optics and water waves.
Accessible solitons of fractional dimension
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.
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.
Trogdon, Thomas; Deconinck, Bernard
2014-01-01
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.
Deceleration of the small solitons in the soliton lattice: KdV-type framework
Shurgalina, Ekaterina; Gorshkov, Konstantin; Talipova, Tatiana; Pelinovsky, Efim
2016-04-01
As it is known the solitary waves (solitons) in the KdV-systems move with speed which exceeds the speed of propagation of long linear waves (sound speed). Due to interaction between them, solitons do not lose their individuality (elastic interaction). Binary interaction of neigborough solitons is the major contribution in the dynamics of soliton gas. Taking into account the integrability of the classic and modified Korteweg-de Vries equations the process of the soliton interaction can be analyzed in the framework of the rigorous analytical two-soliton solutions. Main physical conclusion from this solution is the phase shift which is positive for large solitons and negative for small solitons. This fact influences the average velocity of individual soliton in the soliton lattice or soliton gas. We demonstrate that soliton of relative small amplitude moves in soliton gas in average in opposite (negative) direction, meanwhile a free soliton moves always in the right direction. Approximated analytical theory is created for the soliton motion in the periodic lattice of big solitons of the same amplitudes, and the critical amplitude of the small soliton changed its averaged speed is found. Numerical simulation is conducted for a statistical assembly of solitons with random amplitudes and phases. The application of developed theory to the long surface and internal waves is discussed.
Luo, Xing-Yu; Chen, Yong
2016-08-01
The extended form of modified Kadomtsev—Petviashvili equation with variable-coefficient is investigated in the framework of Painlevé analysis. The Lax pairs are obtained by analysing two Painlevé branches of this equation. Starting with the Lax pair, the N-times Darboux transformation is constructed and the N-soliton solution formula is given, which contains 2n free parameters and two arbitrary functions. Furthermore, with different combinations of the parameters, several types of soliton solutions are calculated from the first order to the third order. The regularity conditions are discussed in order to avoid the singularity of the solutions. Moreover, we construct the generalized Darboux transformation matrix by considering a special limiting process and find a rational-type solution for this equation. Supported by the Global Change Research Program of China under Grant No. 2015CB953904, National Natural Science Foundation of China under Grant Nos. 11275072 and 11435005, Doctoral Program of Higher Education of China under Grant No. 20120076110024, The Network Information Physics Calculation of basic research innovation research group of China under Grant No. 61321064, Shanghai Collaborative Innovation Center of Trustworthy Software for Internet of Things under Grant No. ZF1213, Shanghai Minhang District talents of high level scientific research project
Jia, Shu-Liang; Gao, Yi-Tian; Hu, Lei; Huang, Qian-Min; Hu, Wen-Qiang
2017-02-01
Under investigation in this paper is a (3 + 1)-dimensional Boiti-Leon-Manna-Pempinelli equation in the incompressible fluid. With the aid of the bilinear form, Nth-order soliton-like solutions are obtained via the Pffafian method, rational solutions are derived with the ansätz method and periodic wave solutions are constructed via the Riemann theta function. The analytic solutions obtained via the Pffafian method are similar to the kink solitons, while, the interaction regions with little peaks are different from those of the usual kink solitons. The rational solutions which have one upper lump and one down deep hole are the bright-dark solitary wave solutions. For the rational solutions which combine the kink solitary wave with breather-like wave, asymptotic behaviors show that the breather-like wave disappears with the evolution of t. Relations between the one-soliton solutions and one-periodic wave solutions are analysed, which exhibit the asymptotic behaviors of the periodic waves.
YAN ZhenYa
2002-01-01
Searching for special solitary wave solutions with compact support is of important significance in soliton theory. In this paper, to understand the role of nonlinear dispersion in pattern formation, a family of the regularized longwave Boussincsq equations with fully nonlinear dispersion (simply called R(m, n) equations), utt + a( un )xx + b(um )xxtt = 0(a, b const.), is studied. New solitary wave solutions with compact support of R(m, n) equations are found. In addition we find another compacton solutions of the two special cases, R(2, 2) equation and R(3, 3) equation. It is found that the nonlinear dispersion term in a nonlinear evolution equation is not a necessary condition of that it possesses compacton solutions.
Oscillating solitons in nonlinear optics
Lin Xiao-Gang; Liu Wen-Jun; Lei Ming
2016-03-01
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 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.
Quadratic solitons as nonlocal solitons
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...
MA Song-Hua; JIANG Yong-Qing; FANG Jian-Ping
2008-01-01
With the help of the conditional similarity reduction method, some new exact solutions of the (2+1)-dimensional modified dispersive water-wave system (MDWW) are obtained. Based on the derived solution, we investigate the evolution of solitons in the background waves.
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.
Gravitating $\\sigma$ Model Solitons
Kim, Yoonbai; Moon, Sei-Hoon
1998-01-01
We study axially symmetric static solitons of O(3) nonlinear $\\sigma$ model coupled to (2+1)-dimensional anti-de Sitter gravity. The obtained solutions are not self-dual under static metric. The usual regular topological lump solution cannot form a black hole even though the scale of symmetry breaking is increased. There exist nontopological solitons of half integral winding in a given model, and the corresponding spacetimes involve charged Ba$\\tilde n$ados-Teitelboim-Zanelli black holes with...
Carbone, Francesco; El, Gennady
2015-01-01
We undertake a detailed comparison of the results of direct numerical simulations of the integrable soliton gas dynamics with the analytical predictions inferred from the exact solutions of the relevant kinetic equation for solitons. We use the KdV soliton gas as a simplest analytically accessible model yielding major insight into the general properties of soliton gases in integrable systems. Two model problems are considered: (i) the propagation of a `trial' soliton through a one-component `cold' soliton gas consisting of randomly distributed solitons of approximately the same amplitude; and (ii) collision of two cold soliton gases of different amplitudes (soliton gas shock tube problem) leading to the formation of an incoherend dispersive shock wave. In both cases excellent agreement is observed between the analytical predictions of the soliton gas kinetics and the direct numerical simulations. Our results confirm relevance of the kinetic equation for solitons as a quantitatively accurate model for macrosco...
WEN Xiao-Yong; MENG Xiang-Hua
2013-01-01
In this paper,the (2+1)-dimensional generalization of shallow water wave equation,which may be used to describe the propagation of ocean waves,is analytically investigated.With the aid of symbolic computation,we prove that the (2+1)-dimensional generalization of shallow water wave equation possesses the Painlevé property under a certain condition,and its Lax pair is constructed by applying the singular manifold method.Based on the obtained Lax representation,the Darboux transformation (DT) is constructed.The first iterated solution,second iterated solution and a special N-soliton solution with an arbitrary function are derived with the resulting DT.Relevant properties are graphically illustrated,which might be helpful to understanding the propagation processes for ocean waves in shallow water.
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.
Xia, Baoqiang; Zhou, Ruguang; Qiao, Zhijun
2016-10-01
In this paper, we propose a new approach to calculate multi-soliton solutions of Camassa-Holm (CH) equation and modified Camassa-Holm (MCH) equation with the aid of Darboux transformation (DT). The new approach simplifies the approach presented by Li and Zhang [Proc. R. Soc. London, Ser. A 460, 2617-2627 (2004)]. We first map the CH and MCH equation to a negative order KdV (NKdV) equation by a reciprocal transformation. Then we proceed to apply the DT to solve the NKdV equation in the usual way. Finally we invert the reciprocal transformation to recover the solutions of the CH equation and MCH equation.
Multidimensional Localized Solitons
Boiti, M; Martina, L; Boiti, Marco
1993-01-01
Abstract: Recently it has been discovered that some nonlinear evolution equations in 2+1 dimensions, which are integrable by the use of the Spectral Transform, admit localized (in the space) soliton solutions. This article briefly reviews some of the main results obtained in the last five years thanks to the renewed interest in soliton theory due to this discovery. The theoretical tools needed to understand the unexpected richness of behaviour of multidimensional localized solitons during their mutual scattering are furnished. Analogies and especially discrepancies with the unidimensional case are stressed.
Li, Li-Li; Tian, Bo; Zhang, Chun-Yi; Zhang, Hai-Qiang; Li, Juan; Xu, Tao
In this paper, a nonisospectral and variable-coefficient Korteweg-de Vries equation is investigated based on the ideas of the variable-coefficient balancing-act method and Hirota method. Via symbolic computation, we obtain the analytic N-soliton solutions, variable-coefficient bilinear form, auto-Bäcklund transformations (in both the bilinear form and Lax pair form), Lax pair and nonlinear superposition formula for such an equation in explicit form. Moreover, some figures are plotted to analyze the effects of the variable coefficients on the stabilities and propagation characteristics of the solitonic waves.
Soliton structure dynamics in inhomogeneous media
Guerrero, L E; González, J A
1998-01-01
We show that soliton interaction with finite-width inhomogeneities can activate a great number of soliton internal modes. We obtain the exact stationary soliton solution in the presence of inhomogeneities and solve exactly the stability problem. We present a Karhunen-Loeve analysis of the soliton structure dynamics as a time-dependent force pumps energy into the traslational mode of the kink. We show the importance of the internal modes of the soliton as they can generate shape chaos for the soliton as well as cases in which the first shape mode leads the dynamics.
Geometric solitons of Hamiltonian flows on manifolds
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.
Formation of quasiparallel Alfven solitons
Hamilton, R. L.; Kennel, C. F.; Mjolhus, E.
1992-01-01
The formation of quasi-parallel Alfven solitons is investigated through the inverse scattering transformation (IST) for the derivative nonlinear Schroedinger (DNLS) equation. The DNLS has a rich complement of soliton solutions consisting of a two-parameter soliton family and a one-parameter bright/dark soliton family. In this paper, the physical roles and origins of these soliton families are inferred through an analytic study of the scattering data generated by the IST for a set of initial profiles. The DNLS equation has as limiting forms the nonlinear Schroedinger (NLS), Korteweg-de-Vries (KdV) and modified Korteweg-de-Vries (MKdV) equations. Each of these limits is briefly reviewed in the physical context of quasi-parallel Alfven waves. The existence of these limiting forms serves as a natural framework for discussing the formation of Alfven solitons.
Vasileva, D.
2014-11-01
We investigate numerically the time evolution and stability of some known 1D soliton solutions of Boussinesq paradigm equation in 1D and in a 2D setting. A moving frame coordinate system helps us to keep the structures in the center of the computational domain, where the grid is much finer. The numerical experiments show that the stable 1D solutions preserve themselves for very large times. The corresponding solutions of the 2D problem for the same parameters and in narrow in the y-direction domains also preserve their shape for very large times. But the solutions of the 2D problem in wide in the y-direction domains seem to be not stable - the waves preserve their shape in relatively long intervals of time (depending on the parameters), but after that the waves lose their constant profile in the y-direction. The number of the maxima, which appear in the y-direction, strongly depends on the size of the domain in this direction, as well as on the problem's parameters.
Solitons: mathematical methods for physicists
Eilenberger, G.
1981-01-01
The book is a self-contained introduction to the theory of solitons. The Korteweg-de Vries equation is investigated and the inverse scattering transformation is treated in detail. Techniques are applied to the Toda lattice and solutions of the sine-Gordon equation. An introduction to the thermodynamics of soliton systems is given. (KAW)
Solitons in spiraling Vogel lattices
Kartashov, Yaroslav V; Torner, Lluis
2012-01-01
We address light propagation in Vogel optical lattices and show that such lattices support a variety of stable soliton solutions in both self-focusing and self-defocusing media, whose propagation constants belong to domains resembling gaps in the spectrum of a truly periodic lattice. The azimuthally-rich structure of Vogel lattices allows generation of spiraling soliton motion.
Caserta, A; Salusti, E
2016-01-01
In this paper we propose the application of a new model of transients of pore pressure p and solute density \\r{ho} in geologic porous media. This model is rooted in the non-linear waves theory, the focus of which is advection and effect of large pressure jumps on strain (due to large p in a non-linear version of the Hooke law). It strictly relates p and \\r{ho} 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 non-linear Burgers solitons. We therefore propose that the actual transport process in porous rocks for large signals is not the linear diffusion, but could be governed by solitons. A test of an eventual presence of solitons in a rock is here proposed, and then applied to Pierre Shale, Bearpaw Shale, Boom Clay and Oznam-Mugu silt and clay. A quick analysis showing the presence of solitons for nuclear waste disposal and salty water intrusions is also analyzed. Finally, in a kind of "theoretical exp...
ABDUL-MAJID WAZWAZ
2016-11-01
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 solutions for each developed breaking soliton equation. We also develop generalized dispersion relations for the typical breaking soliton equations and the generalized negative-order breaking soliton equations. The results provide useful information on the dynamics of the relevant nonlinear negative-order equations.
Gravitating $\\sigma$ Model Solitons
Kim, Y; Kim, Yoonbai; Moon, Sei-Hoon
1998-01-01
We study axially symmetric static solitons of O(3) nonlinear $\\sigma$ model coupled to (2+1)-dimensional anti-de Sitter gravity. The obtained solutions are not self-dual under static metric. The usual regular topological lump solution cannot form a black hole even though the scale of symmetry breaking is increased. There exist nontopological solitons of half integral winding in a given model, and the corresponding spacetimes involve charged Ba$\\tilde n$ados-Teitelboim-Zanelli black holes without non-Abelian scalar hair.
Soliton interactions of integrable models
Ruan Hangyu E-mail: hyruan@mail.nbip.net; Chen Yixin
2003-08-01
The solution of integrable (n+1)-dimensional KdV system in bilinear form yields a dromion solution that is localized in all directions. The interactions between two dromions are studied both in analytical and in numerical for three (n+1)-dimensional KdV-type equations (n=1, 2, 3). The same interactive properties between two dromions (solitons) are revealed for these models. The interactions between two dromions (solitons) may be elastic or inelastic for different form of solutions.
Soliton interactions of integrable models
Ruan Hang Yu
2003-01-01
The solution of integrable (n+1)-dimensional KdV system in bilinear form yields a dromion solution that is localized in all directions. The interactions between two dromions are studied both in analytical and in numerical for three (n+1)-dimensional KdV-type equations (n=1, 2, 3). The same interactive properties between two dromions (solitons) are revealed for these models. The interactions between two dromions (solitons) may be elastic or inelastic for different form of solutions.
mKdV和mBBM方程的新型孤子解%New type soliton solutions to mKdV and mBBM equations
刘煜; 刘伟庆; 吕卫东
2012-01-01
Peakon solution and compacton solution are new type soliton solutions to nonlinear wave equations. In this paper, we researched two nonlinear wave equations- modified Korteweg-de Vries (mKdV) equation and modified Benjamin-Bona-Mahbny( mBBM) equation, respectively, and obtained three kinds of new type soliton solutions; peakon solutions, double-peak soliton solutions and peaked compacton solution. These results further enriched the patterns of explicit and exact solutions to mKdV and mBBM equations. The graphs of these solutions were given through numerical simulation, one of which was a double-peak solitary wave. One of three ansatz solutions proposed could also be used in many other nonlinear wave equations such as Klein-Gordon equation, φ4equation, Sine-Gordon equation and Landau-Ginzburg-Higgs equation.%尖峰孤子解和紧孤子解是非线性方程的新型孤子解.利用相关文献提出的方法分别研究修正的KdV方程(mKdV)和修正的BBM方程(mBBM),得到3种形式的孤子解:尖峰孤子解、双峰孤子解和尖峰紧孤子解.通过数值模拟得到解的图像,其中之一为双峰形的孤立波.这些结果进一步丰富了这2个非线性波方程的精确解的形式和内容.该文提出的3个拟解之一还可以用于其他多个非线性波方程,如:Klein-Gordon方程、φ4方程、Sine-Gordon方程和Landau -Ginzburg- Higgs方程.
Sabry, R.
An improved homogeneous balance (IHB) method is introduced. On using the IHB method, a new auto-Bäcklund transformation and multi-solitonic solutions were obtained for a generalized variable-coefficient Burgers equation. The obtained solitary waves were found to propagate with a variable propagating speed which depends on the coefficients of the studied model. Also, fusion of two single solitary waves into a one-resonant solitary wave is pointed out.
Solitons in generalized Galileon theories
Carrillo González, Mariana; Masoumi, Ali; Solomon, Adam R.; Trodden, Mark
2016-12-01
We consider the existence and stability of solitons in generalized Galileons, scalar-field theories with higher-derivative interactions but second-order equations of motion. It has previously been proven that no stable, static solitons exist in a single Galileon theory using an argument invoking the existence of zero modes for the perturbations. Here we analyze the applicability of this argument to generalized Galileons and discuss how this may be avoided by having potential terms in the energy functional for the perturbations or by including time dependence. Given the presence of potential terms in the Lagrangian for the perturbations, we find that stable, static solitons are not ruled out in conformal and (anti-)de Sitter Galileons. For the case of Dirac-Born-Infeld and conformal Galileons, we find that solitonic solutions moving at the speed of light exist, the former being stable and the latter unstable if the background soliton satisfies a certain condition.
Solitons in generalized galileon theories
Carrillo-Gonzalez, Mariana; Solomon, Adam R; Trodden, Mark
2016-01-01
We consider the existence and stability of solitons in generalized galileons, scalar field theories with higher-derivative interactions but second-order equations of motion. It has previously been proven that no stable, static solitons exist in a single galileon theory using an argument invoking the existence of zero modes for the perturbations. Here we analyze the applicability of this argument to generalized galileons and discuss how this may be avoided by having potential terms in the energy functional for the perturbations, or by including time dependence. Given the presence of potential terms in the Lagrangian for the perturbations, we find that stable, static solitons are not ruled out in conformal and (A)dS galileons. For the case of DBI and conformal galileons, we find that solitonic solutions moving at the speed of light exist, the former being stable and the latter unstable if the background soliton satisfies a certain condition.
New Soliton Solutions of Chaffee-Infante Equations Using the Exp-Function Method
Sakthivel, Rathinasamy; Chun, Changbum
2010-03-01
In this paper, the exp-function method is applied by using symbolic computation to construct a variety of new generalized solitonary solutions for the Chaffee-Infante equation with distinct physical structures. The results reveal that the exp-function method is suited for finding travelling wave solutions of nonlinear partial differential equations arising in mathematical physics
Exact bright and dark spatial soliton solutions in saturable nonlinear media
Calvo, Gabriel F. [Departamento de Matematicas, E.T.S. de Ingenieros Industriales, Instituto de Matematica Aplicada a la Ciencia y la Ingenieria (IMACI), E.T.S.I. Industriales, Avda. Camilo Jose Cela, 3, Universidad de Castilla-La Mancha, 13071 Ciudad Real (Spain); Belmonte-Beitia, Juan [Departamento de Matematicas, E.T.S. de Ingenieros Industriales, Instituto de Matematica Aplicada a la Ciencia y la Ingenieria (IMACI), E.T.S.I. Industriales, Avda. Camilo Jose Cela, 3, Universidad de Castilla-La Mancha, 13071 Ciudad Real (Spain)], E-mail: Juan.Belmonte@uclm.es; Perez-Garcia, Victor M. [Departamento de Matematicas, E.T.S. de Ingenieros Industriales, Instituto de Matematica Aplicada a la Ciencia y la Ingenieria (IMACI), E.T.S.I. Industriales, Avda. Camilo Jose Cela, 3, Universidad de Castilla-La Mancha, 13071 Ciudad Real (Spain)
2009-08-30
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.
Lienard Equation and Exact Solutions for Some Soliton-Producing Nonlinear Equations
ZHANG Wei-Guo; CHANG Qian-Shun; ZHANG Qi-Ren
2004-01-01
In this paper, we first consider exact solutions for Lienard equation with nonlinear terms of any order. Then,explicit exact bell and kink profile solitary-wave solutions for many nonlinear evolution equations are obtained by means of results of the Lienard equation and proper deductions, which transform original partial differential equations into the Lienard one. These nonlinear equations include compound KdV, compound KdV-Burgers, generalized Boussinesq,generalized KP and Ginzburg-Landau equation. Some new solitary-wave solutions are found.
Darboux Transformations and Soliton Solutions for Classical Boussinesq-Burgers Equation
XU Rui
2008-01-01
Two basic Darboux transformations of a spectral problem associated with a classical Boussinesq-Burgers equation are presented in this letter.They are used to generate new solutions of the classical Boussinesq-Burgers equation.
张解放; 刘宇陆
2003-01-01
The truncated expansion method for finding explicit and exact soliton- like solution of variable coefficient nonlinear evolution equation was described. The crucial idea of the method was first the assumption that coefficients of the truncated expansion formal solution are functions of time satisfying a set of algebraic equations, and then a set of ordinary different equations of undetermined functions that can be easily integrated were obtained. The simplicity and effectiveness of the method by application to a general variable coefficient KdV-MKdV equation with three arbitrary functions of time is illustrated.
B-spline soliton solution of the fifth order KdV type equations
Zahra, W. K.; Ouf, W. A.; El-Azab, M. S.
2013-10-01
In this paper, we develop a numerical solution based on sextic B-spline collocation method for solving the generalized fifth-order nonlinear evolution equations. Applying Von-Neumann stability analysis, the proposed technique is shown to be unconditionally stable. The accuracy of the presented method is demonstrated by a test problem. The numerical results are found to be in good agreement with the exact solution.
Generalized sine-Gordon solitons
Santos, C dos [Centro de Fisica e Departamento de Fisica e Astronomia, Faculdade de Ciencias da Universidade do Porto, 4169-007 Porto (Portugal); Rubiera-Garcia, D, E-mail: cssilva@fc.up.pt, E-mail: rubieradiego@gmail.com [Departamento de Fisica, Universidad de Oviedo, Avenida Calvo Sotelo 18, 33007 Oviedo, Asturias (Spain)
2011-10-21
In this paper, we construct analytical self-dual soliton solutions in (1+1) dimensions for two families of models which can be seen as generalizations of the sine-Gordon system but where the kinetic term is non-canonical. For that purpose we use a projection method applied to the sine-Gordon soliton. We focus our attention on the wall and lump-like soliton solutions of these k-field models. These solutions and their potentials reduce to those of the Klein-Gordon kink and the standard lump for the case of a canonical kinetic term. As we increase the nonlinearity on the kinetic term the corresponding potentials get modified and the nature of the soliton may change, in particular, undergoing a topology modification. The procedure constructed here is shown to be a sort of generalization of the deformation method for a specific class of k-field models. (paper)
Conservation Laws and Soliton Solutions for Generalized Seventh Order KdV Equation
YAO Ruo-Xia; XU Gui-Qiong; LI Zhi-Bin
2004-01-01
With the assistance of the symbolic computation system Maple,rich higher order polynomial-type conservation laws and a sixth order t/x-dependent conservation law are constructed for a generalized seventh order nonlinear evolution equation by using a direct algebraic method.From the compatibility conditions that guaranteeing the existence of conserved densities,an integrable unnamed seventh order KdV-type equation is found.By introducing some nonlinear transformations,the one-,two-,and three-solition solutions as well as the solitary wave solutions are obtained.
Topological and non-topological soliton solutions to some time-fractional differential equations
M Mirzazadeh
2015-07-01
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 nonlinear fractional Klein–Gordon equation and generalized Hirota–Satsuma coupled KdV system. These equations have been widely applied in many branches of nonlinear sciences such as nonlinear optics, plasma physics, superconductivity and quantum mechanics. So, finding exact solutions of such equations are very helpful in the theoretical and numerical studies.
Soliton solutions of the generalized sinh-Gordon equation by the binary (′/)-expansion method
A Neirameh
2015-10-01
The aim of this paper is to extend the applications of (′/)-expansion method to solve a generalized sinh-Gordon equation. In fact, the binary (′/)-expansion method is introduced for finding different new exact solutions. It is shown that this method is a powerful mathematical tool for solving nonlinear evolution equations with time-dependent coefficients in mathematical physics.
Solitons and periodic solutions to a couple of fractional nonlinear evolution equations
M Mirzazadeh; M Eslami; Anjan Biswas
2014-03-01
This paper studies a couple of fractional nonlinear evolution equations using first integral method. These evolution equations are foam drainage equation and Klein–Gordon equation (KGE), the latter of which is considered in (2 + 1) dimensions. For the fractional evolution, the Jumarie’s modified Riemann–Liouville derivative is considered. Exact solutions to these equations are obtained.
Perturbative Painlevé Analysis of General KdV System and Its Exact Soliton Solutions
LIN Ji; YE Li-Jun; LI Hua-Mei
2005-01-01
Using the standard Painlevé analysis and the perturbative method, the Painlevé test for the logarithmic branch is investigated. Nine arbitrary functions are obtained and the Backlund transformation of the logarithmic branch is given. Using the new type Backlund transformation, many exact solutions are obtained.
Soliton solutions for a quasilinear Schrödinger equation via Morse theory
Duchao Liu; Peihao Zhao
2015-08-01
In this paper, Morse theory is used to show the existence of nontrivial weak solutions to a class of quasilinear Schrödinger equation of the form $$- u - \\frac{p}{2^{p-1}} u _p (u^2) = f(x, u)$$ in a bounded smooth domain $ \\subset \\mathbb{R}^N$ with Dirichlet boundary condition.
Lie symmetry analysis and soliton solutions of time-fractional $K(m, n)$ equation
G W WANG; M S HASHEMI
2017-01-01
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 are extracted by means of a transformation.
Solitons in Bose–Einstein condensates
Radha Balakrishnan; Indubala I Satija
2011-11-01
The Gross–Pitaevskii equation (GPE) describing the evolution of the Bose–Einstein condensate (BEC) order parameter for weakly interacting bosons supports dark solitons for repulsive interactions and bright solitons for attractive interactions. After a brief introduction to BEC and a general review of GPE solitons, we present our results on solitons that arise in the BEC of hard-core bosons, which is a system with strongly repulsive interactions. For a given background density, this system is found to support both a dark soliton and an antidark soliton (i.e., a bright soliton on a pedestal) for the density proﬁle. When the background has more (less) holes than particles, the dark (antidark) soliton solution dies down as its velocity approaches the sound velocity of the system, while the antidark (dark) soliton persists all the way up to the sound velocity. This persistence is in contrast to the behaviour of the GPE dark soliton, which dies down at the Bogoliubov sound velocity. The energy–momentum dispersion relation for the solitons is shown to be similar to the exact quantum low-lying excitation spectrum found by Lieb for bosons with a delta-function interaction.
Baxter, J Erik
2015-01-01
We investigate the stability of spherically symmetric, purely magnetic, soliton and black hole solutions of four-dimensional ${\\mathfrak {su}}(N)$ Einstein-Yang-Mills theory with a negative cosmological constant $\\Lambda $. These solutions are described by $N-1$ magnetic gauge field functions $\\omega _{j}$. We consider linear, spherically symmetric, perturbations of these solutions. The perturbations decouple into two sectors, known as the sphaleronic and gravitational sectors. For any $N$, there are no instabilities in the sphaleronic sector if all the magnetic gauge field functions $\\omega _{j}$ have no zeros, and satisfy a set of $N-1$ inequalities. In the gravitational sector, we are able to prove that there are solutions which have no instabilities in a neighbourhood of stable embedded ${\\mathfrak {su}}(2)$ solutions, provided the magnitude of the cosmological constant $\\left| \\Lambda \\right| $ is sufficiently large.
