Perturbation of chiral solitons

This paper studies the perturbation of soliton due to the chiral nonlinear Schrödinger's equation by the aid of soliton perturbation theory. The perturbation term that is studied is the quantum potential perturbation of the chiral soliton that is known as Bohm potential. The stable fixed point of the chiral soliton parameters is obtained.     

Dark soliton in one-dimensional Bose–Einstein condensate under a periodic perturbation of trap

The perturbation of a confining trap leads to the collective oscillation of a Bose--Einstein condensate, thereby the propagation of a dark soliton in the condensate is affected. In this study, periodic perturbation is employed to match the soliton oscillation. We find that the soliton dynamics depends sensitively on the coupling between the moving direction of the trap and that of the soliton. The soliton energy/depth evolves periodically, and a relevant shift in the soliton trajectory occurs as compared with the unperturbed case. Overall, the soliton oscillation frequency changes little even if the perturbation amplitude and frequency vary.     

Stochastic perturbation of dispersion-managed optical solitons

The stochastic perturbation of dispersion-managed optical solitons is studied in this paper, in addition to deterministic preturbation terms, by the aid of soliton perturbation theory. The super-Gaussian pulses are considered and the corresponding Langevin equations are derived and analyzed. It is shown that in presence of the perturbation terms, the soliton propagates down the fiber with a fixed mean energy.OCIS Codes: 060.2310; 060.4510; 060.5530; 190.4370     

Dynamically Stable Solitons in Optical Fibers

The existence of a dynamically stable soliton in optical fibers is established by virtue of the multiple-scale perturbation technique applied in a new way to the perturbed nonlinear Schrodinger's equation. We show that, by introducing a proper definition of the phase of the soliton, one can obtain the corrections to the pulse where the standard soliton perturbation approach fails.     

Optical solitons in resonant and nonresonant nonlinear media in the presence of perturbations

We studied the optical solitons in nonlinear resonant and nonresonant media in the presence of perturbations, assuming that the transient effects are stimulated by the light scanning beam. We treated a slight deviation from the exact necessary condition for the soliton existence (2betanu=1), as a small perturbation for the integrable system, studying its influence upon the soliton propagation conditions. The approximation is constructed by the help of an algebraic version of the soliton perturbation theory using a Riemann boundary problem in connection with the inverse scattering method. We have obtained the soliton equation and we have solved it in the presence of a small perturbation in the adiabatic approximation. In this case we have demonstrated that for a Lorentz profile line the amplitude of the soliton remains unchanged, the only effect of the perturbation results in a phase shift.     

Soliton perturbation theory of Biswas–Milovic equation

This paper studies the perturbed Biswas–Milovic equation by the aid of soliton perturbation theory. The adiabatic variation of the soliton parameters is derived from the modified integrals of motion. The velocity of the soliton is also obtained when these perturbation terms are turned on. There are four types of nonlinear media that are taken into consideration.     

Solitons in random media with long-range correlation

Abstract

A statistical approach of the propagation of solitons in media with a spatially random potential is developed. Applying the inverse scattering transform several regimes are demonstrated which are determined by the mass and the velocity of the incoming soliton as well as by the correlation length of the random potential. Namely, the mass of the soliton is conserved if its initial amplitude is large enough. If the initial mass is small, then the mass decays with the length of the system. The decay rate is exponential in the case of a white noise perturbation, but it obeys a power law if the carrier wavenumber of the soliton lies in the tail of the spectrum of the potential. Furthermore, the scattered radiation propagates in a backward direction in the case of a white noise perturbation, while it propagates in a forward direction (with the same carrier wavenumber as the soliton) in the case of a coloured noise with long-range correlation.     

Stochastic perturbation in quasi—ideal dispersion—managed soliton system

The model of stochastic perturbation is built up systematically in quasi-ideal dispersion-managed soliton system,its influence on soliton propagation is investigated by both the variational approach and the numerical simulation,and it is found that the stochastic perturbation leads to disintegration of soliton and enhances the interaction between solitons.The nonlinear gain and filter are introduced to suppress effectively the influence on both soliton propagation and interaction.     