Soliton solutions in two-dimensional Lorentz-violating higher derivative scalar theory
Passos, E; Brito, F A; Menezes, R; Mota-Silva, J C; Santos, J R L
2016-01-01
This paper shows a new approach to obtain analytical topological defects for a 2D Myers-Pospelov Lagrangian for two scalar fields. Such a Lagrangian presents higher-order kinetic terms, which lead us to equations of motion which are non-trivial to be integrated. Here we describe three possible scenarios for the equations of motion, named by time-like, space-like and light-like respectively. We started our investigation with a kink-like travelling wave Ansatz for the free theory, which led us to constraints for the dispersion relations of each scenario. We also introduced a method to obtain analytical solution for the general theory in the three mentioned scenarios. We exemplified the method and discussed the behavior of the defects solutions.
Vargas, Edgar Villagran; Hustert, Reinhold; Gumrich, Peter; Jackson, Andrew D; Heimburg, Thomas
2010-01-01
Close to melting transitions it is possible to propagate solitary electromechanical pulses which reflect many of the experimental features of the nerve pulse including mechanical dislocations and reversible heat production. Here we show that one also obtains the possibility of periodic pulse generation when the boundary condition for the nerve is the conservation of the overall length of the nerve. This condition generates an undershoot beneath the baseline (`hyperpolarization') and a `refractory period', i.e., a minimum distance between pulses. In this paper, we outline the theory for periodic solutions to the wave equation and compare these results to action potentials from the femoral nerve of the locust (locusta migratoria). In particular, we describe the frequently occurring minimum-distance doublet pulses seen in these neurons and compare them to the periodic pulse solutions.
Fission and Fusion of Solitons for the (1+1)-Dimensional Kupershmidt Equation
YING Jin-Ping
2001-01-01
By means of the heat conduction equation and the standard truncated Painlevé expansion, the (1+1) dimensional Kupershmidt equation is solved. Some significant exact multi-soliton solutions are given. Especially; for the interaction of the multi-solitons of the Kupershmidt equation, we find that a single (resonant) kink or bell soliton may be fissioned to several kink or bell solitons. Inversely, several kink or bell solitons may also be fused to one kink or bell soliton.
Two-soliton interaction as an elementary act of soliton turbulence in integrable systems
Pelinovsky, E.N. [Department of Information Systems, National Research University – Higher School of Economics, Nizhny Novgorod (Russian Federation); Department of Nonlinear Geophysical Processes, Institute of Applied Physics, Russian Academy of Sciences, Nizhny Novgorod (Russian Federation); Shurgalina, E.G.; Sergeeva, A.V.; Talipova, T.G. [Department of Nonlinear Geophysical Processes, Institute of Applied Physics, Russian Academy of Sciences, Nizhny Novgorod (Russian Federation); Department of Applied Mathematics, Nizhny Novgorod State Technical University, Nizhny Novgorod (Russian Federation); El, G.A., E-mail: g.el@lboro.ac.uk [Department of Mathematical Sciences, Loughborough University (United Kingdom); Grimshaw, R.H.J. [Department of Mathematical Sciences, Loughborough University (United Kingdom)
2013-01-03
Two-soliton interactions play a definitive role in the formation of the structure of soliton turbulence in integrable systems. To quantify the contribution of these interactions to the dynamical and statistical characteristics of the nonlinear wave field of soliton turbulence we study properties of the spatial moments of the two-soliton solution of the Korteweg–de Vries (KdV) equation. While the first two moments are integrals of the KdV evolution, the 3rd and 4th moments undergo significant variations in the dominant interaction region, which could have strong effect on the values of the skewness and kurtosis in soliton turbulence.
Complex solitons with real energies
Cen, Julia; Fring, Andreas
2016-09-01
Using Hirota’s direct method and Bäcklund transformations we construct explicit complex one and two-soliton solutions to the complex Korteweg-de Vries (KdV) equation, the complex modified KdV (mKdV) equation and the complex sine-Gordon equation. The one-soliton solutions of trigonometric and elliptic type turn out to be { P }{ T }-symmetric when a constant of integration is chosen to be purely imaginary with one special choice corresponding to solutions recently found by Khare and Saxena. We show that alternatively complex { P }{ T }-symmetric solutions to the KdV equation may also be constructed alternatively from real solutions to the mKdV by means of Miura transformations. The multi-soliton solutions obtained from Hirota’s method break the { P }{ T }-symmetric, whereas those obtained from Bäcklund transformations are { P }{ T }-invariant under certain conditions. Despite the fact that some of the Hamiltonian densities are non-Hermitian, the total energy is found to be positive in all cases, that is irrespective of whether they are { P }{ T }-symmetric or not. The reason is that the symmetry can be restored by suitable shifts in space-time and the fact that any of our N-soliton solutions may be decomposed into N separate { P }{ T }-symmetrizable one-soliton solutions.
Spatial solitons in photonic lattices with large-scale defects
Yang Xiao-Yu; Zheng Jiang-Bo; Dong Liang-Wei
2011-01-01
We address the existence, stability and propagation dynamics of solitons supported by large-scale defects surrounded by the harmonic photonic lattices imprinted in the defocusing saturable nonlinear medium. Several families of soliton solutions, including flat-topped, dipole-like, and multipole-like solitons, can be supported by the defected lattices with different heights of defects. The width of existence domain of solitons is determined solely by the saturable parameter. The existence domains of various types of solitons can be shifted by the variations of defect size, lattice depth and soliton order. Solitons in the model are stable in a wide parameter window, provided that the propagation constant exceeds a critical value, which is in sharp contrast to the case where the soliton trains is supported by periodic lattices imprinted in defocusing saturable nonlinear medium. We also find stable solitons in the semi-infinite gap which rarely occur in the defocusing media.
张解放; 郑春龙; 孟剑平; 方建平
2003-01-01
With the help of variable separation approach, a quite general excitation of a new (2+l)-dimensional long dispersive wave system is derived. The chaotic behaviour, such as chaotic line soliton patterns, chaotic dromion patterns, chaotic-period patterns, and chaotic-chaotic patterns, in some new localized excitations are found by selecting appropriate functions.
Stability of solitons in PT-symmetric couplers
Driben, Rodislav
2011-01-01
Families of analytical solutions are found for symmetric and antisymmetric solitons in the dual-core system with the Kerr nonlinearity and PT-balanced gain and loss. The crucial issue is stability of the solitons. A stability region is obtained in an analytical form, and verified by simulations, for the PT-symmetric solitons. For the antisymmetric ones, the stability border is found in a numerical form. Moving solitons of both types collide elastically. The two soliton species merge into one in the "supersymmetric" case, with equal coefficients of the gain, loss and inter-core coupling. These solitons feature a subexponential instability, which may be suppressed by periodic switching ("management").
Regularized degenerate multi-solitons
Correa, Francisco
2016-01-01
We report complex PT-symmetric multi-soliton solutions to the Korteweg de-Vries equation that asymptotically contain one-soliton solutions, with each of them possessing the same amount of finite real energy. We demonstrate how these solutions originate from degenerate energy solutions of the Schroedinger equation. Technically this is achieved by the application of Darboux-Crum transformations involving Jordan states with suitable regularizing shifts. Alternatively they may be constructed from a limiting process within the context Hirota's direct method or on a nonlinear superposition obtained from multiple Baecklund transformations. The proposed procedure is completely generic and also applicable to other types of nonlinear integrable systems.
Gandzha, I S; Dutykh, D S
2015-01-01
We consider the high-order nonlinear Schr\\"odinger equation derived earlier by Sedletsky [Ukr. J. Phys. 48(1), 82 (2003)] for the first-harmonic envelope of slowly modulated gravity waves on the surface of finite-depth irrotational, inviscid, and incompressible fluid with flat bottom. This equation takes into account the third-order dispersion and cubic nonlinear dispersive terms. We rewrite this equation in dimensionless form featuring only one dimensionless parameter $kh$, where $k$ is the carrier wavenumber and $h$ is the undisturbed fluid depth. We show that one-soliton solutions of the classical nonlinear Schr\\"{o}dinger equation are transformed into quasi-soliton solutions with slowly varying amplitude when the high-order terms are taken into consideration. These quasi-soliton solutions represent the secondary modulations of gravity waves.
Weakly deformed soliton lattices
Dubrovin, B. (Moskovskij Gosudarstvennyj Univ., Moscow (USSR). Dept. of Mechanics and Mathematics)
1990-12-01
In this lecture the author discusses periodic and quasiperiodic solutions of nonlinear evolution equations of phi{sub t}=K (phi, phi{sub x},..., phi{sup (n)}), the so-called soliton lattices. After introducing the theory of integrable systems of hydrodynamic type he discusses their Hamiltonian formalism, i.e. the theory of Poisson brackets of hydrodynamic type. Then he describes the application of algebraic geometry to the effective integration of such equations. (HSI).
ZHANG Jie-Fang; YANG Qin
2005-01-01
@@ We present both the bright and dark solitons of Bose-Einstein condensates with a time-dependent atomic scattering length in an expulsive parabolic potential. As a discussed example, we select the experimental parameter,i.e. the Feshbach-managed nonlinear coefficient reading a(t) = g0 exp(λt), and obtain the results which can be recovered in the literature [Phys. Rev. Lett. 94 (2005) 050402].
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 t...... 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....
Chladni solitons and the onset of the snaking instability for dark solitons in confined superfluids
2014-01-01
Complex solitary waves composed of intersecting vortex lines are predicted in a channeled superfluid. Their shapes in a cylindrical trap include a cross, spoke wheels, and Greek $\\Phi$, and trace the nodal lines of unstable vibration modes of a planar dark soliton in analogy to Chladni's figures of membrane vibrations. The stationary solitary waves extend a family of solutions that include the previously known solitonic vortex and vortex rings. Their bifurcation points from the dark soliton i...
Chladni solitons and the onset of the snaking instability for dark solitons in confined superfluids
Mateo, A. Muñoz; Brand, J.
2014-01-01
Complex solitary waves composed of intersecting vortex lines are predicted in a channeled superfluid. Their shapes in a cylindrical trap include a cross, spoke wheels, and Greek $\\Phi$, and trace the nodal lines of unstable vibration modes of a planar dark soliton in analogy to Chladni's figures of membrane vibrations. The stationary solitary waves extend a family of solutions that include the previously known solitonic vortex and vortex rings. Their bifurcation points from the dark soliton i...
Zhang, Han
2011-01-01
Solitons, as stable localized wave packets that can propagate long distance in dispersive media without changing their shapes, are ubiquitous in nonlinear physical systems. Since the first experimental realization of optical bright solitons in the anomalous dispersion single mode fibers (SMF) by Mollenauer et al. in 1980 and optical dark solitons in the normal dispersion SMFs by P. Emplit et al. in 1987, optical solitons in SMFs had been extensively investigated. In reality a SMF always supports two orthogonal polarization modes. Taking fiber birefringence into account, it was later theoretically predicted that various types of vector solitons, including the bright-bright vector solitons, dark-dark vector solitons and dark-bright vector solitons, could be formed in SMFs. However, except the bright-bright type of vector solitons, other types of vector solitons are so far lack of clear experimental evidence. Optical solitons have been observed not only in the SMFs but also in mode locked fiber lasers. It has be...
Gunasekaran, Sharmila; Kunduri, Hari K
2016-01-01
The domain of outer communication of five-dimensional asymptotically flat stationary spacetimes may possess non-trivial 2-cycles (bubbles). Spacetimes containing such 2-cycles can have non-zero energy, angular momenta, and charge even in the absence of horizons. A mass variation formula has been established for spacetimes containing bubbles and possibly a black hole horizon. This `first law of black hole and soliton mechanics' contains new intensive and extensive quantities associated to each 2-cycle. We consider examples of such spacetimes for which we explicitly calculate these quantities and show how regularity is essential for the formulae relating them to hold. We also derive new explicit expressions for the angular momenta and charge for spacetimes containing solitons purely in terms of fluxes supporting the bubbles.
Gunasekaran, Sharmila; Hussain, Uzair; Kunduri, Hari K.
2016-12-01
The domain of outer communication of five-dimensional asymptotically flat stationary spacetimes may possess nontrivial 2-cycles (bubbles). Spacetimes containing such 2-cycles can have nonzero energy, angular momenta, and charge even in the absence of horizons. A mass variation formula has been established for spacetimes containing bubbles and possibly a black hole horizon. This "first law of black hole and soliton mechanics" contains new intensive and extensive quantities associated with each 2-cycle. We consider examples of such spacetimes for which we explicitly calculate these quantities and show how regularity is essential for the formulas relating them to hold. We also derive new explicit expressions for the angular momenta and charge for spacetimes containing solitons purely in terms of fluxes supporting the bubbles.
M.T. Darvishi; M. Najafi; Kavitha; M. Venkatesh
2012-01-01
The multiple exp-function method is a new approach to obtain multiple wave solutions of nonlinear partial differential equations (NLPDEs). By this method one can obtain multi-soliton solutions of NLPDEs. In this paper, using computer algebra systems, we apply the multiple exp-function method to construct the exact multiple wave solutions of a (2+1)-dimensional Boiti-Leon-Manna-Pempinelli equation. Also, we extend the equation to a (3+1)-dimensional case and obtain some exact solutions for the new equation by applying the multiple exp-function method. By these applications, we obtain single-wave, double-wave and multi-wave solutions for these equations.
Yang, Jin-Wei; Gao, Yi-Tian, E-mail: gaoyt163@163.com; Wang, Qi-Min; Su, Chuan-Qi; Feng, Yu-Jie; Yu, Xin
2016-01-15
In this paper, a fourth-order variable-coefficient nonlinear Schrödinger equation is studied, which might describe a one-dimensional continuum anisotropic Heisenberg ferromagnetic spin chain with the octuple–dipole interaction or an alpha helical protein with higher-order excitations and interactions under continuum approximation. With the aid of auxiliary function, we derive the bilinear forms and corresponding constraints on the variable coefficients. Via the symbolic computation, we obtain the Lax pair, infinitely many conservation laws, one-, two- and three-soliton solutions. We discuss the influence of the variable coefficients on the solitons. With different choices of the variable coefficients, we obtain the parabolic, cubic, and periodic solitons, respectively. We analyse the head-on and overtaking interactions between/among the two and three solitons. Interactions between a bound state and a single soliton are displayed with different choices of variable coefficients. We also derive the quasi-periodic formulae for the three cases of the bound states.
Gravitational two solitons in Levi-Cività spacetime
Igata, Takahisa; Tomizawa, Shinya
2016-09-01
Applying the Pomeransky inverse scattering method to the four-dimensional vacuum Einstein equations and using the Levi-Cività solution as a seed, we construct a two-soliton solution with cylindrical symmetry. In our previous work, we constructed the one-soliton solution with a real pole and showed that the singularities that the Levi-Cività background has on an axis can be removed by the choice of certain special parameters, but it still has unavoidable null singularities, as usual one-solitons do. In this work, we show that for the two-soliton solutions, any singularities can be removed by suitable parameter-setting and such solutions describe the propagation of gravitational wave packets. Moreover, in terms of the two-soliton solutions, we mention a time shift phenomenon, the coalescence and the split of solitons as the nonlinear effect of gravitational waves.
Gravitational two solitons in Levi-Civita spacetime
Igata, Takahisa
2015-01-01
Applying the Pomeransky inverse scattering method to the four-dimensional vacuum Einstein equations and using the Levi-Civita solution as a seed, we construct a two-soliton solution with cylindrical symmetry. In our previous work, we constructed the one-soliton solution with a real pole and showed that the singularities that the Levi-Civita background has on an axis can be removed by the choice of certain special parameters, but it still has unavoidable null singularities, as usual one solitons do. In this work, we show that for the two-soliton solutions, any singularities can be removed by suitable parameter-setting and such solutions describe the propagation of gravitational wave packets. Moreover, in terms of the two-soliton solutions, we mention a time shift phenomenon, the coalescence and the split of solitons as the nonlinear effect of gravitational waves.
Relativistic quasi-solitons and embedded solitons with circular polarization in cold plasmas
Sánchez-Arriaga, G
2016-01-01
The existence of localized electromagnetic structures is discussed in the framework of the 1-dimensional relativistic Maxwell-fluid model for a cold plasma with immobile ions. New partially localized solutions are found with a finite-difference algorithm designed to locate numerically exact solutions of the Maxwell-fluid system. These solutions are called quasi-solitons and consist of a localized electromagnetic wave trapped in a spatially extended electron plasma wave. They are organized in families characterized by the number of nodes $p$ of the vector potential and exist in a continuous range of parameters in the $\\omega-V$ plane, where $V$ is the velocity of propagation and $\\omega$ is the vector potential angular frequency. A parametric study shows that the familiar fully localized relativistic solitons are special members of the families of partially localized quasi-solitons. Soliton solution branches with $p>1$ are therefore parametrically embedded in the continuum of quasi-solitons. On the other hand,...
Kalashnikov, Vladimir L
2010-01-01
The analytical theory of chirped dissipative soliton solutions of nonlinear complex Ginzburg-Landau equation is exposed. Obtained approximate solutions are easily traceable within an extremely broad range of the equation parameters and allow a clear physical interpretation as a representation of the strongly chirped pulses in mode-locked both solid-state and fiber oscillators. Scaling properties of such pulses demonstrate a feasibility of sub-mJ pulse generation in the continuous-wave mode-locking regime directly from an oscillator operating at the MHz repetition rate.
The soliton properties of dipole domains in superlattices
张启义; 田强
2002-01-01
The formation and propagation of dipole domains in superlattices are studied both by the modified discrete driftmodel and by the nonlinear Schrodinger equation. The spatiotemporal distribution of the electric field and electrondensity are presented. The numerical results are compared with the soliton solutions of the nonlinear Schrodingerequation and analysed. It is shown that the numerical solutions agree with the soliton solutions of the nonlinearSchrodinger equation. The dipole electric-field domains in semiconductor superlattices have the properties of solitons.
Xia, Ya-Rong; Xin, Xiang-Peng; Zhang, Shun-Li
2017-01-01
This paper mainly discusses the (2+1)-dimensional modified dispersive water-wave (MDWW) system which will be proved nonlinear self-adjointness. This property is applied to construct conservation laws corresponding to the symmetries of the system. Moreover, via the truncated Painlevé analysis and consistent tanh-function expansion (CTE) method, the soliton-cnoidal periodic wave interaction solutions and corresponding images will be eventually achieved. Supported by National Natural Science Foundation of China under Grant Nos. 11371293, 11505090, the Natural Science Foundation of Shaanxi Province under Grant No. 2014JM2-1009, Research Award Foundation for Outstanding Young Scientists of Shandong Province under Grant No. BS2015SF009 and the Science and Technology Innovation Foundation of Xi’an under Grant No. CYX1531WL41
Cheng, Wenguang; Li, Biao
2016-04-01
The truncated Painlevé method is developed to obtain the nonlocal residual symmetry and the Bäcklund transformation for the (2+1)-dimensional KdV-mKdV equation. The residual symmetry is localised after embedding the (2+1)-dimensional KdV-mKdV equation to an enlarged one. The symmetry group transformation of the enlarged system is computed. Furthermore, the (2+1)-dimensional KdV-mKdV equation is proved to be consistent Riccati expansion (CRE) solvable. The soliton-cnoidal wave interaction solution in terms of the Jacobi elliptic functions and the third type of incomplete elliptic integral is obtained by using the consistent tanh expansion (CTE) method, which is a special form of CRE.
Control of soliton characteristics of the condensate by an arbitrary x-dependent external potential
Yang Ru-Shu; Yao Chun-Mei; Chen Ri-Xin
2009-01-01
This paper presents a family of soliton solutions of the one-dimensional nonlinear Schrodinger equation which describes the dynamics of the dark solitons in Bose-Einstein condensates with an arbitrary x-dependent external potential. The obtained results show that the external potential has an important effect on the dark soliton dynamical characteristics of the condensates. The amplitude,width,and velocity of the output soliton are relative to the source position of the external potential. The smaller the amplitude of the soliton is,the narrower its width is,and the slower the soliton propagates. The collision of two dark solitons is nearly elastic.
Manakov Soliton Pairs in Biased Photovoltaic Photorefractive Crystals
侯春风; 杜春光; 阿不都热苏力; 李师群
2002-01-01
We study, theoretically, incoherently coupled screening-photovoltaic soliton pairs in biased photovoltaic photorefractive crystals. It is shown that when the total intensity of two coupled solitons is much lower than the effective dark irradiance, the coupled soliton equations reduce to the Manakov equations. The dark-dark, bright-bright and dark-bright soliton pair solutions of these Manakov equations are obtained under an appropriate external bias field and a photovoltaic field, and the characteristics of these Manakov soliton pairs are also discussed in detail.
Effect of Soliton Propagation in Fiber Amplifiers
无
2001-01-01
The propagation of optical solitons in fiber amplifiers is discussed by considering a model that includes linear high order dispersion, two-photon absorption, nonlinear high-order dispersion, self-induced Ramam and five-order nonlinear effects. Based on travelling wave method, the solutions of the nonlinear Schrdinger equations, and the influence on soliton propagation as well as high-order effect in the fiber amplifier are discussed in detail. It is found that because of existing five-order nonlinear effect, the solution is not of secant hyperbola type, but shows high gain state of the fiber amplifier which is very favourable to the propagation of solitons.
Multi-indexed Extensions of Soliton Potential and Extended Integer Solitons of KdV Equation
Ho, Choon-Lin
2014-01-01
We discover new infinite set of initial profiles of KdV solitons, which are both exactly solvable for the Schrodinger equation and for the Gel'fand-Levitan-Marchenko equation in the inverse scattering transform method of KdV equation. These new solutions are based on the multi-indexed extensions of the reflectionless soliton potential.
Wilets, Lawrence
1989-01-01
Successful modeling of quantum chromodynamics with a relativistic quark-soliton field theory has been developed over the past decade. As introduced by R Freidberg and T D Lee, the foundation of the model involves the chromodielectric properties of the physical vacuum, which yield absolute color confinement. The model allows for the consistent calculation of the dynamics of hadrons and hadronic reactions. The book summarizes and expands upon the extensive literature on the subject, concentrating on the Friedberg-Lee model and variations thereof. New results and future directions are included. T
Low-amplitude vector screening solitons
Keqing Lu(卢克清); Xiangping Zhu(朱香平); Wei Zhao(赵卫); Yanlong Yang(杨延龙); Jinping Li(李金萍); Yanpeng Zhang(张彦鹏); Junchang Zhang(张君昌)
2004-01-01
We show self-coupled and cross-coupled vector beam evolution equations in the low-amplitude regime for screening solitons,which can exhibit the analytical solutions of bright-bright and dark-dark vector solitons.Our analysis indicates that these self-coupled vector solitons are obtained irrespective of the intensities of the two optical beams,whereas these cross-coupled vector solitons can be established when the intensities of the two optical beams are equal.Relevant examples are provided where the photorefractive crystal is lithium niobate(LiNbO3).The stability properties of these vector solitons have been investigated numerically and it has been found that they are stable.
The Geometrodynamics of Sine-Gordon Solitons
Gegenberg, J
1998-01-01
The relationship between N-soliton solutions to the Euclidean sine-Gordon equation and Lorentzian black holes in Jackiw-Teitelboim dilaton gravity is investigated, with emphasis on the important role played by the dilaton in determining the black hole geometry. We show how an N-soliton solution can be used to construct ``sine-Gordon'' coordinates for a black hole of mass M, and construct the transformation to more standard ``Schwarzchild-like'' coordinates. For N=1 and 2, we find explicit closed form solutions to the dilaton equations of motion in soliton coordinates, and find the relationship between the soliton parameters and the black hole mass. Remarkably, the black hole mass is non-negative for arbitrary soliton parameters. In the one-soliton case the coordinates are shown to cover smoothly a region containing the whole interior of the black hole as well as a finite neighbourhood outside the horizon. A Hamiltonian analysis is performed for slicings that approach the soliton coordinates on the interior, a...
刘煜
2009-01-01
According to the characteristics of peaked soliton solution, the undetermined coefficient method for solving nonlinear wave equations for their peaked soliton solutions is submitted and by means of the method several kinds of peaked soliton solutions are obtained for five nonlinear wave equations: the Camassa-Holm, fifth-order KdV-like, generalized Ostrovsky, combined KdV-mKdV and Klein-Gordon equations. The solutions given in literature about Camassa-Holm equation become the special cases of the solutions in this paper. The graphs of some solutions are given through numerical simulation. The special conditions under which the wave equation will have peaked soliton solution is briefly described. The method used in this paper can also be used for solving many other nonlinear equations.%根据尖峰孤子解的特点,提出了一种待定系数法求非线性波方程尖峰孤子解的思路和方法,并利用该方法求解了5个非线性波方程,即CH(Camassa-Holm)方程、五阶KdV-like方程、广义Ostrovskv方程、组合KdV-mKdV方程和Klein-Gordon方程,比较简便地得到了这些方程的尖峰孤子解.文献中关于CH方程的结果成为本文结果的特例.通过数值模拟给出了部分解的图像.简要说明了非线性波方程存在尖峰孤子解所须满足的特定条件.该方法也适用于求其他非线性波方程的尖峰孤子解.
The kink-soliton and antikink-soliton in quasi-one-dimensional nonlinear monoatomic lattice
XU; Quan; TIAN; Qiang
2005-01-01
The quasi-one-dimensional nonlinear monoatomic lattice is analyzed. The kink-soliton and antikink-soliton are presented. When the interaction of the lattice is strong in the x-direction and weak in the y-direction, the two-dimensional (2D) lattice changes to a quasi-one-dimensional lattice. Taking nearest-neighbor interaction into account, the vibration equation can be transformed into the KPI, KPII and MKP equation. Considering the cubic nonlinear potential of the vibration in the lattice, the kink-soliton solution is presented. Considering the quartic nonlinear potential and the cubic interaction potential, the kink-soliton and antikink-soliton solutions are presented.
Solitons in a chain of PT-invariant dimers
Suchkov, Sergey V; Dmitriev, Sergey V; Kivshar, Yuri S
2011-01-01
Dynamics of a chain of interacting parity-time invariant nonlinear dimers is investigated. A dimer is built as a pair of coupled elements with equal gain and loss. A relation between stationary soliton solutions of the model and solitons of the discrete nonlinear Schrodinger (DNLS) equation is demonstrated. Approximate solutions for solitons whose width is large in comparison to the lattice spacing are derived, using a continuum counterpart of the discrete equations. These solitons are mobile, featuring nearly elastic collisions. Stationary solutions for narrow solitons, which are immobile due to the pinning by the effective Peierls-Nabarro potential, are constructed numerically, starting from the anti-continuum limit. The solitons with the amplitude exceeding a certain critical value suffer an instability leading to blowup, which is a specific feature of the nonlinear PT-symmetric chain, making it dynamically different from DNLS lattices. A qualitative explanation of this feature is proposed. The instability...
M. Falek; LIU Xiao-Ping; M. Merad; LIU Chun-Ping
2008-01-01
In a recent artcle [Commun. Theor. Phys. (Beijing, China) 47 (2007) 270], Cao et al. Gave some nontrivial solutions of a Riccati equation by using symbolic and algebra computation. They took these solutions, which are in the form of q-deformed hyperbolic and triangular functions as new solutions. In this comment, we will show that these solutions are just the special cases of some known solutions of the Riccati equation and thus they are not new solutions.
Regularized degenerate multi-solitons
Correa, Francisco; Fring, Andreas
2016-09-01
We report complex {P}{T} -symmetric multi-soliton solutions to the Korteweg de-Vries equation that asymptotically contain one-soliton solutions, with each of them possessing the same amount of finite real energy. We demonstrate how these solutions originate from degenerate energy solutions of the Schrödinger equation. Technically this is achieved by the application of Darboux-Crum transformations involving Jordan states with suitable regularizing shifts. Alternatively they may be constructed from a limiting process within the context Hirota's direct method or on a nonlinear superposition obtained from multiple Bäcklund transformations. The proposed procedure is completely generic and also applicable to other types of nonlinear integrable systems.
Spherical solitons in ion-beam plasma
Das, G.C.; Ibohanbi Singh, K. (Manipur Univ., Imphal (India). Dept. of Mathematics)
1991-01-01
By using the reductive perturbation technique, the soliton solution of an ion-acoustic wave radially ingoing in a spherically bounded plasma consisting of ions and ion-beams with multiple electron temperatures is obtained. In sequel to the earlier investigations, the solitary waves are studied as usual through the derivation of a modified Korteweg-de Vries (K-dV) equation in different plasma models arising due to the variation of the isothermality of the plasmas. The characteristics of the solitons are finally compared with those of the planar and the cylindrical solitons. (orig.).
Vector Lattice Vortex Solitons
WANG Jian-Dong; YE Fang-Wei; DONG Liang-Wei; LI Yong-Ping
2005-01-01
@@ Two-dimensional vector vortex solitons in harmonic optical lattices are investigated. The stability properties of such solitons are closely connected to the lattice depth Vo. For small Vo, vector vortex solitons with the total zero-angular momentum are more stable than those with the total nonzero-angular momentum, while for large Vo, this case is inversed. If Vo is large enough, both the types of such solitons are stable.
2006-01-29
Jakubowski, and R. Squier, “Collisions of two solitons in an arbitrary number of coupled nonlinear Schrodinger equations ”, Physical Review Letters 90...on Nonlinear Evolution Equations and Wave Phenomena, Athens, Georgia, April 11-14, 2005. 89. D. N. Christodoulides, “ Discrete solitons in...Solitons for signal processing applications: 1. Navigating discrete solitons in two-dimensional nonlinear waveguide array networks: Among
Miki Wadati
2001-11-01
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.
Soliton and kink jams in traffic flow with open boundaries.
Muramatsu, M; Nagatani, T
1999-07-01
Soliton density wave is investigated numerically and analytically in the optimal velocity model (a car-following model) of a one-dimensional traffic flow with open boundaries. Soliton density wave is distinguished from the kink density wave. It is shown that the soliton density wave appears only at the threshold of occurrence of traffic jams. The Korteweg-de Vries (KdV) equation is derived from the optimal velocity model by the use of the nonlinear analysis. It is found that the traffic soliton appears only near the neutral stability line. The soliton solution is analytically obtained from the perturbed KdV equation. It is shown that the soliton solution obtained from the nonlinear analysis is consistent with that of the numerical simulation.
A Mass Formula for EYM Solitons
Corichi, A; Sudarsky, D; Corichi, Alejandro; Nucamendi, Ulises; Sudarsky, Daniel
2001-01-01
The recently introduced Isolated Horizon formalism, together with a simple phenomenological model for colored black holes is used to predict a formula for the ADM mass of the solitons of the EYM system in terms of horizon properties of black holes {\\it for all} values of the horizon area. In this note, this formula is tested numerically --up to a large value of the area-- for spherically symmetric solutions and shown to yield the known masses of the solitons.
Chladni Solitons and the Onset of the Snaking Instability for Dark Solitons in Confined Superfluids
Muñoz Mateo, A.; Brand, J.
2014-12-01
Complex solitary waves composed of intersecting vortex lines are predicted in a channeled superfluid. Their shapes in a cylindrical trap include a cross, spoke wheels, and Greek Φ , and trace the nodal lines of unstable vibration modes of a planar dark soliton in analogy to Chladni's figures of membrane vibrations. The stationary solitary waves extend a family of solutions that include the previously known solitonic vortex and vortex rings. Their bifurcation points from the dark soliton indicating the onset of new unstable modes of the snaking instability are predicted from scale separation for Bose-Einstein condensates (BECs) and superfluid Fermi gases across the BEC-BCS crossover, and confirmed by full numerical calculations. Chladni solitons could be observed in ultracold gas experiments by seeded decay of dark solitons.
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.
Protonic transport through solitons in hydrogen-bonded systems
Kavitha, L.; Jayanthi, S.; Muniyappan, A.; Gopi, D.
2011-09-01
We offer an alternative route for investigating soliton solutions in hydrogen-bonded (HB) chains. We invoke the modified extended tangent hyperbolic function method coupled with symbolic computation to solve the governing equation of motion for proton dynamics. We investigate the dynamics of proton transfer in HB chains through bell-shaped soliton excitations, which trigger the bio-energy transport in most biological systems. This solitonic mechanism of proton transfer could play functional roles in muscular contraction, enzymatic activity and oxidative phosphorylation.
Soliton induced singularities in 2d gravity and their evaporation
Vaz, C; Vaz, Cenalo; Witten, Louis
1995-01-01
Positive energy singularities induced by Sine-Gordon solitons in 1+1 dimensional dilaton gravity with positive and negative cosmological constant are considered. When the cosmological constant is positive, the singularities combine a white hole, a timelike singularity and a black hole joined smoothly near the soliton center. When the cosmological constant is negative, the solutions describe two timelike singularities joined smoothly near the soliton center. We describe these spacetimes and examine their evaporation in the one loop approximation.
Liu Xiao-Bei; Li Biao
2011-01-01
We present three families of soliton solutions to the generalized (3+1)-dimensional nonlinear Schr(o)dinger equation with distributed coefficients. We investigate the dynamics of these solitons in nonlinear optics with some selected parameters.Different shapes of bright solitons,a train of bright solitons and dark solitons are observed.The obtained results may raise the possibilities of relevant experiments and potential applications.
Multicolor Bound Soliton Molecule
Luo, Rui; Lin, Qiang
2015-01-01
We show a new class of bound soliton molecule that exists in a parametrically driven nonlinear optical cavity with appropriate dispersion characteristics. The composed solitons exhibit distinctive colors but coincide in time and share a common phase, bound together via strong inter-soliton four-wave mixing and Cherenkov radiation. The multicolor bound soliton molecule shows intriguing spectral locking characteristics and remarkable capability of spectrum management to tailor soliton frequencies, which may open up a great avenue towards 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
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.
Breathing dissipative solitons in optical microresonators
Lucas, Erwan; Guo, Hairun; Gorodetsky, Michael; Kippenberg, Tobias
2016-01-01
Dissipative solitons are self-localized structures resulting from a double balance between dispersion and nonlinearity as well as dissipation and a driving force. They occur in a wide variety of fields ranging from optics, hydrodynamics to chemistry and biology. Recently, significant interest has focused on their temporal realization in driven optical microresonators, known as dissipative Kerr solitons. They provide access to coherent, chip-scale optical frequency combs, which have already been employed in optical metrology, data communication and spectroscopy. Such Kerr resonator systems can exhibit numerous localized intracavity patterns and provide rich insights into nonlinear dynamics. A particular class of solutions consists of breathing dissipative solitons, representing pulses with oscillating amplitude and duration, for which no comprehensive understanding has been presented to date. Here, we observe and study single and multiple breathing dissipative solitons in two different microresonator platforms...
Soliton concepts and the protein structure
Krokhotin, Andrei; Peng, Xubiao
2011-01-01
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 to identify the modular building blocks of proteins with the dark soliton solution of a generalized discrete nonlinear Schrodinger equation. For this we show 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 identify their possible values in Protein Data Bank. We show that with a collection of 200 sets of parameters, each determining a soliton profile that describes a different short loop, we cover over 90% of all proteins with experimental accuracy. We also present two examples that describe how the loop library can be employed both to model and to analyze the structure of folded proteins.
Vector nematicons: Coupled spatial solitons in nematic liquid crystals
Horikis, Theodoros P.; Frantzeskakis, Dimitrios J.
2016-11-01
Families of soliton pairs, namely vector solitons, are found within the context of a coupled nonlocal nonlinear Schrödinger system of equations, as appropriate for modeling beam propagation in nematic liquid crystals. In the focusing case, bright soliton pairs have been found to exist provided their amplitudes satisfy a specific condition. In our analytical approach, focused on the defocusing regime, we rely on a multiscale expansion methods, which reveals the existence of dark-dark and antidark-antidark solitons, obeying an effective Korteweg-de Vries equation, as well as dark-bright solitons, obeying an effective Mel'nikov system. These pairs are discriminated by the sign of a constant that links all physical parameters of the system to the amplitude of the stable continuous wave solutions, and, much like the focusing case, the solitons' amplitudes are linked, leading to mutual guiding.
3D simulation for solitons used in optical fibers
Vasile, F.; Tebeica, C. M.; Schiopu, P.; Vladescu, M.
2016-12-01
In this paper is described 3D simulation for solitions used in optical fibers. In the scientific works is started from nonlinear propagation equation and the solitons represents its solutions. This paper presents the simulation of the fundamental soliton in 3D together with simulation of the second order soliton in 3D. These simulations help in the study of the optical fibers for long distances and in the interactions between the solitons. This study helps the understanding of the nonlinear propagation equation and for nonlinear waves. These 3D simulations are obtained using MATLAB programming language, and we can observe fundamental difference between the soliton and the second order/higher order soliton and in their evolution.
Numerical stability of solitons waves through splices in optical fibers
de Oliveira, Camila Fogaça; Cirilo, Eliandro Rodrigues; Romeiro, Neyva Maria Lopes; Natti, Érica Regina Takano
2015-01-01
The propagation of soliton waves is simulated through splices in optical fibers, in which fluctuations of dielectric parameters occur. The mathematical modeling of these local fluctuations of dielectric properties of fibers was performed by Gaussian functions. By simulating soliton wave propagation in optical fibers with Gaussian fluctuations in their dielectric properties, it was observed that the perturbed soliton numerical solution presented higher sensitivity to fluctuations in the dielectric parameter $\\beta$, a measure of the intensity of nonlinearity in the fiber. In order to verify whether the fluctuations of $\\beta$ parameter in the splices of the optical fiber generate unstable solitons, the propagation of a soliton wave, subject to this perturbation, was simulated for large time intervals. Considering various geometric configurations and intensities of the fluctuations of parameter $\\beta$, it was found that the perturbed soliton wave stabilizes, i.e., the amplitude of the wave oscillations decreas...
Adiabatic theory of solitons fed by dispersive waves
Pickartz, Sabrina; Bandelow, Uwe; Amiranashvili, Shalva
2016-09-01
We consider scattering of low-amplitude dispersive waves at an intense optical soliton which constitutes a nonlinear perturbation of the refractive index. Specifically, we consider a single-mode optical fiber and a group velocity matched pair: an optical soliton and a nearly perfectly reflected dispersive wave, a fiber-optical analog of the event horizon. By combining (i) an adiabatic approach that is used in soliton perturbation theory and (ii) scattering theory from quantum mechanics, we give a quantitative account of the evolution of all soliton parameters. In particular, we quantify the increase in the soliton peak power that may result in the spontaneous appearance of an extremely large, so-called champion soliton. The presented adiabatic theory agrees well with the numerical solutions of the pulse propagation equation. Moreover, we predict the full frequency band of the scattered dispersive waves and explain an emerging caustic structure in the space-time domain.
Coupled spatial multi-mode solitons in microcavity wires
Slavcheva, G; Pimenov, A
2016-01-01
A modal expansion approach is developed and employed to investigate and elucidate the nonlinear mechanism behind the multistability and formation of coupled multi-mode polariton solitons in microcavity wires. With pump switched on and realistic dissipation parameters, truncating the expansion up to the second-order wire mode, our model predicts two distinct coupled soliton branches: stable and ustable. Modulational stability of the homogeneous solution and soliton branches stability are studied. Our simplified 1D model is in remarkably good agreement with the full 2D mean-field Gross-Pitaevskii model, reproducing correctly the soliton existence domain upon variation of pump amplitude and the onset of multistability.
Radiation by solitons due to higher-order dispersion
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...
Discrete solitons in graphene metamaterials
Bludov, Yuliy V.; Smirnova, Daria A.; Kivshar, Yuri S.; Peres, N. M. R.; Vasilevskiy, Mikhail
2014-01-01
We study nonlinear properties of multilayer metamaterials created by graphene sheets separated by dielectric layers. We demonstrate that such structures can support localized nonlinear modes described by the discrete nonlinear Schr\\"{o}dinger equation and that its solutions are associated with stable discrete plasmon solitons. We also analyze the nonlinear surface modes in truncated graphene metamaterials being a nonlinear analog of surface Tamm states. Fundação para a Ciência e a Tecnolog...
Discrete solitons in graphene metamaterials
Bludov, Yu. V.; Smirnova, D. A.; Kivshar, Yu. S.; Peres, N. M. R.; Vasilevskiy, M. I.
2015-01-01
We study nonlinear properties of multilayer metamaterials created by graphene sheets separated by dielectric layers. We demonstrate that such structures can support localized nonlinear modes described by the discrete nonlinear Schrödinger equation and that its solutions are associated with stable discrete plasmon solitons. We also analyze the nonlinear surface modes in truncated graphene metamaterials being a nonlinear analog of surface Tamm states.
HOU Chunfeng; LI Yan; YUAN Baohong; SUN Xiudong
2000-01-01
The low-amplitude spatial solitons in biased photovoltaic photorefractive crystals are investigated theoretically. The analytical solutions for both the bright and the dark low-amplitude screening-photovoltaic spatial solitons in photorefractive crystals are obtained. The expressions for the width of these solitons are given. The explicit expressions for the spatial deflection and angular deviation of the bright low-amplitude screening-photovoltaic spatial soliton are also presented by taking into account the effect of diffusion.
Dynamics of optical solitons in dual-core fibers via two integration schemes
Arnous, A. H.; Mahmood, S. A.; Younis, M.
2017-06-01
This article studies the dynamics of optical solitons in dual-core fibers with group velocity mismatch, group velocity dispersion and linear coupling coefficient under Kerr law nonlinearity via two integration schemes, namely, Q-function scheme and trial solution approach. The Q-function scheme extracts dark and singular 1-soliton solutions, along with the corresponding existence restriction. This scheme, however, fails to retrieve bright 1-soliton solution. Moreover, the trial solution approach extracts bright, dark and singular 1-soliton solutions. The constraint conditions, for the existence of the soliton solutions, are also listed. Additionally, a couple of other solutions known as singular periodic solutions, fall out as a by-product of this scheme. The obtained results have potential applications in the study of solitons based optical communication.
Non-linear effects for cylindrical gravitational two-soliton
Tomizawa, Shinya
2015-01-01
Using a cylindrical soliton solution to the four-dimensional vacuum Einstein equation, we study non-linear effects of gravitational waves such as Faraday rotation and time shift phenomenon. In the previous work, we analyzed the single-soliton solution constructed by the Pomeransky's improved inverse scattering method. In this work, we construct a new two-soliton solution with complex conjugate poles, by which we can avoid light-cone singularities unavoidable in a single soliton case. In particular, we compute amplitudes of such non-linear gravitational waves and time-dependence of the polarizations. Furthermore, we consider the time shift phenomenon for soliton waves, which means that a wave packet can propagate at slower velocity than light.
Optical analogue of relativistic Dirac solitons in binary waveguide arrays
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.
Ultradiscrete soliton equations derived from ultradiscrete permanent formulae
Nakamura, Shinya, E-mail: s-nakamura@moegi.waseda.jp [Major in Pure and Applied Mathematics, Graduate School of Fundamental Science and Engineering, Waseda University, 3-4-1, Okubo, Shinjuku-ku, Tokyo 169-8555 (Japan)
2011-07-22
We propose formulae of ultradiscrete permanent. Utilizing the formulae, ultradiscrete soliton equations and their multi-soliton solutions are obtained by a simple process. Changing variables and parameters of the formulae, we can derive the ultradiscrete Toda, KdV and hungry Lotka-Volterra equations. An extended version of the ultradiscrete hungry Lotka-Volterra equation is also proposed.
Soliton Collisions in the Ion Acoustic Plasma Equations
Li, Y; Li, Yi
1999-01-01
Numerical experiments involving the interaction of two solitary waves of the ion acoustic plasma equations are described. An exact 2-soliton solution of the relevant KdV equation was fitted to the initial data, and good agreement was maintained throughout the entire interaction. The data demonstrates that the soliton interactions are virtually elastic
Soliton dynamics in computational anatomy.
Holm, Darryl D; Ratnanather, J Tilak; Trouvé, Alain; Younes, Laurent
2004-01-01
Computational anatomy (CA) has introduced the idea of anatomical structures being transformed by geodesic deformations on groups of diffeomorphisms. Among these geometric structures, landmarks and image outlines in CA are shown to be singular solutions of a partial differential equation that is called the geodesic EPDiff equation. A recently discovered momentum map for singular solutions of EPDiff yields their canonical Hamiltonian formulation, which in turn provides a complete parameterization of the landmarks by their canonical positions and momenta. The momentum map provides an isomorphism between landmarks (and outlines) for images and singular soliton solutions of the EPDiff equation. This isomorphism suggests a new dynamical paradigm for CA, as well as new data representation.
Solitons in magneto-optic waveguides by extended trial function scheme
Ekici, Mehmet; Zhou, Qin; Sonmezoglu, Abdullah; Moshokoa, Seithuti P.; Ullah, Malik Zaka; Biswas, Anjan; Belic, Milivoj
2017-07-01
This paper obtains soliton solutions to magneto-optic waveguides that appear with Kerr, power and log-law nonlinearities. The extended trial function method is employed to obtain these solutions. Thus, bright, dark and singular soliton solutions are retrieved. In addition, Gaussons are obtained for log-law nonlinear waveguides. All of these solutions appear with constraints that guarantees the existence of solitons and Gaussons.
Parabola solitons for the nonautonomous KP equation in fluids and plasmas
Yu, Xin, E-mail: yuxin@buaa.edu.cn; Sun, Zhi-Yuan
2016-04-15
Under investigation in this paper is a nonautonomous Kadomtsev–Petviashvili (KP) equation in fluids and plasmas. The integrability of this equation is examined via the Painlevé analysis and its multi-soliton solutions are constructed. A constraint is proposed to ensure the existence of parabola solitons for such KP equation. Based on the constructed solutions, the solitonic propagation and interaction, including the elastic interaction, inelastic interaction and soliton resonance for parabola solitons, are discussed. The results might be useful for shallow water wave and rogue wave.
Special Bi-Solitons for Asymmetric Nizhnik-Novikov-Veselov Equation
L(U) Zhuo-Sheng
2011-01-01
Employing a constructive algorithm and the symbolic computation, we obtain a new explicit bi-soliton-like solution of the asymmetric Nizhnik-Novikov-Veselov equation.The solution contains two arbitrary functions which indicates that it can model various bi-soliton-like waves.In particular, specially choosing the arbitrary functions, we lind some interesting bi-solitons with special shapes, which possess the traveling property of the traditional bi-solitons.We show the evolution of such bi-solitons by figures.
Solitonic Information Transmission in General Relativity
SHANG Yu; WANG Gui-Dong; WU Xiao-Ning; WANG Shi-Kun; LAU Yun-Kau
2007-01-01
An exact solution of the vacuum Einstein's field equations is presented,in which there exists a congruence of null geodesics whose shear behaves like a travelling wave of the KdV equation.On the basis of this exact solution,the feasibility of solitonic information transmission by exploiting the nonlinearity intrinsic to the Einstein field equations is discussed.
Solitons in nucleon-nucleus collisions
Fogaca, D.A.; Navarra, F.S. [Sao Paulo Univ., SP (Brazil). Inst. de Fisica]. E-mail: hadron@terra.com.br
2004-07-01
Under certain conditions, the equations of non-relativistic hydrodynamics may provide a Korteweg-de Vries equation (KdV) which gives a soliton solution. We show that this solution and its properties are related to the microscopic features of the nuclear matter equation of state. (author)
Filippov, Alexandre T
2010-01-01
If you have not already heard about solitons, you will sooner or later encounter them. The soliton, a solitary wave impulse preserving its shape and strikingly similar to a particle, is one of the most fascinating and beautiful phenomena in the physics of nonlinear waves. In this engaging book, the concept of the soliton is traced from the beginning of the last century to modern times, with recent applications in biology, oceanography, solid state physics, electronics, elementary particle physics, and cosmology. The main concepts and results of theoretical physics related to solitons can be ex
Analytical solitons for Langmuir waves in plasma physics with cubic nonlinearity and perturbations
Zhou, Qin [Wuhan Donghu Univ. (China). School of Electronics and Information Engineering; Mirzazadeh, M. [Guilan Univ. (Iran, Islamic Republic of). Dept. of Engineering Sciences
2016-07-01
We presented an analytical study on dynamics of solitons for Langmuir waves in plasma physics. The mathematical model is given by the perturbed nonlinear Schroedinger 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.
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.
Nonlinear compression of optical solitons
M N Vinoj; V C Kuriakose
2001-11-01
In this paper, we consider nonlinear Schrödinger (NLS) equations, both in the anomalous and normal dispersive regimes, which govern the propagation of a single ﬁeld in a ﬁber medium with phase modulation and ﬁbre gain (or loss). The integrability conditions are arrived from linear eigen value problem. The variable transformations which connect the integrable form of modiﬁed NLS equations are presented. We succeed in Hirota bilinearzing the equations and on solving, exact bright and dark soliton solutions are obtained. From the results, we show that the soliton is alive, i.e. pulse area can be conserved by the inclusion of gain (or loss) and phase modulation effects.
New cylindrical gravitational soliton waves and gravitational Faraday rotation
Tomizawa, Shinya
2013-01-01
In terms of gravitational solitons, we study gravitational non-linear effects of gravitational solitary waves such as Faraday rotation. Applying the Pomeransky's procedure for inverse scattering method, which has been recently used for constructing stationary black hole solutions in five dimensions to a cylindrical spacetime in four dimensions, we construct a new cylindrically symmetric soliton solution. This is the first example to be applied to the cylindrically symmetric case. In particular, we clarify the difference from the Tomimatsu's single soliton solution, which was constructed by the Belinsky-Zakharov's procedure.
Novel loop-like solitons for the generalized Vakhnenko equation
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.
Comte, J C; Marquié, P; Remoissenet, M
1999-12-01
We introduce a nonlinear Klein-Gordon lattice model with specific double-well on-site potential, additional constant external force and dissipation terms, which admits exact discrete kink or traveling wave fronts solutions. In the non-dissipative or conservative regime, our numerical simulations show that narrow kinks can propagate freely, and reveal that static or moving discrete breathers, with a finite but long lifetime, can emerge from kink-antikink collisions. In the general dissipative regime, the lifetime of these breathers depends on the importance of the dissipative effects. In the overdamped or diffusive regime, the general equation of motion reduces to a discrete reaction diffusion equation; our simulations show that, for a given potential shape, discrete wave fronts can travel without experiencing any propagation failure but their collisions are inelastic.
On the existence of stationary Ricci solitons
Figueras, Pau
2016-01-01
Previously the DeTurck 'trick' has been used to render the stationary Einstein's equation a well posed elliptic system that may be solved numerically by geometric flow or directly. Whilst in the static case for pure gravity with zero or negative cosmological constant there is a simple proof that solving the modified "harmonic" Einstein's equation leads to a solution of the original Einstein system - i.e. not a Ricci soliton - in the stationary case this argument no longer works. Here we provide a new argument that extends the static result to the case of stationary spacetimes that possess a "$t$-$\\phi$" reflection symmetry. Defining a "soliton charge" from the asymptotic behaviour of the solution, we show that this quantity is always non-positive. Provided asymptotic conditions are chosen such that this charge vanishes, then stationary solitons cannot exist.
Soliton absorption spectroscopy
Kalashnikov, V L
2010-01-01
We analyze optical soliton propagation in the presence of weak absorption lines with much narrower linewidths as compared to the soliton spectrum width using the novel perturbation analysis technique based on an integral representation in the spectral domain. The stable soliton acquires spectral modulation that follows the associated index of refraction of the absorber. The model can be applied to ordinary soliton propagation and to an absorber inside a passively modelocked laser. In the latter case, a comparison with water vapor absorption in a femtosecond Cr:ZnSe laser yields a very good agreement with experiment. Compared to the conventional absorption measurement in a cell of the same length, the signal is increased by an order of magnitude. The obtained analytical expressions allow further improving of the sensitivity and spectroscopic accuracy making the soliton absorption spectroscopy a promising novel measurement technique.
Podivilov, Evgeniy V; Bednyakova, Anastasia E; Fedoruk, Mikhail P; Babin, Sergey A
2016-01-01
Dissipative solitons are stable localized coherent structures with linear frequency chirp generated in normal-dispersion mode-locked lasers. The soliton energy in fiber lasers is limited by the Raman effect, but implementation of intracavity feedback for the Stokes wave enables synchronous generation of a coherent Raman dissipative soliton. Here we demonstrate a new approach for generating chirped pulses at new wavelengths by mixing in a highly-nonlinear fiber of two frequency-shifted dissipative solitons, as well as cascaded generation of their clones forming a "dissipative soliton comb" in the frequency domain. We observed up to eight equidistant components in a 400-nm interval demonstrating compressibility from ~10 ps to ~300 fs. This approach, being different from traditional frequency combs, can inspire new developments in fundamental science and applications.
Stokes Soliton in Optical Microcavities
Yang, Qi-Fan; Yang, Ki Youl; Vahala, Kerry
2016-01-01
Solitons are wavepackets that resist dispersion through a self-induced potential well. They are studied in many fields, but are especially well known in optics on account of the relative ease of their formation and control in optical fiber waveguides. Besides their many interesting properties, solitons are important to optical continuum generation, in mode-locked lasers and have been considered as a natural way to convey data over great distances. Recently, solitons have been realized in microcavities thereby bringing the power of microfabrication methods to future applications. This work reports a soliton not previously observed in optical systems, the Stokes soliton. The Stokes soliton forms and regenerates by optimizing its Raman interaction in space and time within an optical-potential well shared with another soliton. The Stokes and the initial soliton belong to distinct transverse mode families and benefit from a form of soliton trapping that is new to microcavities and soliton lasers in general. The di...
ZHANG Ai-Xia; XUE Ju-Kui
2008-01-01
We present an analytical study on the dynamics of bright and dark solitons in Bose-Einstein condensates with time-varying atomic scattering length in a time-varying external parabolic potential.A set of exact soliton solutions of the one-dimensional Gross-Pitaevskii equation are obtained,including fundamental bright solitons,higher-order bright solitons,and dark solitons.The results show that the soliton's parameters(amplitude,width,and period)can be changed in a controllable manner by changing the scattering length and external potential.This may be helpful to design experiments.