A multidimensional superposition principle: numerical simulation and analysis of soliton invariant manifolds I

Abstract

In the framework of a multidimensional superposition principle involving an analytical approach to nonlinear PDEs, a numerical technique for the analysis of soliton invariant manifolds is developed. This experimental methodology is based on the use of computer simulation data of soliton–perturbation interactions in a system under investigation, and it allows the determination of the dimensionality of similar manifolds and partially (in the small amplitude perturbation limit) to restore the related superposition formulae. Its application for cases of infinite dimensionality, and the question of approximation by lower dimensional manifolds and, respectively, by superposition formulae of a lower order are considered as well. The ideas and implementation details are illustrated and verified by using examples with the integrable, MKdV and KdV equations, and also nonintegrable, Kawahara and Regularized Long Waves equation, soliton models.     

Quantum perturbation theory of solitons

We develop a systematic perturbation theory for amplitudes involving a single soliton (extended finite energy solution of a classical field theory). These methods allow one in principle to compute to any desired order quantum corrections to soliton masses, form factors and Green functions. The major technical problem encountered is an infrared divergence of the naive perturbation theory rules. This divergence is dominated by a modification of the usual functional methods so as to properly define the soliton as a momentum eigenstate. The extension of these methods to soliton-soliton scattering is discussed.     

Optical soliton perturbation in a non-Kerr law media

This paper studies the optical soliton perturbation by the aid of soliton perturbation theory. The various perturbation terms, that arise in the study of optical solitons, are exhaustively studied in this paper. The adiabatic parameter dynamics of optical solitons are obtained in presence of these perturbation terms. The types of nonlinearities that are considered are Kerr law, power law, parabolic law as well as the dual-power law.     

Autophasing of solitons

The effect of an external wave perturbation with a slowly varying frequency on a soliton of the nonlinear Schrödinger equation is investigated. The equations that describe the time evolution of the perturbed-soliton parameters are derived. The necessary and sufficient soliton phase locking conditions that relate the rate of change in the frequency of the perturbation, its amplitude, wave number, and phase to the initial values of parameters for the soliton have been found.     

Josephson结中混沌孤振子的超辐射

考虑两个耦合的长Josephson结，运用直接微扰法，讨论周期微扰下混沌孤振子的超辐射功率，结果表明：周期微扰下的孤子作混沌运动，当孤子逐渐与周期微扰同步时，辐射功率不断增大，其上限虽受限的有界条件制约，但通常比孤子对的辐射功率更大，理论分析和数值模拟均很好地说明了这一点，这为混沌孤振子的实际应用提供理论依据。     

光折变有机聚合物中的双色光空间孤子

对光折变有机聚合物中的双色光空间孤子进行了理论分析,证明双色信号光的两个频率成分相互作用可以在折射率改变为正的光折变有机聚合物中形成暗暗和亮暗空间孤子,在折射率改变为负的光折变有机聚合物中形成亮亮和亮暗空间孤子。与单色光孤子的情况不同,对于双色光孤子情况,通过与一形成暗孤子的频率成分相互作用,另一频率成分在折射率改变为正的有机聚合物中也可形成亮孤子;通过与一形成亮孤子的频率成分相互作用,另一频率成分在折射率改变为负的材料中也可形成暗孤子。     

三维非线性Schrdinger方程的直接微扰方法

将直接微扰方法应用于含微扰的三维非线性Schrdinger方程,获得了该方程的包括零阶和一阶修正的近似解析解.借助得到的解析解,分析了微扰对孤子参数的影响。     

The （l＋l）-dimensional spatial solitons in media with weak nonlinear nonlocality

We study the propagation of (1+1)-dimensional spatial soliton in a nonlocal Kerr-type medium with weak nonlocality. First, we show that an equation for describing the soliton propagation in weak nonlocality is a nonlinear Schr?dinger equation with perturbation terms. Then, an approximate analytical solution of the equation is found by the perturbation method. We also find some interesting properties of the intensity profiles of the soliton.     

KdV孤子的含时微扰理论

研究了周期性含时微扰对KdV(Korteweg de Vries)孤子的影响. 将微扰项展为时间变量的傅里叶级数,发现其常数项是导致长期项的根源. 在一阶近似下,消除长期项,求出了孤子参数(高度、宽度和速度)随时间的缓慢变化. 傅氏级数中的其他项决定了微扰对孤子波形的一阶修正. 关键词： KdV孤子 孤子微扰论     

Nonlinear molecular excitations in a completely inhomogeneous DNA chain

We study the nonlinear dynamics of a completely inhomogeneous DNA chain which is governed by a perturbed sine-Gordon equation. A multiple scale perturbation analysis provides perturbed kink-antikink solitons to represent open state configuration with small fluctuation. The perturbation due to inhomogeneities changes the velocity of the soliton. However, the width of the soliton remains constant.