Dynamics of solitons in multicomponent long wave–short wave resonance interaction system
T Kanna; K Sakkaravarthi; M Vijayajayanthi; M Lakshmanan
2015-03-01
In this paper, we study the formation of solitons, their propagation and collision behaviour in an integrable multicomponent (2+1)-dimensional long wave–short wave resonance interaction (-LSRI) system. First, we briefly revisit the earlier results on the dynamics of bright solitons and demonstrate the fascinating energy exchange collision of bright solitons appearing in the short-wave components of the -LSRI system. Then, we explicitly construct the exact one-and two-multicomponent dark soliton solutions of the -LSRI system by using the Hirota’s direct method and explore its propagation dynamics. Also, we study the features of dark soliton collisions.
Stability of gravitating charged-scalar solitons in a cavity
Ponglertsakul, Supakchai; Dolan, Sam R
2016-01-01
We present new regular solutions of Einstein-charged scalar field theory in a cavity. The system is enclosed inside a reflecting mirror-like boundary, on which the scalar field vanishes. The mirror is placed at the zero of the scalar field closest to the origin, and inside this boundary our solutions are regular. We study the stability of these solitons under linear, spherically symmetric perturbations of the metric, scalar and electromagnetic fields. If the radius of the mirror is sufficiently large, we present numerical evidence for the stability of the solitons. For small mirror radius, some of the solitons are unstable. We discuss the physical interpretation of this instability.
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 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...
STABILITY OF BRIGHT SCREENING-PHOTOVOLTAIC SPATIAL SOLITONS
LIU JING-SONG; ZHANG DU-YING; LIANG CHANG-HONG
2000-01-01
We present a theoretical analysis of the stability of screening-photovoltaic (SP) spatial solitons in biased photovoltaic-photorefractive materials in the case of neglecting the loss of the material and the effect of diffusion.When an incident optical beam is a SP soliton, this beam propagates along a linear path with its shape kept unchanged.When the maximum amplitude, width and functional form of an incident optical beam are slightly different from those of a SP soliton, the beam reshapes itself and tries to evolve into a solitary wave after a short distance. That is, these SP solitons are stable against small perturbations. However, optical beams that significantly differ from SP soliton solutions tend to experience larger cycles of compression and expansion, and their maximum amplitudes oscillate with propagation distances. The larger the perturbations, the stronger the oscillation.
Breathing Bright Solitons in a Bose-Einstein Condensate
崇桂书; 海文华; 谢琼涛
2003-01-01
A Bose-Einstein condensate with time varying scattering length in time-dependent harmonic trap is analytically investigated and soliton-like solutions of the Gross-Pitaeviskii equation are obtained to describe single soliton,bisoliton and N-soliton properties of the matter wave. The influences of the geometrical property and modulate frequency of trapping potential on soliton behaviour are discussed. When the trap potential has a very small trap aspect ratio or oscillates with a high frequency, the matter wave preserves its shape nearly like a soliton train in propagation, while the breathing behaviour, which displays the periodic collapse and revival of the matter wave,is found for a relatively large aspect ratio or slow varying potential. Meanwhile mass centre of the matter wave translates and/or oscillates for different trap aspect ratio and trap frequencies.
Soliton-Complex Dynamics in Strongly Dispersive Medium
Bogdan, M M; Maugin, G A; Bogdan, Mikhail M.; Kosevich, Arnold M.; Maugin, Gerard A.
1999-01-01
The concept of soliton complex in a nonlinear dispersive medium is proposed. It is shown that strongly interacting identical topological solitons in the medium can form bound soliton complexes which move without radiation. This phenomenon is considered to be universal and applicable to various physical systems. The soliton complex and its "excited" states are described analytically and numerically as solutions of nonlinear dispersive equations with the fourth and higher spatial or mixed derivatives. The dispersive sine-Gordon, double and triple sine-Gordon, and piecewise-linear models are studied in detail. Mechanisms and conditions of the formation of soliton complexes, and peculiarities of their stationary dynamics are investigated. A phenomenological approach to the description of the complexes and the classification of all the possible complex states are proposed. Some examples of physical systems, where the phenomenon can be experimentally observed, are briefly discussed.
Abundant Multisoliton Structure of (3+1)-Dimensional Breaking Soliton Equation
ZHAO Hong; BAI Cheng-Lin
2004-01-01
Using the extended homogeneous balance method, we obtained abundant exact solution structures of the (3+ 1 )-dimensional breaking soliton equation. By means of the leading order term analysis, the nonlinear transformations of the (3t1)-dimensional breaking soliton equation are given first, and then some special types of single solitary wave solutions and the multisoliton solutions are constructed.
Kerr-Newman Electron as Spinning Soliton
Burinskii, Alexander
2015-10-01
Measurable parameters of the electron indicate that its background should be described by the Kerr-Newman (KN) solution. The spin/mass ratio of the electron is extreme large, and the black hole horizons disappear, opening a topological defect of space-time - the Kerr singular ring of Compton size, which may be interpreted as a closed fundamental string of low energy string theory. The singular and two-sheeted structure of the corresponding Kerr space has to be regularised, and we consider the old problem of regularising the source of the KN solution. As a development of the earlier Keres-Israel-Hamity-López model, we describe the model of smooth and regular source forming a gravitating and relativistically rotating soliton based on the chiral field model and the Higgs mechanism of broken symmetry. The model reveals some new remarkable properties: (1) the soliton forms a relativistically rotating bubble of Compton radius, which is filled by the oscillating Higgs field in a pseudo-vacuum state; (2) the boundary of the bubble forms a domain wall which interpolates between the internal flat background and the external exact Kerr-Newman (KN) solution; (3) the phase transition is provided by a system of chiral fields; (4) the vector potential of the external the KN solution forms a closed Wilson loop which is quantised, giving rise to a quantised spin of the soliton; (5) the soliton is bordered by a closed string, which is a part of the general complex stringy structure.
The Soliton Transmissions in Optical Fibers
Leos Bohac
2010-01-01
Full Text Available The objective of this paper is to familiarize readers with the basic analytical propagation model of short optical pulses in optical fiber. Based on this model simulation of propagation of the special type of pulse, called a soliton, will be carried out. A soliton transmission is especially attractive in the fiber optic telecommunication systems as it does not change a pulses shape during propagating right-down the fiber link to the receiver. The model of very short pulse propagation is based on the numerical solution of the nonlinear Schroedinger equation (NLSE, although in some specific cases it is possible to solve it analytically.
Christian, J M; McDonald, G S [Joule Physics Laboratory, School of Computing, Science and Engineering, Materials and Physics Research Centre, University of Salford, Salford M5 4WT (United Kingdom); Chamorro-Posada, P, E-mail: j.christian@salford.ac.u [Departamento de Teoria de la Senal y Comunicaciones e Ingenieria Telematica, Universidad de Valladolid, ETSI Telecomunicacion, Campus Miguel Delibes s/n, 47011 Valladolid (Spain)
2010-02-26
We report, to the best of our knowledge, the first exact analytical algebraic solitons of a generalized cubic-quintic Helmholtz equation. This class of governing equation plays a key role in photonics modelling, allowing a full description of the propagation and interaction of broad scalar beams. New conservation laws are presented, and the recovery of paraxial results is discussed in detail. The stability properties of the new solitons are investigated by combining semi-analytical methods and computer simulations. In particular, new general stability regimes are reported for algebraic bright solitons.
Positons: slowly diminishing analogs of solitons
Matveev, V B
2002-01-01
The introduction to the theory of positons is presented. The positons are the remote-acting analogues of solitons and represent slowly diminishing and oscillating solitons of the nonlinear integrated equations of KdV type. The positon and soliton-positon solutions of the KdV equation were for the first time obtained and analyzed about 10 years ago and thereafter designed for a number of other models: mKdV, Toda chains, NSch, sn-Gordon equation and its lattice analog. By the proper selection of the scattering data the single positon and multipositon potentials are characterized by the remarkable property: the corresponding reflection coefficient is equal to zero and the transition coefficient is equal to one (the latter property, as it is known, has no place for the standard short-acting nonreflection potentials
Slunyaev, Alexey; Klein, Marco; Clauss, Günther F.
2016-04-01
Envelope soliton solutions are key elements governing the nonlinear wave dynamics within a simplified theory for unidirectional weakly modulated weakly nonlinear wave groups on the water surface. Within integrable models the solitons preserve their structure in collisions with other waves; they do not disperse and can carry energy infinitively long. Steep and short soliton-like wave groups have been shown to exist in laboratory tests [1] and, even earlier, in numerical simulations [2, 3]. Thus, long-living wave groups may play important role in the dynamics of intense sea waves and wave-structure interactions. The solitary wave groups may change the wave statistics and can be taken into account when developing approaches for the deterministic forecasting of dangerous waves, including so-called rogue waves. An experimental campaign has been conducted in the wave basin of the Technical University of Berlin on simulations of intense solitary wave groups. The first successful experimental observation of intense envelope solitons took place in this facility [1]. The new experiments aimed at following main goals: 1) to reproduce intense envelope solitons with different carrier wave lengths; 2) to estimate the rate of envelope soliton dissipation; 3) to consider the reflection of envelope solitons on a vertical wall; 4) to consider head-on collisions of envelope solitons, and 5) to consider overtaking interactions of envelope solitons. Up to 9 wave gauges were used in each experimental run, which enabled registration of the surface movement at different distances from the wavemaker, at different locations across the wave flume and near the wall. Besides surface displacements, the group envelope shapes were directly recorded, with use of phase shifts applied to the modulated waves generated by the wavemaker. [1] A. Slunyaev, G.F. Clauss, M. Klein, M. Onorato, Simulations and experiments of short intense envelope solitons of surface water waves. Phys. Fluids 25, 067105
Hassaïne, M; Yéra, J C
2004-01-01
The spacelike reduction of the Chern-Simons Lagrangian yields a modified Nonlinear Schr\\"odinger Equation (jNLS) where in the non-linearity the particle density is replaced by current. When the phase is linear in the position, this latter is an ordinary NLS with time-dependent coefficients which admits interesting solutions. Their arisal is explained by the conformal properties of non-relativistic spacetime. Only the usual travelling soliton is consistent with the jNLS, but the addition of a six-order potential converts it into an integrable equation.
Peakon and Foldon Excitations In a (2+1)-Dimensional Breaking Soliton System
郑春龙; 张解放; 黄文华; 陈立群
2003-01-01
Starting from the standard truncated Painlevé expansion and a variable separation approach, a general variable separation solution of the breaking soliton system is derived. In addition to the usual localized coherent soliton excitations like dromions, lumps, rings, breathers, instantons, oscillating soliton excitations, and previously revealed chaotic and fractal localized solutions, some new types of excitations, peakons and foldons, are obtained by introducing appropriate lower-dimensional piecewise smooth functions and multiple valued functions.
Dynamics of solitons in Bose-Einstein condensate with time-dependent atomic scattering length
Li Hua-Mei
2006-01-01
The evolution of solitons in Bose-Einstein condensates (BECs) with time-dependent atomic scattering length in an expulsive parabolic potential is studied. Based on the extended hyperbolic function method, we successfully obtain the bright and dark soliton solutions. In addition, some new soliton solutions in this model are found. The results in this paper include some in the literature (Phys. Rev. Lett. 94 (2005) 050402 and Chin. Phys. Lett. 22 (2005) 1855).
Soliton states of Maxwell’s equations and nonlinear Schrodinger equation
陈翼强
1997-01-01
Similarities and fundamental differences between Maxwell’s equations and nonlinear Schrodinger equation in predicting a soliton evolution in a uniform nonlinear anisotropic medium are analyzed.It is found that in some cases,the soliton solutions to the nonlinear Schrodinger equation cannot be recovered from Maxwell’s equations while in others the soliton solutions to Maxwell’s equations are lost from the nonlinear Schrodinger equation through approximation,although there are cases where the soliton solutions to the two sets of the equations demonstrate only quantitative difference.The origin of the differences is also discussed.
Sakkaravarthi, K; Kanna, T; Vijayajayanthi, M; Lakshmanan, M
2014-11-01
We consider a general multicomponent (2+1)-dimensional long-wave-short-wave resonance interaction (LSRI) system with arbitrary nonlinearity coefficients, which describes the nonlinear resonance interaction of multiple short waves with a long wave in two spatial dimensions. The general multicomponent LSRI system is shown to be integrable by performing the Painlevé analysis. Then we construct the exact bright multisoliton solutions by applying the Hirota's bilinearization method and study the propagation and collision dynamics of bright solitons in detail. Particularly, we investigate the head-on and overtaking collisions of bright solitons and explore two types of energy-sharing collisions as well as standard elastic collision. We have also corroborated the obtained analytical one-soliton solution by direct numerical simulation. Also, we discuss the formation and dynamics of resonant solitons. Interestingly, we demonstrate the formation of resonant solitons admitting breather-like (localized periodic pulse train) structure and also large amplitude localized structures akin to rogue waves coexisting with solitons. For completeness, we have also obtained dark one- and two-soliton solutions and studied their dynamics briefly.
龙林园; 杨立新; 徐衍聪
2015-01-01
利用Painlevé分析、Hirota多元线性法和直接拟设技巧，研究了一维带有耗散项的五次复Swift‐Hohenberg方程的解析解。找到了方程的精确解并证明方程系数之间存在着某种关系。得到了包括特殊类型的孤波解、暗孤子解和以雅可比椭圆函数形式表示的周期解等，为光学的进一步研究提供了一系列孤子解。%Analytic solutions for the dimensional quintic complex Swift‐Hohenberg equation with a dissipative term are investigated by using Painlevé analysis ,the Hirota multi‐linear method and a direct ansatz technique .This paer finds exact solutions exist to the equation and proves that there is certain relation among the coefficients .T he set of solutions consist of particular types of solitary wave solutions ,dark soliton solutions and periodic solutions in terms of elliptic Jacobi functions are obtainde .In fact ,these muliti‐parameter families of solutions can act as a seeding set of solutions which can be very useful in optical studies .
Solitons and other waves on a quantum vortex filament
Van Gorder, Robert A
2014-01-01
The quantum form of the local induction approximation (LIA, a model approximating the motion of a thin vortex filament in superfluid) including superfluid friction effects is put into correspondence with a type of cubic complex Ginsburg-Landau equation, in a manner analogous to the Hasimoto map taking the classical LIA into the cubic nonlinear Schr\\"odinger equation. From this formulation, we determine the form and behavior of Stokes waves, 1-solitons, and other traveling wave solutions under normal and binormal friction. The most important of these solutions is the soliton on a quantum vortex filament, which is a natural generalization of the 1-soliton solution constructed mathematically by Hasimoto which motivated subsequent real-world experiments. We also conjecture on the possibility of chaos in such systems, and on the existence more complicated solitons such as breathers.
Bright Chirp-free and Chirped Nonautonomous solitons under Dispersion and Nonlinearity Management
Yang, Zhan-Ying; Zhang, Tao; Yue, Rui-Hong
2011-01-01
We present a series of chirp-free and chirped analytical nonautonomous soliton solutions to the generalized nonlinear Schrodinger equation (NLSE) with distributed coefficients by Darboux transformation from a trivial seed. For chirpfree nonautonomous soliton, the dispersion management term can change the motion of nonautonomous soliton and do not affect its shape at all. Especially,the classical optical soliton can be presented with variable dispersion term and nonlinearity when there is no gain. For chirped nonautonomous soliton, dispersion management can affect the shape and motion of nonautonomous solitons meanwhile. The periodic dispersion term can be used to control its "breathing" shape, and it does not affect the trajectory of nonautonomous soliton center with a certain condition.
Interaction of discrete nonlinear Schr\\"odinger solitons with a linear lattice impurity
Brazhnyi, Valeriy A; Rodrigues, A S
2013-01-01
The interaction of moving discrete solitons with a linear Gaussian defect is investigated. Solitons with profiles varying from hyperbolic secant to exponentially localized are considered such that the mobility of soliton is maintained; the condition for which is obtained. Studies on scattering of the soliton by an attractive defect potential reveal the existence of total reflection and transmission windows which become very narrow with increasing initial soliton amplitude. Transmission regions disappear beyond the small-amplitude limit. The regions of complete reflection and partial capture correspond to the windows of the existence and nonexistence of solution of the stationary problem. Interaction of the discrete soliton with a barrier potential is also investigated. The critical amplitude of the defect at which splitting of the soliton into two parts occurs was estimated from a balance equation. The results were confirmed through direct numerical integration of the dynamical equation showing very good agre...
Chirped Peregrine solitons in a class of cubic-quintic nonlinear Schrödinger equations
Chen, Shihua; Baronio, Fabio; Soto-Crespo, Jose M.; Liu, Yi; Grelu, Philippe
2016-06-01
We shed light on the fundamental form of the Peregrine soliton as well as on its frequency chirping property by virtue of a pertinent cubic-quintic nonlinear Schrödinger equation. An exact generic Peregrine soliton solution is obtained via a simple gauge transformation, which unifies the recently-most-studied fundamental rogue-wave species. We discover that this type of Peregrine soliton, viable for both the focusing and defocusing Kerr nonlinearities, could exhibit an extra doubly localized chirp while keeping the characteristic intensity features of the original Peregrine soliton, hence the term chirped Peregrine soliton. The existence of chirped Peregrine solitons in a self-defocusing nonlinear medium may be attributed to the presence of self-steepening effect when the latter is not balanced out by the third-order dispersion. We numerically confirm the robustness of such chirped Peregrine solitons in spite of the onset of modulation instability.
Villari, Leone Di Mauro; Biancalana, Fabio; Conti, Claudio
2016-01-01
We have very little experience of the quantum dynamics of the ubiquitous nonlinear waves. Observed phenomena in high energy physics are perturbations to linear waves, and classical nonlinear waves, like solitons, are barely affected by quantum effects. We know that solitons, immutable in classical physics, exhibit collapse and revivals according to quantum mechanics. However this effect is very weak and has never been observed experimentally. By predicting black hole evaporation Hawking first introduced a distinctly quantum effect in nonlinear gravitational physics.Here we show the existence of a general and universal quantum process whereby a soliton emits quantum radiation with a specific frequency content, and a temperature given by the number of quanta, the soliton Schwarzschild radius, and the amount of nonlinearity, in a precise and surprisingly simple way. This result may ultimately lead to the first experimental evidence of genuine quantum black hole evaporation. In addition, our results show that bla...
Novozhilov, V Yu; Novozhilov, Victor; Novozhilov, Yuri
2002-01-01
We discuss specific features of color chiral solitons (asymptotics, possibility of confainment, quantization) at example of isolated SU(2) color skyrmions, i.e. skyrmions in a background field which is the vacuum field forming the gluon condensate.
Temporal dark polariton solitons
Kartashov, Yaroslav V
2016-01-01
We predict that strong coupling between waveguide photons and excitons of quantum well embedded into waveguide results in the formation of hybrid dark and anti-dark light-matter solitons. Such temporal solitons exist due to interplay between repulsive excitonic nonlinearity and giant group velocity dispersion arising in the vicinity of excitonic resonance. Such fully conservative states do not require external pumping to counteract losses and form continuous families parameterized by the power-dependent phase shift and velocity of their motion. Dark solitons are stable in the considerable part of their existence domain, while anti-dark solitons are always unstable. Both families exist outside forbidden frequency gap of the linear system.
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.......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....
Ho, Keang-Po
2003-01-01
The characteristic function of soliton phase jitter is found analytically when the soliton is perturbed by amplifier noise. In additional to that from amplitude jitter, the nonlinear phase noise due to frequency and timing jitter is also analyzed. Because the nonlinear phase noise is not Gaussian distributed, the overall phase jitter is also non-Gaussian. For a fixed mean nonlinear phase shift, the contribution of nonlinear phase noise from frequency and timing jitter decreases with distance ...
Time dependent solitons of noncommutative Chern-Simons theory coupled to scalar fields
Hadasz, L; Rocek, M; Von Unge, R; Hadasz, Leszek; Lindstrom, Ulf; Rocek, Martin; Unge, Rikard von
2003-01-01
We study one- and two-soliton solutions of noncommutative Chern-Simons theory coupled to a nonrelativistic or a relativistic scalar field. In the nonrelativistic case it is not possible to find the dynamics of the solitons using traditional moduli space techniques. To do better we have found exact time dependent one soliton solutions to the full equations of motion. They represent solitons moving in straight lines with constant velocity. Surprisingly we find that the set of allowed velocities is quantized! The allowed velocities are proportional to the square root of an integer. In the relativistic case we find the metric on the two soliton moduli space and using techinques developed in the nonrelativistic case we also find exact time dependent one-soliton solutions. Again the allowed velocities are quantized, though in a slightly more complicated fashion.
Bednarek, I; Bednarek, Ilona; Manka, Ryszard
1996-01-01
The evolution of a soliton star filled with fermions is studied in the framework of general relativity. Such a system can be described by the surface tension $\\sigma$, the bag constant $B$, and the fermion number density affects the spacetime inside the soliton. Whether it is described by Friedman or de Sitter metric depends on the prevailing parameter. The whole spacetime is devided by the surface of the soliton into the false vacuum region inside the soliton and the true vacuum region outside, the latter being described by the Schwarzschild line element. The aim of this paper is to study the equations of motion of the domain wall in two cases. In the first case the de Sitter metric describes the interior in the first case, and in the second case it is replaced by the Friedman metric. In both of them the Schwarzschild metric is outside the soliton. From the analysis of obtained equations one can draw conclusions concerning further evolution of a soliton star.
Breatherlike solitons extracted from the Peregrine rogue wave.
Yang, Guangye; Wang, Yan; Qin, Zhenyun; Malomed, Boris A; Mihalache, Dumitru; Li, Lu
2014-12-01
Based on the Peregrine solution (PS) of the nonlinear Schrödinger (NLS) equation, the evolution of rational fraction pulses surrounded by zero background is investigated. These pulses display the behavior of a breatherlike solitons. We study the generation and evolution of such solitons extracted, by means of the spectral-filtering method, from the PS in the model of the optical fiber with realistic values of coefficients accounting for the anomalous dispersion, Kerr nonlinearity, and higher-order effects. The results demonstrate that the breathing solitons stably propagate in the fibers. Their robustness against small random perturbations applied to the initial background is demonstrated too.
Breather-like solitons extracted from the Peregrine rogue wave
Yang, Guangye; Qin, Zhenyun; Malomed, Boris A; Mihalache, Dumitru; Li, Lu
2014-01-01
Based on the Peregrine solution (PS) of the nonlinear Schr\\"odinger (NLS) equation, the evolution of rational fraction pulses surrounded by zero background is investigated. These pulses display the behavior of a breather-like solitons. We study the generation and evolution of such solitons extracted, by means of the spectral-filtering method, from the PS in the model of the optical fiber with realistic values of coefficients accounting for the anomalous dispersion, Kerr nonlinearity, and higher-order effects. The results demonstrate that the breathing solitons stably propagate in the fibers. Their robustness against small random perturbations applied to the initial background is demonstrated too.
Noise of quantum solitons and their quasi-coherent states
段路明; 郭光灿
1997-01-01
Quantum noise of optical solitons is analysed based on the exact solutions of the quantum nonlinear Schrodmger equation (QNSE) and the construction of the quantum soliton states. The noise limits are obtained for the local photon number and for the local quadrature phase amplitude. They are larger than the vacuum fluctuation. So in the fundamental soliton states the variance of the local photon number and the local quadrature phase amplitude cannot be squeezed The sohton states with the minimum noise are quasi-coherent states, in which the quantum dispersion effects are negligible.
Rajan, M. S. Mani
2016-08-01
In this manuscript, the ultrashort soliton pulse propagation through nonlinear tunneling in cubic quintic media is investigated. The effect of chirping on propagation characteristics of the soliton pulse is analytically investigated using similarity transformation. In particular, we investigate the propagation dynamics of ultrashort soliton pulse through dispersion barrier for both chirp and chirp-free soliton. By investigating the obtained soliton solution, we found that chirping has strong influence on soliton dynamics such as pulse compression with amplification. These two important dynamics of chirped soliton in cubic quintic media open new possibilities to improve the solitonic communication system. Moreover, we surprisingly observe that a dispersion well is formed for the chirped case whereas a barrier is formed for the chirp-free case, which has certain applications in the construction of logic gate devices to achieve ultrafast switching.
一类非线性发展方程的复合型双孤子新解∗%New complexion two-soliton solutions of a class of nonlinear evolution equation
套格图桑; 伊丽娜
2015-01-01
通过下列步骤，构造了一类非线性发展方程的无穷序列复合型双孤子新解：步骤一，给出两种函数变换，把一类非线性发展方程化为二阶非线性常微分方程；步骤二，再通过函数变换，二阶非线性常微分方程转化为一阶非线性常微分方程组，并获得了该方程组的首次积分；步骤三，利用首次积分与两种椭圆方程的新解与Bäcklund变换，构造了一类非线性发展方程的无穷序列复合型双孤子新解。%New infinite sequence complexion two-soliton solutions of a kind of nonlinear evolution equation are constructed with the help of function transformations and two kinds of elliptic equations. Step one,according to two function transformations, a kind of nonlinear evolution equation is changed into a nonlinear ordinary differential equation of second order. Step two, using function transformation, the nonlinear ordinary differential equation of second order is transformed into a set of nonlinear ordinary differential equations of first order, and the first integral of the set of equations is obtained. Finally, the first integral with new solutions and Bäcklund transformation of two kinds of elliptic equations are used to search for new infinite sequence complexion two-soliton solutions of a kind of nonlinear evolution equation.
Variable Separation Solution for （1＋1）-Dimensional Nonlinear Models Related to Schroedinger Equation
XUChang-Zhi; ZHANGJie-Fang
2004-01-01
A variable separation approach is proposed and successfully extended to the (1+1)-dimensional physics models. The new exact solution of (1+1)-dimensional nonlinear models related to Schr6dinger equation by the entrance of three arbitrary functions is obtained. Some special types of soliton wave solutions such as multi-soliton wave solution,non-stable soliton solution, oscillating soliton solution, and periodic soliton solutions are discussed by selecting the arbitrary functions appropriately.
XU Chang-Zhi; ZHANG Jie-Fang
2004-01-01
A variable separation approach is proposed and successfully extended to the (1+1)-dimensional physics models. The new exact solution of (1+ 1)-dimensional nonlinear models related to Schrodinger equation by the entrance of three arbitrary functions is obtained. Some special types of soliton wave solutions such as multi-soliton wave solution,non-stable soliton solution, oscillating soliton solution, and periodic soliton solutions are discussed by selecting the arbitrary functions appropriately.
Spatiotemporal accessible solitons in fractional dimensions
Zhong, Wei-Ping; Belić, Milivoj R.; Malomed, Boris A.; Zhang, Yiqi; Huang, Tingwen
2016-07-01
We report solutions for solitons of the "accessible" type in globally nonlocal nonlinear media of fractional dimension (FD), viz., for self-trapped modes in the space of effective dimension 2 functions that include Gegenbauer polynomials, associated Laguerre polynomials, and associated Legendre functions. The validity of these solutions is verified by direct simulations. The model can be realized in various physical settings emulated by FD spaces; in particular, it applies to excitons trapped in quantum wells.
Acoustic solitons in waveguides with Helmholtz resonators: transmission line approach.
Achilleos, V; Richoux, O; Theocharis, G; Frantzeskakis, D J
2015-02-01
We report experimental results and study theoretically soliton formation and propagation in an air-filled acoustic waveguide side loaded with Helmholtz resonators. We propose a theoretical modeling of the system, which relies on a transmission-line approach, leading to a nonlinear dynamical lattice model. The latter allows for an analytical description of the various soliton solutions for the pressure, which are found by means of dynamical systems and multiscale expansion techniques. These solutions include Boussinesq-like and Korteweg-de Vries pulse-shaped solitons that are observed in the experiment, as well as nonlinear Schrödinger envelope solitons, that are predicted theoretically. The analytical predictions are in excellent agreement with direct numerical simulations and in qualitative agreement with the experimental observations.
Interaction of spatial photorefractive solitons
Królikowski, W.; Denz, C.; Stepken, A.
1998-01-01
beam or the complete annihilation of some of them, depending on the relative phase of the interacting beams. In the case of mutually incoherent solitons, we show that the photorefractive nonlinearity leads to an anomalous interaction between solitons. Theoretical and experimental results reveal...... 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....
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.
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.
Transverse stability of Kawahara solitons
Karpman, V.I.
1993-01-01
The transverse stability of the planar solitons described by the fifth-order Korteweg-de Vries equation (Kawahara solitons) is studied. It is shown that the planar solitons are unstable with respect to bending if the coefficient at the fifth-derivative term is positive and stable if it is negative...
Bipolar solitons of the focusing nonlinear Schrödinger equation
Liu, Zhongxuan; Feng, Qi; Lin, Chengyou; Chen, Zhaoyang; Ding, Yingchun
2016-11-01
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.
Bipolar solitons of the focusing nonlinear Schrödinger equation
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.
Numerical Computation of High Dimensional Solitons Via Drboux Transformation
ZixiangZHOU
1997-01-01
Darboux transformation gives explicit soliton solutions of nonlinear partial differential equations.Using numerical computation in each step of constructing Darboux transformation,one can get the graphs of the solitons practically,In n dimensions(n≥3),this method greatly increases the speed and deduces the memory usage of computation comparing to the software for algebraic computation.A technical problem concerning floating overflow is discussed.
The baryon number two system in the Chiral Soliton Model
Sarti, Valentina Mantovani; Vento, Vicente; Park, Byung-Yoon
2012-01-01
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 intersoliton interaction on these relative orientations reveals that studies of dense hadronic matter using this model should take into account their implications.
Dispersion managed solitons in the presence of saturated nonlinearity
Hundertmark, Dirk; Lee, Young-Ran; Ried, Tobias; Zharnitsky, Vadim
2017-10-01
The averaged dispersion managed nonlinear Schrödinger equation with saturated nonlinearity is considered. It is shown that under rather general assumptions on the saturated nonlinearity, the ground state solution corresponding to the dispersion managed soliton can be found for both zero residual dispersion and positive residual dispersion. The same applies to diffraction management solitons, which are a discrete version describing certain waveguide arrays.
包永梅; 高娃
2011-01-01
By using a transformation, the variable coefficient generalized KdV-Burgers equation is reduced to nonlinear ordinary differential equation （NLODE）. Several exact soliton-like solutions for the variable coefficient generalized KdV-Burgers equation are obtained through use of the corresponding reduced NLODE. Form this example we can see that this method can be applied to solve a large number of nonlinear evolution equations.%利用一种函数变换将变系数广义KdV—Burgers方程约化为非线性常微分方程（NLODE）．并由此NLODE出发获得变系数广义KdV—Burgers方程的若干精确类孤子解。由此可见，用这种方法还可以求解一大类变系数非线性演化方程。
Axion dark matter, solitons, and the cusp-core problem
Marsh, David J E
2015-01-01
Self-gravitating bosonic fields can support stable and localised field configurations. For real fields, these solutions oscillate in time and are known as oscillatons. The density profile is static, and is soliton. Such solitons should be ubiquitous in models of axion dark matter, with the soliton characteristic mass and size depending on some inverse power of the axion mass. Stable configurations of non-relativistic axions are studied numerically using the Schr\\"{o}dinger-Poisson system. This method, and the resulting soliton density profiles, are reviewed. Using a scaling symmetry and the uncertainty principle, the core size of the soliton can be related to the central density and axion mass, $m_a$, in a universal way. Solitons have a constant central density due to pressure-support, unlike the cuspy profile of cold dark matter (CDM). One consequence of this fact is that solitons composed of ultra-light axions (ULAs) may resolve the `cusp-core' problem of CDM. In DM halos, thermodynamics will lead to a CDM-...
Zhao, Xue-Hui; Tian, Bo; Chai, Jun; Wu, Yu-Xiao; Guo, Yong-Jiang
2016-11-01
Under investigation in this paper is a generalized variable-coefficient Boussinesq system, which describes the propagation of the shallow water waves in the two-layered fluid flow. Bilinear forms, Bäcklund transformation and Lax pair are derived by virtue of the Bell polynomials. Hirota method is applied to construct the one- and two-soliton solutions. Propagation and interaction of the solitons are illustrated graphically: kink- and bell-shape solitons are obtained; shapes of the solitons are affected by the variable coefficients α1, α3 and α4 during the propagation, kink- and anti-bell-shape solitons are obtained when α3 > 0, anti-kink- and bell-shape solitons are obtained when α3 < 0; Head-on interaction between the two bidirectional solitons, overtaking interaction between the two unidirectional solitons are presented; interactions between the two solitons are elastic.
Bright Solitons in a PT-Symmetric Chain of Dimers
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.
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.
Electron-Acoustic Compressive Soliton and Electron Density Hole in Aurora
王德焴
2003-01-01
Electron-acoustic solitary waves have been studied in an electron-beam plasma system. It is found that the solution of compressive soliton only exists within a limited range of soliton velocity around the electron beam velocity. A compressive electron-acoustic soliton always accompanies with a cold electron density hole. This theoretical model is used to explain the ‘fast solitary wave' event observed by the FAST satellite in the midaltitude auroral zone.
Zhang Xiao-Fei; Zhang Pei; He Wan-Quan; Liu Xun-Xu
2011-01-01
By using a unified theory of the formation of various types of vector-solitons in two-component Bose-Einstein condensates with tunable interactions, we obtain a family of exact vector-soliton solutions for the coupled nonlinear Schr(o)dinger equations. Moreover, the Bogoliubov equation shows that there exists stable dark soliton in specific situations. Our results open up new ways in considerable experimental interest for the quantum control of multi-component Bose-Einstein condensates.
Numerical Exploration of Soliton Creation
Lamm, Henry
2013-01-01
We explore the classical production of solitons in the easy axis O(3) model in 1+1 dimensions, for a wide range of initial conditions that correspond to the scattering of small breathers. We characterize the fractal nature of the region in parameter space that leads to soliton production and find certain trends in the data. We identify a tension in the initial conditions required for soliton production - low velocity incoming breathers are more likely to produce solitons, while high velocity incoming breathers provide momentum to the final solitons and enable them to separate. We find new "counter-spinning" initial conditions that can alleviate some of this tension.
Head on collision of multi-solitons in an electron-positron-ion plasma having superthermal electrons
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.
Solitons in nonlinear lattices
Kartashov, Yaroslav V; Torner, Lluis
2010-01-01
This article offers a comprehensive survey of results obtained for solitons and complex nonlinear wave patterns supported by purely nonlinear lattices (NLs), which represent a spatially periodic modulation of the local strength and sign of the nonlinearity, and their combinations with linear lattices. A majority of the results obtained, thus far, in this field and reviewed in this article are theoretical. Nevertheless, relevant experimental settings are surveyed too, with emphasis on perspectives for implementation of the theoretical predictions in the experiment. Physical systems discussed in the review belong to the realms of nonlinear optics (including artificial optical media, such as photonic crystals, and plasmonics) and Bose-Einstein condensation (BEC). The solitons are considered in one, two, and three dimensions (1D, 2D, and 3D). Basic properties of the solitons presented in the review are their existence, stability, and mobility. Although the field is still far from completion, general conclusions c...
Bonilla, L. L.; Carretero, M.; Terragni, F.; Birnir, B.
2016-08-01
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.
Stokes solitons in optical microcavities
Yang, Qi-Fan; Yi, Xu; Yang, Ki Youl; Vahala, Kerry
2017-01-01
Solitons are wave packets that resist dispersion through a self-induced potential well. They are studied in many fields, but are especially well known in optics on account of the relative ease of their formation and control in optical fibre waveguides. Besides their many interesting properties, solitons are important to optical continuum generation, in mode-locked lasers, and have been considered as a natural way to convey data over great distances. Recently, solitons have been realized in microcavities, thereby bringing the power of microfabrication methods to future applications. This work reports a soliton not previously observed in optical systems, the Stokes soliton. The Stokes soliton forms and regenerates by optimizing its Raman interaction in space and time within an optical potential well shared with another soliton. The Stokes and the initial soliton belong to distinct transverse mode families and benefit from a form of soliton trapping that is new to microcavities and soliton lasers in general. The discovery of a new optical soliton can impact work in other areas of photonics, including nonlinear optics and spectroscopy.
Soliton crystals in Kerr resonators
Cole, Daniel C; Del'Haye, Pascal; Diddams, Scott A; Papp, Scott B
2016-01-01
Solitons are pulses that propagate without spreading due to a balance between nonlinearity and dispersion (or diffraction), and are universal features of systems exhibiting these effects. Solitons play an important role in plasma physics, fluid dynamics, atomic physics, biology, and optics. In the context of integrated photonics, bright dissipative cavity solitons in Kerr-nonlinear resonators are envisioned to play an important role in next-generation communication, computation, and measurement systems. Here we report the discovery of soliton crystals in Kerr resonators-collectively ordered ensembles of co-propagating solitons with discrete allowed temporal separations. Through analysis of optical spectra, we identify a complicated but discrete space of interacting soliton configurations, including crystals exhibiting vacancies (Schottky defects), shifted pulses (Frenkel defects), and superstructure. Time-domain characterization of the output-coupled soliton pulse train directly confirms our inference of the ...
Soliton switching in a site-dependent ferromagnet
Senjudarvannan, R.; Sathishkumar, P.; Vijayalakshmi, S.
2017-02-01
Switching of soliton in a ferromagnetic medium offers the possibility of developing a new innovative approach for information storage technologies. The nonlinear spin dynamics of a site-dependent Heisenberg ferromagnetic spin chain with Gilbert damping under the influence of external magnetic field is expressed in the form of the Landau-Lifshitz-Gilbert equation in the classical continuum limit. The corresponding evolution equation is developed through stereographic projection technique by projecting the unit sphere of spin onto a complex plane. The exact soliton solutions are constructed by solving the associated evolution equation through the modified extended tanh-function method. The impact of damping and external magnetic field on the magnetic soliton under the invariant inhomogeneity is investigated and finally, the magnetization switching in the form of shape changing solitons are demonstrated.
Thick brane solitons breaking $Z_2$ symmetry
Peyravi, Marzieh; Lobo, Francisco S N
2015-01-01
New soliton solutions for thick branes in 4 + 1 dimensions are considered in this article. In particular, brane models based on the sine-Gordon (SG), $\\varphi^{4}$ and $\\varphi^{6}$ scalar fields are investigated; in some cases $Z_{2}$ symmetry is broken. Besides, these soliton solutions are responsible for supporting and stabilizing the thick branes. In these models, the origin of the symmetry breaking resides in the fact that the modified scalar field potential may have non-degenerate vacuua and these non-degenerate vacuua determine the cosmological constant on both sides of the brane. At last, in order to explore the particle motion in the neighborhood of the brane, the geodesic equations along the fifth dimension are studied.
Li Biao; Li Yuqi [Nonlinear Science Center, Ningbo University, Ningbo 315211 (China); Zhang Xiaofei; Liu, W M, E-mail: biaolee2000@yahoo.com.cn [Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing 100190 (China)
2011-09-14
We present two families of one-soliton solutions and three families of two-soliton solutions for a generalized nonlinear Schroedinger equation, which is characterized by the time-dependent scattering length and varying potentials. Then, we investigate the propagation of one-soliton and interactions of two-soliton by some selected control functions. The results show that the intensities of one- and two-soliton first increase rapidly to a peak value, and then decay very slowly to the background value; thus, the lifetimes of both one-soliton and two-soliton in Bose-Einstein condensates can be extended largely at least to the order of the lifetime of a Bose-Einstein condensate in real experiments. Our results open up new ways of considerable experimental interest for the management of matter-wave solitons in Bose-Einstein condensates.
Vortex solitons at the interface separating square and hexagonal lattices
Jović Savić, Dragana, E-mail: jovic@ipb.ac.rs; Piper, Aleksandra; Žikić, Radomir; Timotijević, Dejan
2015-06-19
Vortex solitons at the interface separating two different photonic lattices – square and hexagonal – are demonstrated numerically. We consider the conditions for the existence of discrete vortex states at such interfaces and develop a concise picture of different scenarios of the vortex solutions behavior. Various vortices with different size and topological charges are considered, as well as various lattice interfaces. A novel type of discrete vortex surface solitons in a form of five-lobe solution is observed. Besides stable three-lobe and six-lobe discrete surface modes propagating for long distances, we observe various oscillatory vortex surface solitons, as well as dynamical instabilities of different kinds of solutions and study their angular momentum. Dynamical instabilities occur for higher values of the propagation constant, or at higher beam powers. - Highlights: • We demonstrate vortex solitons at the square–hexagonal photonic lattice interface. • A novel type of five-lobe surface vortex solitons is observed. • Different phase structures of surface solutions are studied. • Orbital angular momentum transfer of such solutions is investigated.
Contributions to the application of solitons in optical communication systems
Mostofi, Amir
properties of solitons have been investigated. (5)The transformation of a dark soliton into a bright one has been numerically investigated as a possible solution to the relative difficulty faced in detecting dark solitons. An important requirement of the model was the Raman-induced energy transfer from the anomalous-dispersion mode to the normal-dispersion one.
Interactions of breathers and solitons of the extended Korteweg de Vries equation
Shek, C. M.; Grimshaw, R. H. J.; Ding, E.
2005-11-01
A popular model for the evolution of weakly nonlinear, weakly dispersive waves in the ocean is the extended Korteweg -- de Vries equation (eKdV), which incorporates both quadratic and cubic nonlinearities. The case of positive cubic nonlinearity allows for both solitons of elevation and depression, as well as breathers (pulsating modes). Multi-soliton solutions are computed analytically, and will yield expressions for breather-soliton interactions. Both the soliton and breather will retain their identities after interactions, but suffer phase shifts. However, the details of the interaction process will depend on the polarity of the interacting soliton, and have been investigated by a computer algebra software. This highly time dependent motion during the interaction process is important in nonlinear science and physical oceanography. As the dynamics of the current and an evolving internal oceanic tide can be modeled by eKdV, this knowledge is relevant to the temporal and spatial variability observed in the oceanic internal soliton fields.
On the problem of periodicity and hidden solitons for the KdV model.
Engelbrecht, Jüri; Salupere, Andrus
2005-03-01
In continuum limit, the Fermi-Pasta-Ulam lattice is modeled by a Korteweg-de Vries (KdV) equation. It is shown that the long-time behavior of a KdV soliton train emerging from a harmonic excitation has a regular periodicity of right- and left-going trajectories. In a soliton train not all the solitons are visible, the solitons with smaller amplitude are hidden and their influence is seen through the changes of phase shifts of larger solitons. In the case of an external harmonic force several resonance schemes are revealed where both visible and hidden solitons have important roles. The weak, moderate, strong, and dominating fields are distinguished and the corresponding solution types presented.
Effects of ion-fluid temperature on dust-ion-acoustic solitons
Fatema Sayed; A A Mamun
2008-03-01
The properties of dust-ion-acoustic (DIA) solitons in an unmagnetized dusty plasma, whose constituents are adiabatic ion-fluid, Boltzmann electrons, and static dust particles, are investigated by employing the reductive perturbation method. The Korteweg-de Vries equation is derived and its stationary solution is numerically analyzed. The parametric regimes for the existence of positive and negative solitons are found. It has been shown that ion-fluid temperature not only significantly modifies the basic features (width and amplitude) of DIA solitons, but also introduces some new features of DIA solitons.
Mixed dimensional infinite soliton trains for nonlinear Schr\\"odinger equations
Lin, LiRen; Tsai, Tai-Peng
2015-01-01
In this note we construct mixed dimensional infinite soliton trains, which are solutions of nonlinear Schr\\"odinger equations whose asymptotic profiles at time infinity consist of infinitely many solitons of multiple dimensions. For example infinite line-point soliton trains in 2D space, and infinite plane-line-point soliton trains in 3D space. This note extends the works of Le Coz, Li and Tsai [5, 6], where single dimensional trains are considered. In our approach, spatial $L^\\infty$ bounds ...
Bergshoeff, Eric; Townsend, Paul K.
1999-01-01
Energy bounds are derived for planar and compactified M2-branes in a hyper-KÃ¤hler background. These bounds are saturated, respectively, by lump and Q-kink solitons, which are shown to preserve half the worldvolume supersymmetry. The Q-kinks have a dual IIB interpretation as strings that migrate bet
Spatiotemporal optical solitons
Malomed, Boris A [Department of Interdisciplinary Studies, School of Electrical Engineering, Faculty of Engineering, Tel Aviv University, Tel Aviv 69978 (Israel); Mihalache, Dumitru [Department of Theoretical Physics, Institute of Atomic Physics, PO Box MG-6, Bucharest (Romania); Wise, Frank [Department of Applied Physics, 212 Clark Hall, Cornell University, Ithaca, NY 14853 (United States); Torner, Lluis [ICFO-Institut de Ciencies Fotoniques, and Department of Signal Theory and Communications, Universitat Politecnica de Catalunya, Barcelona 08034 (Spain)
2005-05-01
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)
Sigma-Model Solitons on Noncommutative Spaces
Dabrowski, Ludwik; Landi, Giovanni; Luef, Franz
2015-12-01
We use results from time-frequency analysis and Gabor analysis to construct new classes of sigma-model solitons over the Moyal plane and over noncommutative tori, taken as source spaces, with a target space made of two points. A natural action functional leads to self-duality equations for projections in the source algebra. Solutions, having nontrivial topological content, are constructed via suitable Morita duality bimodules.
Hamiltonian methods in the theory of solitons
Fadeev, Ludwig
1987-01-01
The main characteristic of this classic exposition of the inverse scattering method and its applications to soliton theory is its consistent Hamiltonian approach to the theory. The nonlinear Schrodinger equation is considered as a main example, forming the first part of the book. The second part examines such fundamental models as the sine-Gordon equation and the Heisenberg equation, the classification of integrable models and methods for constructing their solutions.
Self-trapped optical beams: Spatial solitons
Andrey A Sukhorukov; Yuri S Kivshar
2001-11-01
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.
Invariant measures and the soliton resolution conjecture
Chatterjee, Sourav
2012-01-01
The soliton resolution conjecture for the focusing nonlinear Schrodinger equation (NLS) is the vaguely worded claim that a global solution of the NLS, for generic initial data, will eventually resolve into a radiation component that disperses like a linear solution, plus a localized component that behaves like a soliton or multi-soliton solution. Considered to be one of the fundamental open problems in the area of nonlinear dispersive equations, this conjecture has eluded a proof or even a precise formulation till date. This paper proves a "statistical version" of this conjecture at mass-subcritical nonlinearity, in the following sense. The uniform probability distribution on the set of all functions with a given mass and energy, if such a thing existed, would be a natural invariant measure for the NLS flow and would reflect the long-term behavior for "generic initial data" with that mass and energy. Unfortunately, such a probability measure does not exist. We circumvent this problem by constructing a sequenc...
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.
New types of multisoliton solutions of some integrable equations via direct methods
Burde, Georgy I.
2016-06-01
Exact explicit solutions, which describe new multisoliton dynamics, have been identified for some KdV type equations using direct methods devised for this purpose. It is found that the equations, having multi-soliton solutions in terms of the KdV-type solitons, possess also an alternative set of multi-soliton solutions which include localized static structures that behave like (static) solitons when they collide with moving solitons. The alternative sets of solutions include the steady-state solution describing the static soliton itself and unsteady solutions describing mutual interactions in a system consisting of a static soliton and several moving solitons. As distinct from common multisoliton solutions those solutions represent combinations of algebraic and hyperbolic functions and cannot be obtained using the traditional methods of soliton theory.
Liu, De-Yin; Tian, Bo; Xie, Xi-Yang
2017-03-01
Bound-state vector soliton solutions for the coupled variable-coefficient higher-order nonlinear Schrödinger equations, which describe the simultaneous propagation of nonlinear waves in the inhomogeneous optical fiber, are investigated. Introducing auxiliary functions, we derive the bilinear forms and corresponding constraints on the variable coefficients. Through symbolic computation, we construct the one- and two-soliton solutions. We see that the variable coefficients in the equations affect the soliton structures. With different choices of the variable coefficients, we obtain the cubic, periodic, and parabolic solitons. Bound-state solitons and interactions are analyzed graphically.
Relativistic solitons and superluminal signals
Maccari, Attilio [Technical Institute ' G. Cardano' , Piazza della Resistenza 1, Monterotondo, Rome 00015 (Italy)]. E-mail: solitone@yahoo.it
2005-02-01
Envelope solitons in the weakly nonlinear Klein-Gordon equation in 1 + 1 dimensions are investigated by the asymptotic perturbation (AP) method. Two different types of solitons are possible according to the properties of the dispersion relation. In the first case, solitons propagate with the group velocity (less than the light speed) of the carrier wave, on the contrary in the second case solitons always move with the group velocity of the carrier wave, but now this velocity is greater than the light speed. Superluminal signals are then possible in classical relativistic nonlinear field equations.
Voronin, A. A.; Zheltikov, A. M.
2017-02-01
Analysis of the group-velocity dispersion (GVD) of atmospheric air with a model that includes the entire manifold of infrared transitions in air reveals a remarkably broad and continuous anomalous-GVD region in the high-frequency wing of the carbon dioxide rovibrational band from approximately 3.5 to 4.2 μm where atmospheric air is still highly transparent and where high-peak-power sources of ultrashort midinfrared pulses are available. Within this range, anomalous dispersion acting jointly with optical nonlinearity of atmospheric air is shown to give rise to a unique three-dimensional dynamics with well-resolved soliton features in the time domain, enabling a highly efficient whole-beam soliton self-compression of such pulses to few-cycle pulse widths.
One paramter family of solitons from minimal surfaces
Dey, Rukmini
2012-01-01
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. We find that the action or the energy of this family of solitons remains invariant in this family and find that the well-known Lorentz symmetry of the B-I equations is responsible for it.
One-Parameter Family of Solitons from Minimal Surfaces
Rukmini Dey; Pradip Kumar
2013-02-01
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. We find that the action or the energy of this family of solitons remains invariant in this family and find that the well-known Lorentz symmetry of the B–I equations is responsible for it.
Controllable Optical Solitons in Optical Fiber System with Distributed Coefficients
ZHANG Xiao-Fei; HE Wan-Quan; ZHANG Pei; ZHANG Peng
2011-01-01
We present how to control the dynamics of optical solitons in optical fibers under nonlinearity and dispersion management, together with the fiber loss or gain. We obtain a family of exact solutions for the nonlinear Schr(o)dinger equation, which describes the propagation of optical pulses in optical fibers, and investigate the dynamical features of solitons by analyzing the exact analytical solutions in different physical situations. The results show that under the appropriate condition, not only the group velocity dispersion and the nonlinearity, but also the loss/gain can be used to manipulate the light pulse.
The decay of Hopf solitons in the Skyrme model
Foster, David
2016-01-01
It is understood that the Skyrme model has a topologically interesting baryonic excitation which can model nuclei. So far no stable knotted solutions, of the Skyrme model, have been found. Here we investigate the dynamics of Hopf solitons decaying to the vacuum solution in the Skyrme model. In doing this we develop a matrix-free numerical method to identify the minimum eigenvalue of the Hessian of the corresponding energy functional. We also show that as the Hopf solitons decay, they emit a cloud of isospinning radiation.
On optical solitons of the Schrödinger-Hirota equation with power law nonlinearity in optical fibers
Aslan, Ebru Cavlak; Tchier, Fairouz; Inc, Mustafa
2017-05-01
In this study, we acquire optical soliton solutions of the Schrödinger-Hirota equation (SHE) in optical fiber. The integration algorithm employed in this work is the Jacobi elliptic function (JEF). We acquire new type JEF solutions, bright and dark optical solitons that are valuable in the field of optoelectronics. Constraint conditions are presented for the obtained solitons. The results show that this method is a powerful and efficient mathematical tool for solving problems in optical fibers. The remarkable features of such solitons are demonstrated by several interesting figures.
Effect of scalar field mass on gravitating charged scalar solitons and black holes in a cavity
Ponglertsakul, Supakchai; Winstanley, Elizabeth
2017-01-01
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.
Effect of scalar field mass on gravitating charged scalar solitons and black holes in a cavity
Ponglertsakul, Supakchai
2016-01-01
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.
Rehman, Momin A.; Mishra, M. K.
2016-01-01
The ion-acoustic solitons in collisionless plasma consisting of warm adiabatic ions, isothermal positrons, and two temperature distribution of electrons have been studied. Using reductive perturbation method, Korteweg-de Vries (K-dV), the modified K-dV (m-KdV), and Gardner equations are derived for the system. The soliton solution of the Gardner equation is discussed in detail. It is found that for a given set of parameter values, there exists a critical value of β=Tc/Th, (ratio of cold to hot electron temperature) below which only rarefactive KdV solitons exist and above it compressive KdV solitons exist. At the critical value of β, both compressive and rarefactive m-KdV solitons co-exist. We have also investigated the soliton in the parametric regime where the KdV equation is not valid to study soliton solution. In this region, it is found that below the critical concentration the system supports rarefactive Gardner solitons and above it compressive Gardner solitons are found. The effects of temperature ratio of two-electron species, cold electron concentration, positron concentration on the characteristics of solitons are also discussed.
Wang, Dengshan; Zhang, Hong-Qing
In this paper, making use of the truncated Laurent series expansion method and symbolic computation we get the auto-Bäcklund transformation of the (2 + 1)-dimensional Nizhnik-Novikov-Veselov equation. As a result, single soliton solution, single soliton-like solution, multi-soliton solution, multi-soliton-like solution, the rational solution and other exact solutions of the (2 + 1)-dimensional Nizhnik-Novikov-Veselov equation are found. These solutions may be useful to explain some physical phenomena.
Detecting Moving Targets by Use of Soliton Resonances
Zak, Michael; Kulikov, Igor
2003-01-01
A proposed method of detecting moving targets in scenes that include cluttered or noisy backgrounds is based on a soliton-resonance mathematical model. The model is derived from asymptotic solutions of the cubic Schroedinger equation for a one-dimensional system excited by a position-and-time-dependent externally applied potential. The cubic Schroedinger equation has general significance for time-dependent dispersive waves. It has been used to approximate several phenomena in classical as well as quantum physics, including modulated beams in nonlinear optics, and superfluids (in particular, Bose-Einstein condensates). In the proposed method, one would take advantage of resonant interactions between (1) a soliton excited by the position-and-time-dependent potential associated with a moving target and (2) eigen-solitons, which represent dispersive waves and are solutions of the cubic Schroedinger equation for a time-independent potential.
Pseudorelativistic effects on solitons in quantum semiconductor plasma.
Wang, Yunliang; Wang, Xiaodan; Jiang, Xiangqian
2015-04-01
A theory for nonlinear excitations in quantum plasmas is presented for narrow-gap semiconductors by considering the combined effects of quantum and pseudorelativity. The system is governed by a coupled Klein-Gordon equation for the collective wave functions of the conduction electrons and Poisson's equation for the electrostatic potential. This gives a closed system, including the effects of charge separation, quantum tunneling, and pseudorelativity. By choosing the typical parameters of semiconductor InSb, the quasistationary soliton solution, which is a multipeaked dark soliton, is obtained numerically and shows depleted electron densities correlated with a localized potential. The dynamical simulation result shows that the dark soliton is stable and has a multipeaked profile, which is consistent with the quasistationary solution. The present model and results may be useful in understanding the nonlinear properties of semiconductor plasma on an ultrafast time scale.
Pseudorelativistic effects on solitons in quantum semiconductor plasma
Wang, Yunliang; Wang, Xiaodan; Jiang, Xiangqian
2015-04-01
A theory for nonlinear excitations in quantum plasmas is presented for narrow-gap semiconductors by considering the combined effects of quantum and pseudorelativity. The system is governed by a coupled Klein-Gordon equation for the collective wave functions of the conduction electrons and Poisson's equation for the electrostatic potential. This gives a closed system, including the effects of charge separation, quantum tunneling, and pseudorelativity. By choosing the typical parameters of semiconductor InSb, the quasistationary soliton solution, which is a multipeaked dark soliton, is obtained numerically and shows depleted electron densities correlated with a localized potential. The dynamical simulation result shows that the dark soliton is stable and has a multipeaked profile, which is consistent with the quasistationary solution. The present model and results may be useful in understanding the nonlinear properties of semiconductor plasma on an ultrafast time scale.
Impurity solitons with quadratic nonlinearities
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 p...
Complex solitary waves and soliton trains in KdV and mKdV equations
Modak, Subhrajit; Singh, Akhil Pratap; Panigrahi, Prasanta Kumar
2016-06-01
We demonstrate the existence of complex solitary wave and periodic solutions of the Korteweg-de Vries (KdV) and modified Korteweg-de Vries (mKdV) equations. The solutions of the KdV (mKdV) equation appear in complex-conjugate pairs and are even (odd) under the simultaneous actions of parity (𝓟) and time-reversal (𝓣) operations. The corresponding localized solitons are hydrodynamic analogs of Bloch soliton in magnetic system, with asymptotically vanishing intensity. The 𝓟𝓣-odd complex soliton solution is shown to be iso-spectrally connected to the fundamental sech2 solution through supersymmetry. Physically, these complex solutions are analogous to the experimentally observed grey solitons of non-liner Schödinger equation, governing the dynamics of shallow water waves and hence may also find physical verification.
Two-component vector solitons in defocusing Kerr-type media with spatially modulated nonlinearity
Zhong, Wei-Ping, E-mail: zhongwp6@126.com [Department of Electronic and Information Engineering, Shunde Polytechnic, Guangdong Province, Shunde 528300 (China); Texas A and M University at Qatar, P.O. Box 23874 Doha (Qatar); Belić, Milivoj [Texas A and M University at Qatar, P.O. Box 23874 Doha (Qatar); Institute of Physics, University of Belgrade, P.O. Box 57, 11001 Belgrade (Serbia)
2014-12-15
We present a class of exact solutions to the coupled (2+1)-dimensional nonlinear Schrödinger equation with spatially modulated nonlinearity and a special external potential, which describe the evolution of two-component vector solitons in defocusing Kerr-type media. We find a robust soliton solution, constructed with the help of Whittaker functions. For specific choices of the topological charge, the radial mode number and the modulation depth, the solitons may exist in various forms, such as the half-moon, necklace-ring, and sawtooth vortex-ring patterns. Our results show that the profile of such solitons can be effectively controlled by the topological charge, the radial mode number, and the modulation depth. - Highlights: • Two-component vector soliton clusters in defocusing Kerr-type media are reported. • These soliton clusters are constructed with the help of Whittaker functions. • The half-moon, necklace-ring and vortex-ring patterns are found. • The profile of these solitons can be effectively controlled by three soliton parameters.
Thermophoresis of an antiferromagnetic soliton
Kim, Se Kwon; Tchernyshyov, Oleg; Tserkovnyak, Yaroslav
2015-07-01
We study the dynamics of an antiferromagnetic soliton under a temperature gradient. To this end, we start by phenomenologically constructing the stochastic Landau-Lifshitz-Gilbert equation for an antiferromagnet with the aid of the fluctuation-dissipation theorem. We then derive the Langevin equation for the soliton's center of mass by the collective coordinate approach. An antiferromagentic soliton behaves as a classical massive particle immersed in a viscous medium. By considering a thermodynamic ensemble of solitons, we obtain the Fokker-Planck equation, from which we extract the average drift velocity of a soliton. The diffusion coefficient is inversely proportional to a small damping constant α , which can yield a drift velocity of tens of m/s under a temperature gradient of 1 K/mm for a domain wall in an easy-axis antiferromagnetic wire with α ˜10-4 .
Breather soliton dynamics in microresonators
Yu, Mengjie; Okawachi, Yoshitomo; Griffith, Austin G; Luke, Kevin; Miller, Steven A; Ji, Xingchen; Lipson, Michal; Gaeta, Alexander L
2016-01-01
The generation of temporal cavity solitons in microresonators results in low-noise optical frequency combs which 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 with a localized temporal structure that exhibits oscillatory behavior. 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 in good agreement with the numerical simulations. Our study presents experimental confirmation of the stability diagram of dissipative cavity solitons predicted by the Lugiato-Lefever equation and is importance to understandin...
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.
ZHANG Xiao-Fei; ZHANG Pei; YANG Qin
2008-01-01
We obtain the integrable relation for the one-dimensional nonlinear Schrodinger equations which describes the dynamics of a Bose-Einstein Condensates with time-dependent scattering length in a harmonic potential. The exact one-and two-soliton solutions are constructed analytically by using the Hirota method. Then we further discuss the dynamics of the one soliton and the interactions between two solitons in currently experimental conditions.
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.
Zayed, Elsayed M. E.; Al-Nowehy, Abdul-Ghani; Elshater, Mona E. M.
2017-06-01
The (G^'/G)-expansion method, the improved Sub-ODE method, the extended auxiliary equation method, the new mapping method and the Jacobi elliptic function method are applied in this paper for finding many new exact solutions including Jacobi elliptic solutions, solitary solutions, singular solitary solutions, trigonometric function solutions and other solutions to the nonlinear Schrödinger equation with fourth-order dispersion and dual power law nonlinearity whose balance number is not positive integer. The used methods present a wider applicability for handling the nonlinear partial differential equations. A comparison of our new results with the well-known results is made. Also, we compare our results with each other yielding from these five integration tools.
Solitons riding on solitons and the quantum Newton's cradle
Ma, Manjun; Navarro, R.; Carretero-González, R.
2016-02-01
The reduced dynamics for dark and bright soliton chains in the one-dimensional nonlinear Schrödinger equation is used to study the behavior of collective compression waves corresponding to Toda lattice solitons. We coin the term hypersoliton to describe such solitary waves riding on a chain of solitons. It is observed that in the case of dark soliton chains, the formulated reduction dynamics provides an accurate an robust evolution of traveling hypersolitons. As an application to Bose-Einstein condensates trapped in a standard harmonic potential, we study the case of a finite dark soliton chain confined at the center of the trap. When the central chain is hit by a dark soliton, the energy is transferred through the chain as a hypersoliton that, in turn, ejects a dark soliton on the other end of the chain that, as it returns from its excursion up the trap, hits the central chain repeating the process. This periodic evolution is an analog of the classical Newton's cradle.
Periodic modulations controlling Kuznetsov–Ma soliton formation in nonlinear Schrödinger equations
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.
Effect of interaction strength on gap solitons of Bose-Einstein condensates in optical lattices
Yang Ru-Shu; Yang Jiang-He
2008-01-01
We have developed a systematic analytical approach to the study on the dynamic properties of the linear and the nonlinear excitations for quasi-one-dimensional Bose-Einstein condensate trapped in optical lattices. A novel linear dispersion relation and an algebraic soliton solution of the condensate are derived analytically under consideration of Bose-Einstein condensate with a periodic potential. By analysing the soliton solution, we find that the interatomic interaction strength has an important effect on soliton dynamic properties of Bose-Einstein condensate.
Generation of bright soliton through the interaction of black solitons
Losano, L; Bazeia, D
2001-01-01
We report on the possibility of having two black solitons interacting inside a silica fiber that presents normal group-velocity dispersion, to generate a pair of solitons, a vector soliton of the black-bright type. The model obeys a pair of coupled nonlinear Schr\\"odinger equations, that follows in accordance with a Ginzburg-Landau equation describing the anisotropic XY model. We solve the coupled equations using a trial-orbit method, which plays a significant role when the Schr\\"odinger equations are reduced to first order differential equations.
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.
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
Halyo, Edi
2009-01-01
We describe solitons that live on the world--volumes of D5 branes wrapped on deformed $A_2$ singularities fibered over $C(x)$. We show that monopoles are D3 branes wrapped on a node of the deformed singularity and stretched along $C(x)$. F and D--term strings are D3 branes wrapped on a node of a singularity that is deformed and resolved respectively. Domain walls require deformed $A_3$ singularities and correspond to D5 branes wrapped on a node and stretched along $C(x)$.
A periodic phase soliton of the ultradiscrete hungry Lotka-Volterra equation
Nakamura, Shinya [Major in Pure and Applied Mathematics, Graduate School of Fundamental Science and Engineering, Waseda University, 3-4-1, Okubo, Shinjuku-ku, Tokyo 169-8555 (Japan)], E-mail: s-nakamura@moegi.waseda.jp
2009-12-11
We propose a new type of solution to the ultradiscrete hungry Lotka-Volterra (uhLV) equation. For the solution, the periodic phase is introduced into the known soliton and the extended soliton becomes a traveling wave showing a periodic variation. We call this type of wave a 'periodic phase soliton' (PPS). The solution has two forms of expression: one is the 'perturbation form' and the other is the 'ultradiscrete permanent form'. We analyze the interaction among PPSs and solitons. Moreover, we give the outline of proof to show that the solution satisfies the bilinear equation of the uhLV equation.
SELF-SIMILAR SOLUTIONS AND BLOW-UP PHENOMENA FOR A TWO-COMPONENT SHALLOW WATER SYSTEM
Shouming ZHOU; Chunlai MU; Liangchen WANG
2013-01-01
In this article,we consider a two-component nonlinear shallow water system,which includes the famous 2-component Camassa-Holm and Degasperis-Procesi equations as special cases.The local well-posedess for this equations is established.Some sufficient conditions for blow-up of the solutions in finite time are given.Moreover,by separation method,the self-similar solutions for the nonlinear shallow water equations are obtained,and which local or global behavior can be determined by the corresponding Emden equation.
Experiments on extreme wave generation using the Soliton on Finite Background
Huijsmans, R H M; Karjanto, N; Andonowati,
2011-01-01
A theoretical model of Soliton on Finite Background of a family of exact solution of the nonlinear Schr\\"{o}dinger equation for extreme wave generation is discussed in this paper. Some characteristics and physical properties of this solution are explained. The comparisons with experimental results from MARIN and with the simulation result from nonlinear wave model HUBRIS are also presented. The occurrence of phase singularity is observed, as predicted by the theoretical model of Soliton on Finite Background.
Belmonte-Beitia, Juan [Departamento de Matematicas, E. T. S. de Ingenieros Industriales, Universidad de Castilla-La Mancha 13071, Ciudad Real (Spain); Perez-Garcia, Victor M. [Departamento de Matematicas, E. T. S. de Ingenieros Industriales, Universidad de Castilla-La Mancha 13071, Ciudad Real (Spain); Vekslerchik, Vadym [Departamento de Matematicas, E. T. S. de Ingenieros Industriales, Universidad de Castilla-La Mancha 13071, Ciudad Real (Spain)
2007-05-15
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.
Solitons of a vector model on the honeycomb lattice
Vekslerchik, V. E.
2016-11-01
We study a simple nonlinear vector model defined on the honeycomb lattice. We propose a bilinearization scheme for the field equations and demonstrate that the resulting system is closely related to the well-studied integrable models, such as the Hirota bilinear difference equation and the Ablowitz-Ladik system. This result is used to derive the N-soliton solutions.
Gap solitons in periodic Schrodinger lattice system with nonlinear hopping
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.
Propagation and interaction of solitons for nonintegrable equations
Omel'yanov, G.
2016-04-01
We describe an approach to the construction of multi-soliton asymptotic solutions for nonintegrable equations. The general idea is realized in the case of N waves, N = 1, 2, 3, and for the KdV-type equation with nonlinearity u 4. A brief review of asymptotic methods as well as results of numerical simulation are included.
Solitons in ideal optical fibers: a numerical development
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.
Solitons in a relativistic plasma with negative ions--
Das, G.C. (Dept. of Mathematics, Manipur Univ. Canchipur, Imphal-795003 (IN)); Karmakar, B. (Dept. of Mathematics, Dinabandhu College, Bongaon, Calcutta (IN)); Ibohanbi Singh, KH. (Dept. of Mathematics, Modern College, Imphal-795001 (IN))
1990-02-01
The interaction of the nonlinearity and the dispersiveness causing the solitary waves are studied in a relativistic plasma with negative ions through the derivation of a nonlinear partial differential equation known as the Korteweg-Devries (K-DV) equation. The negative ions play a salient feature on the existence and behavior of the solitons and could be of interest in laboratory plasmas. First, the observations are made in a nonisothermal plasma, and later the reduction to the nonisothermality of the plasma shows entirely different characteristics as compared to the solitons in the isothermal plasmas. A comparison with the various solutions has been emphasized.
Interaction of fast magnetoacoustic solitons in dense plasmas
Jahangir, R.; Saleem, Khalid [National Centre for Physics (NCP) Shahdra Valley Road, Islamabad (Pakistan); Quaid-i-Azam University, Islamabad (Pakistan); Masood, W. [National Centre for Physics (NCP) Shahdra Valley Road, Islamabad (Pakistan); COMSATS Institute of Information Technology, Pak Road, Chak Shahzad, Islamabad (Pakistan); Siddiq, M.; Batool, Nazia [National Centre for Physics (NCP) Shahdra Valley Road, Islamabad (Pakistan)
2015-09-15
One dimensional propagation of fast magnetoacoustic solitary waves in dense plasmas with degenerate electrons is investigated in this paper in the small amplitude limit. In this regard, Korteweg deVries equation is derived and discussed using the plasma parameters that are typically found in white dwarf stars. The interaction of fast magnetoacoustic solitons is explored by using the Hirota bilinear formalism, which admits multi soliton solutions. It is observed that the values of the propagation vectors determine the interaction of solitary waves. It is further noted that the amplitude of the respective solitary waves remain unchanged after the interaction; however, they do experience a phase shift.
Interaction of solitons with a string of coupled quantum dots
Kumar, Vijendra; Swami, O. P.; Taneja, S.; Nagar, A. K.
2016-05-01
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.
Ion-acoustic solitons in negative ion plasma with two-electron temperature distributions
Mishra, M. K.; Tiwari, R. S.; Chawla, J. K. [Department of Physics, University of Rajasthan, Jaipur-302004 (India)
2012-06-15
Ion-acoustic solitons in a warm positive and negative ion species with different masses, concentrations, and charge states with two electron temperature distributions are studied. Using reductive perturbation method, Korteweg de-Vries (KdV) and modified-KdV (m-KdV) equations are derived for the system. The soliton solution of the KdV and m-KdV equations is discussed in detail. It is found that if the ions have finite temperatures, then there exist two types of modes, namely slow and fast ion-acoustic modes. It is also investigated that the parameter determining the nature of soliton (i.e., whether the system will support compressive or rarefactive solitons) is different for slow and fast modes. For the slow mode, the parameter is the relative temperature of the two ion species; whereas for the fast mode, it is the relative concentration of the two ion species. At a critical concentration of negative ions, both compressive and rarefactive solitons coexist. The amplitude and width of the solitons are discussed in detail at critical concentration for m-KdV solitons. The effect of the relative temperature of the two-electron and cold-electron concentration on the characteristics of the solitons are also discussed.
Lucas, Erwan; Kippenberg, Tobias J
2016-01-01
Temporal dissipative Kerr solitons in a continuous-wave laser-driven nonlinear optical microresonator enable compact, high-repetition rate sources of ultrashort pulses and coherent broadband optical frequency combs. A central parameter in the soliton formation process, is the effective detuning of the pump laser to the thermally- and Kerr-shifted cavity resonance, which, together with the free spectral range and dispersion, governs the soliton pulse duration. Here, we introduce a technique to probe, stabilize, and control the effective detuning of a driven nonlinear crystalline resonator while monitoring the dissipative Kerr soliton properties, which enables to study the detuning-dependent soliton properties and accurate comparisons of the theoretical predictions with experiments. We demonstrate that the experimentally measured relation between detuning and soliton duration deviates by less than 1% from the analytical solution, demonstrating its excellent predictive power. In contrast, avoided mode crossings,...
宣恒农; 左苗
2011-01-01
We present three families of exact matter-wave soliton solutions for an effective one-dimension two- component Bose-Einstein condensates （BECs） with tunable interactions, harmonic potential and gain or loss term. We investigate the dynamics of bright-bright solitons, bright-dark solitons and dark-dark solitons for the time-dependent expulsive harmonic trap potential, periodically modulated harmonic trap potential, and kinklike modulated harmonic trap potential. Through the Feshbach resonance, these dynamics can be realized in experiments by suitable control of time-dependent trap parameters, atomic interactions, and interaction with thermal cloud.
Generation of dark solitons in erbium-doped fiber lasers based Sb(2)Te(3) saturable absorbers.
Liu, Wenjun; Pang, Lihui; Han, Hainian; Tian, Wenlong; Chen, Hao; Lei, Ming; Yan, Peiguang; Wei, Zhiyi
2015-10-05
Dark solitons, which have better stability in the presence of noise, have potential applications in optical communication and ultrafast optics. In this paper, the dark soliton formation in erbium-doped fiber lasers based Sb(2)Te(3) saturable absorber (SA) is first experimentally demonstrated. The Sb(2)Te(3) SA is fabricated by using the pulsed laser deposition method. The generated dark solitons are centered at the wavelength of 1530 nm and repetition rate of 94 MHz. Analytic solutions for dark solitons are also obtained theoretically.
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
Soliton-based ultra-high speed optical communications
Akira Hasegawa
2001-11-01
Multi-terabit/s, ultra-high speed optical transmissions over several thousands kilometers on ﬁbers are becoming a reality. Most use RZ (Return to Zero) format in dispersion-managed ﬁbers. This format is the only stable waveform in the presence of ﬁber Kerr nonlinearity and dispersion in all optical transmission lines with loss compensated by periodic ampliﬁcations. The nonlinear Schrödinger equation assisted by the split step numerical solutions is commonly used as the master equation to describe the information transfer in optical ﬁbers. All these facts are the outcome of research on optical solitons in ﬁbers in spite of the fact that the commonly used RZ format is not always called a soliton format. The overview presented here attempts to incorporate the role of soliton-based communications research in present day ultra-high speed communications.
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.
Haris, H.; Harun, S. W.; Anyi, C. L.; Muhammad, A. R.; Ahmad, F.; Tan, S. J.; Nor, R. M.; Zulkepely, N. R.; Ali, N. M.; Arof, H.
2016-04-01
We report an observation of soliton and bound-state soliton in passive mode-locked fibre laser employing graphene film as a passive saturable absorber (SA). The SA was fabricated from the graphene flakes, which were obtained from electrochemical exfoliation process. The graphene flakes was mixed with polyethylene oxide solution to form a polymer composite, which was then dried at room temperature to produce a film. The film was then integrated in a laser cavity by attaching it to the end of a fibre ferrule with the aid of index matching gel. The fibre laser generated soliton pulses with a 20.7 MHz repetition rate, 0.88 ps pulse width, 0.0158 mW average output power, 0.175 pJ pulse energy and 18.72 W peak power at the wavelength of 1564 nm. A bound soliton with pulse duration of ~1.04 ps was also obtained at the pump power of 110.85 mW by carefully adjusting the polarization of the oscillating laser. The formation of bound soliton is due to the direct pulse to pulse interaction. The results show that the proposed graphene-based SA offers a simple and cost efficient approach of generating soliton and bound soliton in mode-locked EDFL set-up.
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.
Solitons, compactons and undular bores in Benjamin–Bona–Mahony-like systems
APARNA SAHA; B TALUKDAR; UMAPADA DAS; SUPRIYA CHATTERJEE
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 islinear 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.
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...
HONG-YU WU; LI-HONG JIANG
2017-09-01
From a generic transformation, a $(3+1)$-dimensional nonlinear Schrödinger equation with spatially modulated nonlinearity is studied and exact spatiotemporal soliton cluster solutions are derived. When the azimuthal parameter $m = 0$, Gaussian solitons are constructed. For the modulation depth $q = 1$ and the azimuthal parameter $m \
Dynamics of solitons and quasisolitons of the cubic third-order nonlinear Schrödinger equation
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...
Wu, Hong-Yu; Jiang, Li-Hong
2017-09-01
From a generic transformation, a (3+1)-dimensional nonlinear Schrödinger equation with spatially modulated nonlinearity is studied and exact spatiotemporal soliton cluster solutions are derived. When the azimuthal parameter m = 0, Gaussian solitons are constructed. For the modulation depth q = 1 and the azimuthal parameter m\
Thermodynamic volume of cosmological solitons
Mbarek, Saoussen; Mann, Robert B.
2017-02-01
We present explicit expressions of the thermodynamic volume inside and outside the cosmological horizon of Eguchi-Hanson solitons in general odd dimensions. These quantities are calculable and well-defined regardless of whether or not the regularity condition for the soliton is imposed. For the inner case, we show that the reverse isoperimetric inequality is not satisfied for general values of the soliton parameter a, though a narrow range exists for which the inequality does hold. For the outer case, we find that the mass Mout satisfies the maximal mass conjecture and the volume is positive. We also show that, by requiring Mout to yield the mass of dS spacetime when the soliton parameter vanishes, the associated cosmological volume is always positive.
Thermodynamic Volume of Cosmological Solitons
Mbarek, Saoussen
2016-01-01
We present explicit expressions of the thermodynamic volume inside and outside the cosmological horizon of Eguchi-Hanson solitons in general odd dimensions. These quantities are calculable and well-defined regardless of whether or not the regularity condition for the soliton is imposed. For the inner case, we show that the reverse isoperimetric inequality is not satisfied for general values of the soliton parameter $a$, though a narrow range exists for which the inequality does hold. For the outer case, we find that the mass $M_{out}$ satisfies the maximal mass conjecture and the volume is positive. We also show that, by requiring $M_{out}$ to yield the mass of dS spacetime when the soliton parameter vanishes, the associated cosmological volume is always positive.
Soliton models for thick branes
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.)
Zdravković, S; Daniel, M
2012-01-01
We here examine the nonlinear dynamics of artificial homogeneous DNA chain relying on the plain-base rotator model. It is shown that such dynamics can exhibit kink and antikink solitons of sine-Gordon type. In that respect we propose possible experimental assays based on single molecule micromanipulation techniques. The aim of these experiments is to excite the rotational waves and to determine their speeds along excited DNA. We propose that these experiments should be conducted either for the case of double stranded (DS) or single stranded (SS) DNA. A key question is to compare the corresponding velocities of the rotational waves indicating which one is bigger. The ratio of these velocities appears to be related with the sign of the model parameter representing ratio of the hydrogen-bonding and the covalent-bonding interaction within the considered DNA chain.
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.
Chaos, solitons and fractals in hidden symmetry models
Maccari, Attilio [Technical Institute ' G. Cardano' , Piazza della Resistenza 1, 00015 Monterotondo, Rome (Italy)] e-mail: solitone@yahoo.it
2006-01-01
A spontaneous symmetry breaking (or hidden symmetry) model is reduced to a system nonlinear evolution equations integrable via an appropriate change of variables, by means of the asymptotic perturbation (AP) method, based on spatio-temporal rescaling and Fourier expansion. It is demonstrated the existence of coherent solutions as well as chaotic and fractal patterns, due to the possibility of selecting appropriately some arbitrary functions. Dromion, lump, breather, instanton and ring soliton solutions are derived and the interaction between these coherent solutions are completely elastic, because they pass through each other and preserve their shapes and velocities, the only change being a phase shift. Finally, one can construct lower dimensional chaotic patterns such as chaotic-chaotic patterns, periodic-chaotic patterns, chaotic soliton and dromion patterns. In a similar way, fractal dromion and lump patterns as well as stochastic fractal excitations can appear in the solution.
Various types of phase transitions in the AdS soliton background
Peng, Yan; Wang, Bin
2011-01-01
We study the basic holographic insulator and superconductor phase transition in the AdS soliton background by generalizing the spontaneous breaking of a global U(1) symmetry to occur via St$\\ddot{u}$ckelberg mechanism. We construct the soliton solutions with backreaction and examine the effects of the backreaction on the condensation of the scalar hair in the generalized St$\\ddot{u}$ckelberg Lagrangian. We disclose rich physics in various phase transitions. In addition to the AdS soliton configuration, we also examine the property of the phase transition in the AdS black hole background.
Head-on collision of ring dark solitons in Bose-Einstein condensates
Xue Ju-Kui; Peng Ping
2006-01-01
The ring dark solitons and their head-on collisions in a Bose-Einstein condensates with thin disc-shaped potential are studied. It is shown that the system admits a solution with two concentric ring solitons, one moving inwards and the other moving outwards, which in small-amplitude limit, are described by the two cylindrical KdV equations in the shifts following the head-on collisions between two ring dark solitary waves are derived. It is shown that the phase shifts decrease with the radial coordinate r according to the r-1/3 law and depend on the initial soliton amplitude and radius.
Evolution and Stability of Dark Holographic Solitons in Photorefractive Dissipative Systems
ZHANG Hui-Lan; LIU Jin-Song
2006-01-01
@@ The dynamics evolution of dark holographic solutions in a dissipative system is investigated namerically provided that the double balance, i.e. diffraction is balanced by nonlinearity and loss is balanced by gain, is satisfied. The influence of the system parameters, such as the linear loss of the crystal, the external biased field and the angel between input beams, on the stable propagation of soliton beams is discussed numerically. Results show that such solitons can be easily amplified or absorbed by adjusting these system parameters. Furthermore, numerical simulations indicate that dissipative dark holographic solitons are stable for small perturbation on amplitude.
Strong Internal Wave Solitons in a 2.5 Layer Model
Voronovich, A.
2003-04-01
"Strong" internal wave (IW) solitons, i.e. IW solitary waves with amplitudes comparable to the characteristic vertical scale of stratification are often observed in field experiments. Theoretical description of such solitons is usually based on a 2-layer model, which approximates stratification by two layers of homogeneous fluid with different densities (another possibility is to assume nearly-exponential density profile). Appropriate solitons are investigated in detail by Choi and Camassa (J. Fluid Mech., v. 396, pp. 1-36, 1999). In geophysical applications, however, stratification can be better represented by layers with constant Brunt-Vaisala frequency profiles. The model consisting of two such layers with a density jump between the layers is referred here as a "2.5 layer model". Motion in this case is not potential, however similarly to homogeneous layers, equation of motion in such system in stationary case and in the Boussinesq approximation is also linear, and non-linearity appears due to dynamic boundary condition between layers only. This allows one in the case of long waves to obtain an explicit equation for IW soliton profile. This equation can be reduced to the equation describing zero-energy particle in a potential well. In the case of homogeneous layers with zero density gradients they reduce to the solitons investigated by Choi and Camassa, and in the limit of small amplitudes they reduce to the appropriate KdV solitons. This solution was applied to the case of solitons measured in the COPE experiment. Soliton profiles calculated are in a good agreement with measurements, and the relation between soliton width and amplitude is also in a fair agreement with the data, especially for large-amplitude solitons. In contrast to the two-layer model solitons in the 2.5 layer model could belong to higher modes. Another interesting feature is a presence in a sufficiently strong soliton of a recirculation core, i.e. a portion of fluid which is entrained within
Spatiotemporal accessible solitons in fractional dimensions
Zhong, Wei-Ping; Malomed, Boris A; Zhang, Yiqi; Huang, Tingwen
2016-01-01
We report solutions for solitons of the "accessible" type in globally nonlocal nonlinear media of fractional dimension (FD), viz., for self-trapped modes in the space of effective dimension $2
On the structure of gradient Yamabe solitons
Cao, Huai-Dong; Zhang, Yingying
2011-01-01
We show that every complete nontrivial gradient Yamabe soliton admits a special global warped product structure with a one-dimensional base. Based on this, we prove a general classification theorem for complete nontrivial locally conformally flat gradient Yamabe solitons.
Waveguides induced by grey screening solitons
Lu Ke-Qing; Zhao Wei; Yang Yan-Long; Zhang Mei-Zhi; Li Jin-Ping; Liu Hong-Jun; Zhang Yan-Peng
2006-01-01
We investigate the properties of waveguides induced by one-dimensional grey screening solitons in biased photore-fractive crystals. The results show that waveguides induced by grey screening solitons are always of single mode for all intensity ratios, i.e. the ratios between the peak intensity of the soliton and the dark irradiance. Our analysis indicates that the energy confined near the centre of the grey soliton and the propagation constant of the guided mode of the waveguide induced by the grey screening soliton increase monotonically with intensity ratio increasing. On the other hand, when the soliton greyness increases, the energy confined near the centre of the grey soliton and the propagation constant of the guided mode of the waveguide induced by the grey screening soliton decrease monotonically. Relevant examples are provided where photorefractive crystal is of the strontium barium niobate type.
Asymptotics of perturbed soliton for Davey-Stewartson; 2, equation
Gadylshin, R R
1998-01-01
It is shown that, under a small perturbation of lump (soliton) for Davey-Stewartson (DS-II) equation, the scattering data gain the nonsoliton structure. As a result, the solution has the form of Fourier type integral. Asymptotic analysis shows that, in spite of dispertion, the principal term of the asymptotic expansion for the solution has the solitary wave form up to large time.
Kerr-Newman electron as spinning soliton
Burinskii, Alexander
2014-01-01
Measurable parameters of the electron indicate that its background should be described by the Kerr-Newman (KN) solution. Spin/mass ratio of the electron is extreme large, and the black hole horizons disappear, opening a topological defect of spacetime -- the Kerr singular ring of the Compton size, which may be interpreted as a closed fundamental string to the low energy string theory. The singular and twosheeted structure of the corresponding Kerr space has to be regularized, and we consider the old problem of regular source of the KN solution. As a development of the earlier Keres-Israel-Hamity-L\\'opez model, we describe the model of smooth and regular source forming a gravitating and relativistically rotating soliton based on the chiral field model and the Higgs mechanism of broken symmetry. The model reveals some new remarkable properties: 1) the soliton forms a relativistically rotating bubble of the Compton radius, which is filled by the oscillating Higgs field in pseudo-vacuum state, 2) boundary of the ...
Soliton Interactions of the “Good” Boussinesq Equation on a Nonzero Background
Zha, Xiao; Sun, He; Xu, Tao; Meng, Xiang-Hua; Li, Heng-Ji
2015-10-01
In this paper, we obtain the soliton solutions for the “good” Boussinesq equation on a constant background. Based on the asymptotic analysis of the solutions, we find that this equation admits both the elastic and resonant soliton interactions, as well as various partially inelastic interactions comprised of such two fundamental interactions. Via picture drawing, we present some examples of soliton interactions on nonzero backgrounds. Our results enrich the knowledge of soliton interactions in the (1+1)-dimensional integrable equation with a single field. Supported by the Science Foundation of China University of Petroleum, Beijing under Grant Nos. 2462015YQ0604 and 2462015QZDX02, the Special Funds of the National Natural Science Foundation of China under Grant No. 11247267, and the National Natural Science Foundation of China under Grant Nos. 11371371 and 11401031
Numerical Calculation of a Standing Soliton
XianchuZHOU; YiRUI
1999-01-01
The governing equation of a standing soliton i.e. a cubic Schroedinger equation with a complex conjugate term was simulated in this article.The simulation showed that the linear damping α affects strongly on the formation of a stable standing soliton.Laedke and Spatschek stable condition is a necessary condition,not a sufficient condition.Arbitrary initial disturbance may develop into standing soliton.The interaction of two standing solitons can be simulated.
Analytical theory of dark nonlocal solitons
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.......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....
Properties of an optical soliton gas
Schwache, A.; Mitschke, F.
1997-06-01
We consider light pulses propagating in an optical fiber ring resonator with anomalous dispersion. New pulses are fed into the resonator in synchronism with its round-trip time. We show that solitary pulse shaping leads to a formation of an ensemble of subpulses that are identified as solitons. All solitons in the ensemble are in perpetual relative motion like molecules in a fluid; thus we refer to the ensemble as a soliton gas. Properties of this soliton gas are determined numerically.
Collapse of Langmuir solitons in inhomogeneous plasmas
Chen, Y A; Nishida, Y; Cheng, C Z
2016-01-01
Propagation of Langmuir solitons in inhomogeneous plasmas is investigated numerically. Through numerical simulation solving Zakharov equations, the solitons are accelerated toward the low density side. As a consequence, isolated cavities moving at ion sound velocities are emitted. When the acceleration is further increased, solitons collapse and the cavities separate into two lumps released at ion sound velocities. The threshold is estimated by an analogy between the soliton and a particle overcoming the self-generated potential well.
Spatial solitons in nonlinear photonic crystals
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....
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.
Control of optical solitons by light waves.
Grigoryan, V S; Hasegawa, A; Maruta, A
1995-04-15
A new method of controlling optical solitons by means of light wave(s) in fibers is presented. By a proper choice of light wave(s), parametric four-wave mixing can control the soliton shape as well as the soliton parameters (amplitude, frequency, velocity, and position).
THE PHYSICAL MECHANISM OF COLLISION BETWEEN SOLITONS
张卓; 唐翌; 颜晓红
2001-01-01
An easy and general way to access more complex soliton phenomena is introduced in this paper. The collisionprocess between two solitons of the KdV equation is investigated in great detail with this novel approach, which is different from the sophisticated method of inverse scattering transformation. A more physical and transparent picture describing the collision of solitons is presented.
Soliton bunching in annular Josephson junctions
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 modulation instability in fiber lasers
Tang, D. Y.; Zhao, L. M.; Wu, X.; Zhang, H.
2009-08-01
We report experimental evidence of soliton modulation instability in erbium-doped fiber lasers. An alternate type of spectral sideband generation was always experimentally observed on the soliton spectrum of the erbium-doped soliton fiber lasers when energy of the formed solitons reached beyond a certain threshold value. Following this spectral sideband generation, if the pump power of the lasers was further increased, either a new soliton would be formed or the existing solitons would experience dynamical instabilities, such as the period-doubling bifurcations or period-doubling route to chaos. We point out that the mechanism for this soliton spectral sideband generation is the modulation instability of the solitons in the lasers. We further show that, owing to the internal energy balance of a dissipative soliton, modulation instability itself does not destroy the stable soliton evolution in a laser cavity. It is the strong resonant wave coupling between the soliton and dispersive waves that leads to the dynamic instability of the solitons.
Attraction of nonlocal dark optical solitons
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...... of dark solitons. (C) 2004 Optical Society of America...
Incoherently Coupled Grey Photovoltaic Spatial Soliton Families
WANG Hong-Cheng; SHE Wei-Long
2005-01-01
@@ A theory is developed for incoherently coupled grey photovoltaic soliton families in unbiased photovoltaic crystals.Both the properties and the forming conditions of these soliton families are discussed in detail The theory canalso be used to investigate the dark photovoltaic soliton families. Some relevant examples are presented, in which the photovoltaic-photorefractive crystal is of lithium niobate type.
Sun, Yan; Tian, Bo; Wu, Xiao-Yu; Liu, Lei; Yuan, Yu-Qiang
2017-04-01
Under investigation in this paper is a variable-coefficient higher-order nonlinear Schrödinger equation, which has certain applications in the inhomogeneous optical fiber communication. Through the Hirota method, bilinear forms, dark one- and two-soliton solutions for such an equation are obtained. We graphically study the solitons with d1(z), d2(z) and d3(z), which represent the variable coefficients of the group-velocity dispersion, third-order dispersion and fourth-order dispersion, respectively. With the different choices of the variable coefficients, we obtain the parabolic, periodic and V-shaped dark solitons. Head-on and overtaking collisions are depicted via the dark two soliton solutions. Velocities of the dark solitons are linearly related to d1(z), d2(z) and d3(z), respectively, while the amplitudes of the dark solitons are not related to such variable coefficients.
A small-amplitude study of solitons near critical plasma compositions
Olivier, Carel P.; Verheest, Frank; Maharaj, Shimul K.
2016-12-01
The properties of small-amplitude solitons are established near critical plasma compositions in a generalized fluid plasma with an arbitrary number of species. The study is conducted via a Taylor series expansion of the Sagdeev potential. It is shown that there are two types of critical compositions, namely rich critical and poor critical compositions. The coexistence of positive and negative polarity solitons is shown to arise at rich critical compositions and near rich critical compositions. At poor critical compositions, no small-amplitude solitons exist, while weak double layers arise near poor critical compositions. A novel analytical expression is obtained for a small-amplitude acoustic speed soliton solution near rich critical compositions. These solitons have a Lorentzian shape with much fatter tails than regular solitons. A case study is also performed for a simple fluid model consisting of cold ions and two Boltzmann electron species. Exact agreement is obtained between the Sagdeev analysis and reductive perturbation theory. For the first time, we derive the same Lorentzian acoustic speed soliton from reductive perturbation theory.
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 ...
Kakad, Amar [Research Institute for Sustainable Humanosphere, Kyoto University, Uji, Kyoto 611-0011 (Japan); Indian Institute of Geomagnetism, New Panvel, Navi Mumbai 410-218 (India); Omura, Yoshiharu [Research Institute for Sustainable Humanosphere, Kyoto University, Uji, Kyoto 611-0011 (Japan); Kakad, Bharati [Indian Institute of Geomagnetism, New Panvel, Navi Mumbai 410-218 (India)
2013-06-15
We perform one-dimensional fluid simulation of ion acoustic (IA) solitons propagating parallel to the magnetic field in electron-ion plasmas by assuming a large system length. To model the initial density perturbations (IDP), we employ a KdV soliton type solution. Our simulation demonstrates that the generation mechanism of IA solitons depends on the wavelength of the IDP. The short wavelength IDP evolve into two oppositely propagating identical IA solitons, whereas the long wavelength IDP develop into two indistinguishable chains of multiple IA solitons through a wave breaking process. The wave breaking occurs close to the time when electrostatic energy exceeds half of the kinetic energy of the electron fluid. The wave breaking amplitude and time of its initiation are found to be dependent on characteristics of the IDP. The strength of the IDP controls the number of IA solitons in the solitary chains. The speed, width, and amplitude of IA solitons estimated during their stable propagation in the simulation are in good agreement with the nonlinear fluid theory. This fluid simulation is the first to confirm the validity of the general nonlinear fluid theory, which is widely used in the study of solitary waves in laboratory and space plasmas.
Energy approach to rivalry dynamics, soliton stability, and pattern formation in neuronal networks
Loxley, P. N.; Robinson, P. A.
2007-10-01
Hopfield’s Lyapunov function is used to view the stability and topology of equilibria in neuronal networks for visual rivalry and pattern formation. For two neural populations with reciprocal inhibition and slow adaptation, the dynamics of neural activity is found to include a pair of limit cycles: one for oscillations between states where one population has high activity and the other has low activity, as in rivalry, and one for oscillations between states where both populations have the same activity. Hopfield’s Lyapunov function is used to find the dynamical mechanism for oscillations and the basin of attraction of each limit cycle. For a spatially continuous population with lateral inhibition, stable equilibria are found for local regions of high activity (solitons) and for bound states of two or more solitons. Bound states become stable when moving two solitons together minimizes the Lyapunov function, a result of decreasing activity in regions between peaks of high activity when the firing rate is described by a sigmoid function. Lowering the barrier to soliton formation leads to a pattern-forming instability, and a nonlinear solution to the dynamical equations is found to be given by a soliton lattice, which is completely characterized by the soliton width and the spacing between neighboring solitons. Fluctuations due to noise create lattice vacancies analogous to point defects in crystals, leading to activity which is spatially inhomogeneous.
The effects of strong magnetic fields and rotation on soliton stars at finite temperature
无
2001-01-01
We study the effects of strong magnetic fields and uniform rotation on the properties of soliton stars in Lee-Wick model when a temperature dependence is introduced into this model. We first recall the properties of the Lee-Wick model and study the properties of soliton solutions, in particular, the stability condition, in terms of the parameters of the model and in terms of the number of fermions N inside the soliton (for very large N) in the presence of strong magnetic fields and uniform rotation. We also calculate the effects of gravity on the stability properties of the soliton stars in the simple approximation of coupling the Newtonian gravitational field to the energy density inside the soliton, treating this as constant throughout. Following Cottingham and Vinh Mau, we also make an analysis at finite temperature and show the possibility of a phase transition which leads to a model with parameters similar to those considered by Lee and his colleagues but in the presence of magnetic fields and rotation. More specifically, the effects of magnetic fields and rotation on the soliton mass and transition temperature are computed explicitly. We finally study the evolution on these magnetized and rotating soliton stars with the temperature from the early universe to the present time.
Bright solitons in a PT-symmetric chain of dimers
Kirikchi, Omar B; Susanto, Hadi
2016-01-01
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 Schrodinger 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 anti-continuum 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, on the contrary of 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 quart...
The Travelling Wave Solutions for (2+1)-dimensional AKNS Equation
CHENG Zhi-long; HAO Xiao-hong
2015-01-01
Based on the travelling wave method, a (2+1)-dimensional AKNS equation is considered. Elliptic solution and soliton solution are presented and it is shown that the soliton solution can be reduced from the elliptic solution. It also proves that the result is consistent with the soliton solution of simplify Hirota bilinear method by Wazwaz and illustrate the solution are right travelling wave solution.
Dynamics of Soliton Cascades in Fiber Amplifiers
Arteaga-Sierra, F R; Agrawal, Govind P
2016-01-01
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 input pulses.
Exact periodic and solitonic states of the spinor condensates in a uniform external potential
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.
Quark structure of chiral solitons
Diakonov, D
2004-01-01
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+.
Surface solitons in trilete lattices
Stojanovic, M; Hadzievski, Lj; Malomed, B A
2011-01-01
Fundamental solitons pinned to the interface between three semi-infinite one-dimensional nonlinear dynamical chains, coupled at a single site, are investigated. The light propagation in the respective system with the self-attractive on-site cubic nonlinearity, which can be implemented as an array of nonlinear optical waveguides, is modeled by the system of three discrete nonlinear Schr\\"{o}dinger equations. The formation, stability and dynamics of symmetric and asymmetric fundamental solitons centered at the interface are investigated analytically by means of the variational approximation (VA) and in a numerical form. The VA predicts that two asymmetric and two antisymmetric branches exist in the entire parameter space, while four asymmetric modes and the symmetric one can be found below some critical value of the inter-lattice coupling parameter -- actually, past the symmetry-breaking bifurcation. At this bifurcation point, the symmetric branch is destabilized and two new asymmetric soliton branches appear, ...
Topological Solitons and Folded Proteins
Chernodub, M N; Niemi, Antti J
2010-01-01
We propose that protein loops can be interpreted as topological domain-wall solitons. They interpolate between ground states that are the secondary structures like alpha-helices and beta-strands. Entire proteins can then be folded simply by assembling the solitons together, one after another. We present a simple theoretical model that realizes our proposal and apply it to a number of biologically active proteins including 1VII, 2RB8, 3EBX (Protein Data Bank codes). In all the examples that we have considered we are able to construct solitons that reproduce secondary structural motifs such as alpha-helix-loop-alpha-helix and beta-sheet-loop-beta-sheet with an overall root-mean-square-distance accuracy of around 0.7 Angstrom or less for the central alpha-carbons, i.e. within the limits of current experimental accuracy.
Limiting amplitudes of fully nonlinear interfacial tides and solitons
Aguiar-González, Borja; Gerkema, Theo
2016-08-01
A new two-fluid layer model consisting of forced rotation-modified Boussinesq equations is derived for studying tidally generated fully nonlinear, weakly nonhydrostatic dispersive interfacial waves. This set is a generalization of the Choi-Camassa equations, extended here with forcing terms and Coriolis effects. The forcing is represented by a horizontally oscillating sill, mimicking a barotropic tidal flow over topography. Solitons are generated by a disintegration of the interfacial tide. Because of strong nonlinearity, solitons may attain a limiting table-shaped form, in accordance with soliton theory. In addition, we use a quasi-linear version of the model (i.e. including barotropic advection but linear in the baroclinic fields) to investigate the role of the initial stages of the internal tide prior to its nonlinear disintegration. Numerical solutions reveal that the internal tide then reaches a limiting amplitude under increasing barotropic forcing. In the fully nonlinear regime, numerical experiments suggest that this limiting amplitude in the underlying internal tide extends to the nonlinear case in that internal solitons formed by a disintegration of the internal tide may not reach their table-shaped form with increased forcing, but appear limited well below that state.
Soliton generation from a multi-frequency optical signal
Panoiu, N-C [Department of Applied Physics and Applied Mathematics, Columbia University, New York, NY 10027 (United States); Mel' nikov, I V [Center for Research in Engineering and Applied Sciences, Morelos State Autonomous University, Av. Universidad 1001, 62210 Cuernavaca (Mexico); Mihalache, D [Department of Theoretical Physics, Institute of Atomic Physics, PO Box MG-6, Bucharest (Romania); Etrich, C [Institute of Solid State Theory and Theoretical Optics, Friedrich Schiller University Jena, Max-Wien-Platz 1, Jena, D-07743 (Germany); Lederer, F [Institute of Solid State Theory and Theoretical Optics, Friedrich Schiller University Jena, Max-Wien-Platz 1, Jena, D-07743 (Germany)
2002-10-01
We present a comprehensive analysis of the generation of optical solitons in a monomode optical fibre from a superposition of soliton-like optical pulses at different frequencies. It is demonstrated that the structure of the emerging optical field is highly dependent on the number of input channels, the inter-channel frequency separation, the time shift between the pulses belonging to adjacent channels, and the polarization of the pulses. Also, it is found that there exists a critical frequency separation above which wavelength-division multiplexing with solitons is feasible and that this critical frequency increases with the number of transmission channels. Moreover, for the case in which only two channels are considered, we analyse the propagation of the emerging two-soliton solutions in the presence of several perturbations important for optical networks: bandwidth-limited amplification, nonlinear amplification, and amplitude and phase modulation. Finally, the influence of the birefringence of the fibre on the structure of the emerging optical field is discussed. (review article)
Optical Vortex Solitons in Parametric Wave Mixing
Alexander, T J; Buryak, A V; Sammut, R A; Alexander, Tristram J.; Kivshar, Yuri S.; Buryak, Alexander V.; Sammut, Rowland A.
2000-01-01
We analyze two-component spatial optical vortex solitons supported by degenerate three- or four-wave mixing in a nonlinear bulk medium. We study two distinct cases of such solitons, namely, parametric vortex solitons due to phase-matched second-harmonic generation in a optical medium with competing quadratic and cubic nonlinear response, and vortex solitons in the presence of third-harmonic generation in a cubic medium. We find, analytically and numerically, the structure of two-component vortex solitons, and also investigate modulational instability of their plane-wave background. In particular, we predict and analyze in detail novel types of vortex solitons, a `halo-vortex', consisting of a two-component vortex core surrounded by a bright ring of its harmonic field, and a `ring-vortex' soliton which is a vortex in a harmonic field that guides a bright localized ring-like mode of a fundamental frequency field.
Algebraic Ricci Solitons of three-dimensional Lorentzian Lie groups
Batat, Wafaa
2011-01-01
We classify Algebraic Ricci Solitons of three-dimensional Lorentzian Lie groups. All algebraic Ricci solitons that we obtain are sol-solitons. In particular, we prove that, contrary to the Riemannian case, Lorentzian Ricci solitons need not to be algebraic Ricci solitons.
Dynamical behaviours and exact travelling wave solutions of modified generalized Vakhnenko equation
JUNJUN XIAO; DAHE FENG; XIA MENG; YUANQUAN CHENG
2017-01-01
By using the bifurcation theory of planar dynamical systems and the qualitative theory of differential equations, we studied the dynamical behaviours and exact travelling wave solutions of the modified generalized Vakhnenko equation (mGVE). As a result, we obtained all possible bifurcation parametric sets and many explicit formulas of smooth and non-smooth travelling waves such as cusped solitons, loop solitons, periodic cusp waves, pseudopeakon solitons, smooth periodic waves and smooth solitons. Moreover, we provided some numerical simulations of these solutions.
Bogoliubov-de Gennes soliton dynamics in unconventional Fermi superfluids
Takahashi, Daisuke A.
2016-01-01
Exact self-consistent soliton dynamics based on the Bogoliubov-de Gennes (BdG) formalism in unconventional Fermi superfluids/superconductors possessing an SU(d ) -symmetric two-body interaction is presented. The derivation is based on the ansatz having the similar form as the Gelfand-Levitan-Marchenko equation in the inverse scattering theory. Our solutions can be regarded as a multicomponent generalization of the solutions recently derived by Dunne and Thies [Phys. Rev. Lett. 111, 121602 (2013), 10.1103/PhysRevLett.111.121602]. We also propose superpositions of occupation states, which make it possible to realize various filling rates even in one-flavor systems, and include Dirac and Majorana fermions. The soliton solutions in the d =2 systems, which describe the mixture of singlet s -wave and triplet p -wave superfluids, exhibit a variety of phenomena such as rotating polar phases by soliton spins, SU(2)-DHN breathers, Majorana triplet states, s -p mixed dynamics, and so on. These solutions are illustrated by animations, where order parameters are visualized by spherical harmonic functions. The full formulation of the BdG theory is also supported, and the double-counting problem of BdG eigenstates and N -flavor generalization are discussed.
Self-bound quark matter in the NJL model revisited: from schematic droplets to solitonic lasagne
Buballa, Michael
2012-01-01
The existence and the properties of self-bound quark matter in the NJL model at zero temperature are investigated in mean-field approximation, focusing on inhomogeneous structures with one-dimensional spatial modulations. It is found that the most stable homogeneous solutions which have previously been interpreted as schematic quark droplets are unstable against formation of a one-dimensional soliton-antisoliton lattice. The solitons repel each other, so that the minimal energy per quark is realized in the single-soliton limit. The properties of the solitons and their interactions are discussed in detail, and the effect of vector interactions is estimated. The results may be relevant for the dynamics of expanding quark matter.
Bambusi, Dario; Grebert, Benoit
2012-01-01
In this paper we study the long time behavior of a discrete approximation in time and space of the cubic nonlinear Schr\\"odinger equation on the real line. More precisely, we consider a symplectic time splitting integrator applied to a discrete nonlinear Schr\\"odinger equation with additional Dirichlet boundary conditions on a large interval. We give conditions ensuring the existence of a numerical soliton which is close in energy norm to the continuous soliton. Such result is valid under a CFL condition between the time and space stepsizes. Furthermore we prove that if the initial datum is symmetric and close to the continuous soliton, then the associated numerical solution remains close to the orbit of the continuous soliton for very long times.
New Generalized Transformation Method and Its Application in Higher-Dimensional Soliton Equation
无
2006-01-01
A new generalized transformation method is presented to find more exact solutions of nonlinear partial differential equation. As an application of the method, we choose the (3+1)-dimensional breaking soliton equation to illustrate the method. As a result many types of explicit and exact traveling wave solutions, which contain solitary wave solutions, trigonometric function solutions, Jacobian elliptic function solutions, and rational solutions, are obtained. The new method can be extended to other nonlinear partial differential equations in mathematical physics.
Quantum states of dark solitons in the 1D Bose gas
Sato, Jun; Kanamoto, Rina; Kaminishi, Eriko; Deguchi, Tetsuo
2016-07-01
We present a series of quantum states that are characterized by dark solitons of the nonlinear Schrödinger equation (i.e. the Gross-Pitaevskii equation) for the one-dimensional Bose gas interacting through the repulsive delta-function potentials. The classical solutions satisfy the periodic boundary conditions and we simply call them classical dark solitons. Through exact solutions we show corresponding aspects between the states and the solitons in the weak coupling case: the quantum and classical density profiles completely overlap with each other not only at an initial time but also at later times over a long period of time, and they move together with the same speed in time; the matrix element of the bosonic field operator between the quantum states has exactly the same profiles of the square amplitude and the phase as the classical complex scalar field of a classical dark soliton not only at the initial time but also at later times, and the corresponding profiles move together for a long period of time. We suggest that the corresponding properties hold rigorously in the weak coupling limit. Furthermore, we argue that the lifetime of the dark soliton-like density profile in the quantum state becomes infinitely long as the coupling constant approaches zero, by comparing it with the quantum speed limit time. Thus, we call the quantum states quantum dark soliton states.
Bragg solitons in systems with separated nonuniform Bragg grating and nonlinearity
Ahmed, Tanvir; Atai, Javid
2017-09-01
The existence and stability of quiescent Bragg grating solitons are systematically investigated in a dual-core fiber, where one of the cores is uniform and has Kerr nonlinearity while the other one is linear and incorporates a Bragg grating with dispersive reflectivity. Three spectral gaps are identified in the system, in which both lower and upper band gaps overlap with one branch of the continuous spectrum; therefore, these are not genuine band gaps. However, the central band gap is a genuine band gap. Soliton solutions are found in the lower and upper gaps only. It is found that in certain parameter ranges, the solitons develop side lobes. To analyze the side lobes, we have derived exact analytical expressions for the tails of solitons that are in excellent agreement with the numerical solutions. We have analyzed the stability of solitons in the system by means of systematic numerical simulations. We have found vast stable regions in the upper and lower gaps. The effect and interplay of dispersive reflectivity, the group velocity difference, and the grating-induced coupling on the stability of solitons are investigated. A key finding is that a stronger grating-induced coupling coefficient counteracts the stabilization effect of dispersive reflectivity.
The 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. .
黄文华; 张解放; 盛正卯
2002-01-01
The variable separation approach is used to find exact solutions of the (2+1)-dimensional long-wave-short-waveresonance interaction equation. The abundance of the coherent soliton structures of this model is introduced by theentrance of an arbitrary function of the seed solutions. For some special selections of the arbitrary function, it is shownthat the coherent soliton structures may be dromions, solitoffs, etc.
Exact Travelling Wave Solutions to a Coupled Nonlinear Evolution Equation[
HUANGDing-Jiang; ZHANGHong-Qing
2004-01-01
By using an improved hyperbola function method, several types of exact travelling wave solutions to a coupled nonlinear evolution equation are obtained, which include kink-shaped soliton solutions, bell-shaped soliton solutions, envelop solitary wave solutions, and new solitary waves. The method can be applied to other nonlinear evolution equations in mathematical physics.
Exact Travelling Wave Solutions to a Coupled Nonlinear Evolution Equation
HUANG Ding-Jiang; ZHANG Hong-Qing
2004-01-01
By using an improved hyperbola function method, several types of exact travelling wave solutions to a coupled nonlinear evolution equation are obtained, which include kink-shaped soliton solutions, bell-shaped soliton solutions, envelop solitary wave solutions, and new solitary waves. The method can be applied to other nonlinear evolution equations in mathematical physics.
Variational principles for stochastic soliton dynamics.
Holm, Darryl D; Tyranowski, Tomasz M
2016-03-01
We develop a variational method of deriving stochastic partial differential equations whose solutions follow the flow of a stochastic vector field. As an example in one spatial dimension, we numerically simulate singular solutions (peakons) of the stochastically perturbed Camassa-Holm (CH) equation derived using this method. These numerical simulations show that peakon soliton solutions of the stochastically perturbed CH equation persist and provide an interesting laboratory for investigating the sensitivity and accuracy of adding stochasticity to finite dimensional solutions of stochastic partial differential equations. In particular, some choices of stochastic perturbations of the peakon dynamics by Wiener noise (canonical Hamiltonian stochastic deformations, CH-SD) allow peakons to interpenetrate and exchange order on the real line in overtaking collisions, although this behaviour does not occur for other choices of stochastic perturbations which preserve the Euler-Poincaré structure of the CH equation (parametric stochastic deformations, P-SD), and it also does not occur for peakon solutions of the unperturbed deterministic CH equation. The discussion raises issues about the science of stochastic deformations of finite-dimensional approximations of evolutionary partial differential equation and the sensitivity of the resulting solutions to the choices made in stochastic modelling.
Numerical investigation of acoustic solitons
Lombard, Bruno; Richoux, Olivier
2014-01-01
Acoustic solitons can be obtained by considering the propagation of large amplitude sound waves across a set of Helmholtz resonators. The model proposed by Sugimoto and his coauthors has been validated experimentally in previous works. Here we examine some of its theoretical properties: low-frequency regime, balance of energy, stability. We propose also numerical experiments illustrating typical features of solitary waves.
Olsen, M.; Smith, H.; Scott, A. C.
1984-09-01
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.
Subwavelength vortical plasmonic lattice solitons.
Ye, Fangwei; Mihalache, Dumitru; Hu, Bambi; Panoiu, Nicolae C
2011-04-01
We present a theoretical study of vortical plasmonic lattice solitons, which form in two-dimensional arrays of metallic nanowires embedded into nonlinear media with both focusing and defocusing Kerr nonlinearities. Their existence, stability, and subwavelength spatial confinement are investigated in detail.
Langmuir Solitons in Magnetized Plasmas
Dysthe, K. B.; Mjølhus, E.; Pécseli, Hans;
1978-01-01
The authors have considered the nonlinear interaction between a high frequency (Langmuir) wave, which propagates at an arbitrary angle to a weak, constant magnetic field, and low frequency (ion-cyclotron or ion-sound) perturbations. In studying Langmuir envelope solitons they have unified...
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...
Conformal Sigma Models with Anomalous Dimensions and Ricci Solitons
Nitta, M
2004-01-01
We present new non-Ricci-flat Kahler metrics with U(N) and O(N) isometries as target manifolds of conformally invariant sigma models with an anomalous dimension. They are so-called Ricci solitons, special solutions to a Ricci-flow equation. These metrics explicitly contain the anomalous dimension and reduce to Ricci-flat Kahler metrics on the canonical line bundles over certain coset spaces in the limit of vanishing anomalous dimension.
Drift solitons and their two-dimensional stability
Gell, Y.
1977-07-01
The nonlinear equation governing low-frequency drift waves is considered. Utilizing the linear dispersion relation for such waves, it is shown that there exists a parameter range for which the drift waves are governed by a modified Korteweg--de Vries equation having a solitary solution in one and two dimensions. The one-dimensional solitons are unstable with respect to perturbations in the direction perpendicular to their motion.
Spatial Kerr solitons in optical fibres of finite size cross section: beyond the Townes soliton
Drouart, F.; Renversez, G.; Nicolet, A.; Geuzaine, C.
2008-12-01
We propose a new and efficient numerical method to find spatial solitons in optical fibres with a nonlinear Kerr effect including microstructured ones. A nonlinear non-paraxial scalar model of the electric field in the fibre is used (nonlinear Helmholtz equation) and an iterative algorithm is proposed to obtain the nonlinear solutions using the finite element method. The field is supposed to be harmonic in time and along the direction of invariance of the fibre but inhomogeneous in the cross section. In our approach, we solve a nonlinear eigenvalue problem in which the propagation constant is the eigenvalue. Several examples dealing with step-index fibres and microstructured optical fibres with a finite size cross section are described. In each geometry, a single self-coherent nonlinear solution is obtained. This solution, which also depends on the size of the structure, is different from the Townes soliton—but converges towards it at small wavelengths.
Gravitating Non-Abelian Solitons and Black Holes with Yang-Mills Fields
Volkov, M S; Volkov, Mikhail S.; Galtsov, Dmitri V.
1999-01-01
We present a review of gravitating particle-like and black hole solutions with non-Abelian gauge fields. The emphasis is given to the description of the structure of the solutions and to the connection with the results of flat space soliton physics. We describe the Bartnik-McKinnon solitons and the non-Abelian black holes arising in the Einstein-Yang-Mills theory, and consider their various generalizations. These include axially symmetric and slowly rotating configurations, solutions with higher gauge groups, $\\Lambda$-term, dilaton, and higher curvature corrections. The stability issue is discussed as well. We also describe the gravitating generalizations for flat space monopoles, sphalerons, and Skyrmions.
Wakes and precursor soliton excitations by a moving charged object in a plasma
Tiwari, Sanat Kumar
2015-01-01
We study the evolution of nonlinear ion acoustic wave excitations due to a moving charged source in a plasma. Our numerical investigations of the full set of cold fluid equations goes beyond the usual weak nonlinearity approximation and shows the existence of a rich variety of solutions including wakes, precursor solitons and pinned solitons that travel with the source velocity. These solutions represent a large amplitude generalization of solutions obtained in the past for the forced Korteweg deVries equation and can find useful applications in a variety of situations in the laboratory and in space wherever there is a large relative velocity between the plasma and a charged object.
Chai, Jun; Tian, Bo, E-mail: tian_bupt@163.com; Zhen, Hui-Ling; Sun, Wen-Rong
2015-08-15
Under investigation in this paper is a fifth-order nonlinear Schrödinger equation, which describes the propagation of attosecond pulses in an optical fiber. Based on the Lax pair, infinitely-many conservation laws are derived. With the aid of auxiliary functions, bilinear forms, one-, two- and three-soliton solutions in analytic forms are generated via the Hirota method and symbolic computation. Soliton velocity varies linearly with the coefficients of the high-order terms. Head-on interaction between the bidirectional two solitons and overtaking interaction between the unidirectional two solitons as well as the bound state are depicted. For the interactions among the three solitons, two head-on and one overtaking interactions, three overtaking interactions, an interaction between a bound state and a single soliton and the bound state are displayed. Graphical analysis shows that the interactions between the two solitons are elastic, and interactions among the three solitons are pairwise elastic. Stability analysis yields the modulation instability condition for the soliton solutions.
Columbo, Lorenzo; Brambilla, Massimo; Prati, Franco; Tissoni, Giovanna
2012-01-01
We propose a hybrid soliton-based system consisting of a centrosymmetric photorefractive crystal, supporting photorefractive solitons, coupled to a vertical cavity surface emitting laser, supporting multistable cavity solitons. The composite nature of the system, which couples a propagative/conservative field dynamics to a stationary/dissipative one, allows to observe a more general and unified system phenomenology and to conceive novel photonic functionalities. The potential of the proposed hybrid system becomes clear when investigating the generation and control of cavity solitons by propagating a plane wave through electro-activated solitonic waveguides in the crystal. By changing the electro-activation voltage of the crystal, we prove that cavity solitons can be turned on and shifted with controlled velocity across the device section. The scheme can be exploited for applications to optical information encoding and processing.
Leblond, Hervé; Malomed, Boris A; Mihalache, Dumitru
2005-03-01
We consider basic types of two-dimensional (2D) vortex solitons in a three-wave model combining quadratic chi((2)) and self-defocusing cubic chi((3))(-) nonlinearities. The system involves two fundamental-frequency (FF) waves with orthogonal polarizations and a single second-harmonic (SH) one. The model makes it possible to introduce a 2D soliton, with hidden vorticity (HV). Its vorticities in the two FF components are S(1,2) = +/-1 , whereas the SH carries no vorticity, S(3) = 0 . We also consider an ordinary compound vortex, with 2S(1) = 2S(2) = S(3) = 2 . Without the chi((3))(-) terms, the HV soliton and the ordinary vortex are moderately unstable. Within the propagation distance z approximately 15 diffraction lengths, Z(diffr), the former one turns itself into a usual zero-vorticity (ZV) soliton, while the latter splits into three ZV solitons (the splinters form a necklace pattern, with its own intrinsic dynamics). To gain analytical insight into the azimuthal instability of the HV solitons, we also consider its one-dimensional counterpart, viz., the modulational instability (MI) of a one-dimensional CW (continuous-wave) state with "hidden momentum," i.e., opposite wave numbers in its two components, concluding that such wave numbers may partly suppress the MI. As concerns analytical results, we also find exact solutions for spreading localized vortices in the 2D linear model; in terms of quantum mechanics, these are coherent states with angular momentum (we need these solutions to accurately define the diffraction length of the true solitons). The addition of the chi((3))(-) interaction strongly stabilizes both the HV solitons and the ordinary vortices, helping them to persist over z up to 50 Z(diffr). In terms of the possible experiment, they are completely stable objects. After very long propagation, the HV soliton splits into two ZV solitons, while the vortex with S(3) = 2S(1,2) = 2 splits into a set of three or four ZV solitons.
Semiclassical geons as solitonic black hole remnants
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.
On Some Classes of New Solutions of Continuous β-FPU Chain
XU Quan; TIAN Qiang
2008-01-01
A continuous β-Fermi-Pasta-Ulam (FPU) chain is investigated by using the knowledge of elliptic equation and Jacobian elliptic functions. We obtain the new solutions, two-kink soliton solution, breather solution and breather lattice solution, of the continuous β-FPU chain, besides the kink-soliton solution and chaos solution.
Dissipative Kerr solitons in optical microresonators
Herr, Tobias; Kippenberg, Tobias J
2015-01-01
This chapter describes the discovery and stable generation of temporal dissipative Kerr solitons in continuous-wave (CW) laser driven optical microresonators. The experimental signatures as well as the temporal and spectral characteristics of this class of bright solitons are discussed. Moreover, analytical and numerical descriptions are presented that do not only reproduce qualitative features but can also be used to accurately model and predict the characteristics of experimental systems. Particular emphasis lies on temporal dissipative Kerr solitons with regard to optical frequency comb generation where they are of particular importance. Here, one example is spectral broadening and self-referencing enabled by the ultra-short pulsed nature of the solitons. Another example is dissipative Kerr soliton formation in integrated on-chip microresonators where the emission of a dispersive wave allows for the direct generation of unprecedentedly broadband and coherent soliton spectra with smooth spectral envelope.
Soliton dynamics in the multiphoton plasma regime
Husko, Chad A; Colman, Pierre; Zheng, Jiangjun; De Rossi, Alfredo; Wong, Chee Wei; 10.1038/srep01100
2013-01-01
Solitary waves have consistently captured the imagination of scientists, ranging from fundamental breakthroughs in spectroscopy and metrology enabled by supercontinuum light, to gap solitons for dispersionless slow-light, and discrete spatial solitons in lattices, amongst others. Recent progress in strong-field atomic physics include impressive demonstrations of attosecond pulses and high-harmonic generation via photoionization of free-electrons in gases at extreme intensities of 1014 Wcm2. Here we report the first phase-resolved observations of femtosecond optical solitons in a semiconductor microchip, with multiphoton ionization at picojoule energies and 1010 Wcm2 intensities. The dramatic nonlinearity leads to picojoule observations of free-electron-induced blue-shift at 1016 cm3 carrier densities and self-chirped femtosecond soliton acceleration. Furthermore, we evidence the time-gated dynamics of soliton splitting on-chip, and the suppression of soliton recurrence due to fast free-electron dynamics. Thes...
Solitones embebidos: estables, inestables, continuos y discretos
J. Fujioka; R. F. Rodríguez; A. Espinosa-Cerón
2006-01-01
En 1997 se descubrió un nuevo tipo de solitones, bautizados en 1999 como solitones embebidos . Estas peculiares ondas no lineales son interesantes porque existen bajo condiciones en las que hasta hace poco se creía que la propagación de ondas solitarias era imposible. En este trabajo se explica qué son los solitones embebidos, en qué modelos se han encontrado, y qué variantes existen(estables, inestables, continuos, discretos, etc.).
Dynamics of Incoherent Photovoltaic Spatial Solitons
ZHANG Yi-Qi; LU Ke-Qing; ZHANG Mei-Zhi; LI Ke-Hao; LIU Shuang; ZHANG Yan-Peng
2009-01-01
Propagation properties of bright and dark incoherent beams are numerically studied in photovoltaic-photorefractive crystal by using coherent density approach for the first time.Numerical simulations not only exhibit that bright incoherent photovoltaic quasi-soliton,grey-like incoherent photovoltaic soliton,incoherent soliton doublet and triplet can be established under proper conditions,but also display that the spatial coherence properties of these incoherent beams can be significantly affected during propagation by the photovoltaic field.
Construction of Multi-Solitons for the Energy-Critical Wave Equation in Dimension 5
Martel, Yvan; Merle, Frank
2016-12-01
We construct 2-solitons of the focusing energy-critical nonlinear wave equation in space dimension 5, that is solutions {u} of the equation such that u(t) - [ W_1(t) + W_2(t)] to 0 quad as tto +∞ in the energy space, where {W_1} and {W_2} are Lorentz transforms of the explicit standing soliton {W(x) = ( 1+ {|x|^2}/{15} )^{-3/2}}, with any speeds {ℓ_1≠ ℓ_2} ({|ℓ_k|< 1}). The existence result also holds for the case of {K}-solitons, for any {K≥ 3}, assuming that the speeds {ℓ_k} are collinear. The main difficulty of the construction is the strong interaction between the solitons due to the slow algebraic decay of {W(x)} as {|x|to +∞}. This is in contrast to previous constructions of multi-solitons for other nonlinear dispersive equations (like generalized KdV and nonlinear Schrödinger equations in energy subcritical cases), where the interactions are exponentially small in time due to the exponential decay of the solitons.
Belmonte-Beitia, J [Departamento de Matematicas, E T S de Ingenieros Industriales and Instituto de Matematica Aplicada a la Ciencia y la IngenierIa (IMACI), Avda Camilo Jose Cela, 3 Universidad de Castilla-La Mancha 13071 Ciudad Real (Spain); Cuevas, J [Grupo de Fisica No Lineal, Departamento de Fisica Aplicada I, Escuela Universitaria Politecnica, C/Virgen de Africa, 7, 41011 Sevilla (Spain)], E-mail: juan.belmonte@uclm.es, E-mail: jcuevas@us.es
2009-04-24
In this paper, we construct, by means of similarity transformations, explicit solutions to the cubic-quintic nonlinear Schroedinger equation with potentials and nonlinearities depending on both time and spatial coordinates. We present the general approach and use it to calculate bright and dark soliton solutions for nonlinearities and potentials of physical interest in applications to Bose-Einstein condensates and nonlinear optics.
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.
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
Soliton-similariton switchable ultrafast fiber laser
Peng, Junsong; Guo, Pan; Gu, Zhaochang; Zou, Weiwen; Luo, Shouyu; Shen, Qishun
2012-01-01
For the first time, we demonstrated alternative generation of dispersion-managed (DM) solitons or similaritons in an all-fiber Erbium-doped laser. DM solitons or similaritons can be chosen to emit at the same output port by controlling birefringence in the cavity. The pulse duration of 87-fs for DM solitons and 248-fs for similaritons have been observed. For proof of similaritons, we demonstrate that the spectral width depends exponentially on the pump power, consistent with theoretical studies. Besides, the phase profile measured by a frequency-resolved optical gating (FROG) is quadratic corresponding to linear chirp. In contrast, DM solitons show non-quadratic phase profile.
Moving stable solitons in Galileon theory
Masoumi, Ali, E-mail: ali@phys.columbia.edu [Physics Department and ISCAP, Columbia University, New York, NY 10027 (United States); Xiao Xiao, E-mail: xx2146@columbia.edu [Physics Department and ISCAP, Columbia University, New York, NY 10027 (United States)
2012-08-29
Despite the no-go theorem Endlich et al. (2011) which rules out static stable solitons in Galileon theory, we propose a family of solitons that evade the theorem by traveling at the speed of light. These domain-wall-like solitons are stable under small fluctuations-analysis of perturbation shows neither ghost-like nor tachyon-like instabilities, and perturbative collision of these solitons suggests that they pass through each other asymptotically, which maybe an indication of the integrability of the theory itself.
Observation of attraction between dark solitons
Dreischuh, A.; Neshev, D.N.; Petersen, D.E.
2006-01-01
We demonstrate a dramatic change in the interaction forces between dark solitons in nonlocal nonlinear media. We present what we believe is the first experimental evidence of attraction of dark solitons. Our results indicate that attraction should be observable in other nonlocal systems, such as ......We demonstrate a dramatic change in the interaction forces between dark solitons in nonlocal nonlinear media. We present what we believe is the first experimental evidence of attraction of dark solitons. Our results indicate that attraction should be observable in other nonlocal systems...
Bifurcations and new exact travelling wave solutions for the bidirectional wave equations
HENG WANG; SHUHUA ZHENG; LONGWEI CHEN; XIAOCHUN HONG
2016-11-01
By using the method of dynamical system, the bidirectional wave equations are considered. Based on this method, all kinds of phase portraits of the reduced travelling wave system in the parametric space are given. All possible bounded travelling wave solutions such as dark soliton solutions, bright soliton solutions and periodic travelling wave solutions are obtained. With the aid of {\\it Maple} software, numerical simulations are conducted for dark soliton solutions, bright soliton solutions and periodic travelling wave solutions to the bidirectional waveequations. The results presented in this paper improve the related previous studies.
Nonautonomous Solitons in the （3＋1）-Dimensional Inhomogeneous Cubic-Quintic Nonlinear Medium
刘翠云; 戴朝卿
2012-01-01
We have constructed explicit nonautonomous soliton solutions of the generalized nonlinear Sehr6dinger equation in the （3＋ 1 ）-dimensionM inhomogeneous cubic-quintic nonlinear medium. The gain parameter has no effects on the motion of the soliton＇s phase or their velocities, and it affects just the evolution of their peaks. As two examples, we discuss the propagation of nonautonomous solitons in the periodic distributed amplification system and the exponential dispersion decreasing system. Results show that the presence of the chirp not only makes the intensity of solitons weaken more promptly, but also broadens their width.
Chiral asymmetry in propagation of soliton defects in crystalline backgrounds
Arancibia, Adrian
2015-01-01
By applying Darboux-Crum transformations to the Lax pair formulation of the Korteweg-de Vries (KdV) equation, we construct new sets of multi-soliton solutions to it as well as to the modified Korteweg-de Vries (mKdV) equation. The obtained solutions exhibit a chiral asymmetry in propagation of different types defects in crystalline backgrounds. We show that the KdV solitons of pulse and compression modulation types, which support bound states in semi-infinite and finite forbidden bands in the spectrum of the perturbed quantum one-gap Lame system, propagate in opposite directions with respect to the asymptotically periodic background. A similar but more complicated picture also appears for the multi-kink-antikink mKdV solitons that propagate with a privileged direction over topologically trivial or topologically nontrivial crystalline background in dependence on position of energy levels of the trapped bound states in spectral gaps of the associated Dirac system. Exotic N=4 nonlinear supersymmetric structure i...
Three-dimensional black holes, gravitational solitons, kinks and wormholes for BHT massive gravity
Oliva, Julio; Tempo, David; Troncoso, Ricardo
2009-07-01
The theory of massive gravity in three dimensions recently proposed by Bergshoeff, Hohm and Townsend (BHT) is considered. At the special case when the theory admits a unique maximally symmetric solution, a conformally flat solution that contains black holes and gravitational solitons for any value of the cosmological constant is found. For negative cosmological constant, the black hole is characterized in terms of the mass and the ``gravitational hair'' parameter, providing a lower bound for the mass. For negative mass parameter, the black hole acquires an inner horizon, and the entropy vanishes at the extremal case. Gravitational solitons and kinks, being regular everywhere, can be obtained from a double Wick rotation of the black hole. A wormhole solution in vacuum that interpolates between two static universes of negative spatial curvature is obtained as a limiting case of the gravitational soliton with a suitable identification. The black hole and the gravitational soliton fit within a set of relaxed asymptotically AdS conditions as compared with the one of Brown and Henneaux. In the case of positive cosmological constant the black hole possesses an event and a cosmological horizon, whose mass is bounded from above. Remarkably, the temperatures of the event and the cosmological horizons coincide, and at the extremal case one obtains the analogue of the Nariai solution, dS2 × S1. A gravitational soliton is also obtained through a double Wick rotation of the black hole. The Euclidean continuation of these solutions describes instantons with vanishing Euclidean action. For vanishing cosmological constant the black hole and the gravitational soliton are asymptotically locally flat spacetimes. The rotating solutions can be obtained by boosting the previous ones in the t-phi plane.
Euclidean 4d exact solitons in a Skyrme type model
Ferreira, L.A. [Instituto de Fisica de Sao Carlos, IFSC/USP, Universidade de Sao Paulo, Caixa Postal 369, CEP 13560-970 Sao Carlos, SP (Brazil) and Instituto de Fisica Teorica, IFT/UNESP, Universidade Estadula Paulista, Rua Pamplona 145, 01405-900 Sao Paulo, SP (Brazil)]. E-mail: laf@if.sc.usp.br
2005-01-27
We introduce a Skyrme type, four-dimensional Euclidean field theory made of a triplet of scalar fields n->, taking values on the sphere S{sup 2}, and an additional real scalar field {phi}, which is dynamical only on a three-dimensional surface embedded in R{sup 4}. Using a special ansatz we reduce the 4d non-linear equations of motion into linear ordinary differential equations, which lead to the construction of an infinite number of exact soliton solutions with vanishing Euclidean action. The theory possesses a mass scale which fixes the size of the solitons in way which differs from Derrick's scaling arguments. The model may be relevant to the study of the low energy limit of pure SU(2) Yang-Mills theory.
Constructing a class of topological solitons in magnetohydrodynamics.
Thompson, Amy; Swearngin, Joe; Wickes, Alexander; Bouwmeester, Dirk
2014-04-01
We present a class of topological plasma configurations characterized by their toroidal and poloidal winding numbers, nt and np, respectively. The special case of nt=1 and np=1 corresponds to the Kamchatnov-Hopf soliton, a magnetic field configuration everywhere tangent to the fibers of a Hopf fibration so that the field lines are circular, linked exactly once, and form the surfaces of nested tori. We show that for nt∈Z+ and np=1, these configurations represent stable, localized solutions to the magnetohydrodynamic equations for an ideal incompressible fluid with infinite conductivity. Furthermore, we extend our stability analysis by considering a plasma with finite conductivity, and we estimate the soliton lifetime in such a medium as a function of the toroidal winding number.
Polarization Properties of Laser Solitons
Pedro Rodriguez
2017-04-01
Full Text Available The objective of this paper is to summarize the results obtained for the state of polarization in the emission of a vertical-cavity surface-emitting laser with frequency-selective feedback added. We start our research with the single soliton; this situation presents two perpendicular main orientations, connected by a hysteresis loop. In addition, we also find the formation of a ring-shaped intensity distribution, the vortex state, that shows two homogeneous states of polarization with very close values to those found in the soliton. For both cases above, the study shows the spatially resolved value of the orientation angle. It is important to also remark the appearance of a non-negligible amount of circular light that gives vectorial character to all the different emissions investigated.
Lan, Zhong-Zhou; Gao, Yi-Tian; Yang, Jin-Wei; Su, Chuan-Qi; Mao, Bing-Qing
2017-03-01
Under investigation in this paper is a (2+1)-dimensional Broer-Kaup-Kupershmidt system for the nonlinear and dispersive long gravity waves on two horizontal directions in the shallow water of uniform depth. Bilinear forms, Bäcklund transformation and Lax pair are derived based on the Bell polynomials and symbolic computation. One- and two-soliton solutions with a real function ϕ(y) are constructed via the Hirota method, where y is the scaled space coordinate. Propagation and interaction of the solitons are illustrated graphically: (i) ϕ(y) affects the shape of the solitons. (ii) Interaction of the solitons including the elastic and inelastic interactions are discussed. When the solitons' interaction is elastic, the amplitude, velocity and shape of the soliton remain invariant after the interaction except for a phase shift, and the smaller-amplitude soliton has a larger phase shift. (iii) Height of the water surface above a horizontal bottom can be a bell-shaped soliton or an upside-down bell-shaped soliton under certain conditions, while horizontal velocity of the water wave always keeps bell-shaped.
Soliton propagation in relativistic hydrodynamics
Fogaça, D A; 10.1016/j.nuclphysa.2007.03.104
2013-01-01
We study the conditions for the formation and propagation of Korteweg-de Vries (KdV) solitons in nuclear matter. In a previous work we have derived a KdV equation from Euler and continuity equations in non-relativistic hydrodynamics. In the present contribution we extend our formalism to relativistic fluids. We present results for a given equation of state, which is based on quantum hadrodynamics (QHD).