立方五次方非线性薛定谔方程的动力学及模式漂移（英文）

利用辛算法研究立方五次方非线性薛定谔方程的动力学,讨论随着五次方系数的增大方程的动力学性质.在相图中计算得到同宿轨交叉和椭圆轨道,系统具有周期解.讨论方程的解模式的漂移,结果表明解模式的漂移速度随着五次方系数的增大而减慢.     

非线性Schr(o)dinger方程的动力学行为分析

采用辛算法数值求解非线性Schrodinger方程的周期初值问题,建立不同的相空间来分析其动力学特性.首先比较分析了不同的相空间中立方非线性Schrodinger方程在不同立方非线性参数下的长时间演化的动力学特性,然后讨论了相空间中立方-五次方非线性Schrodinger方程在不同立方和五次方非线性参数下的长时间演化的动力学特性,数值结果显示,对于不同的立方非线性参数,随着五次方非线性参数的增加,动力学行为的演化路径是不一样的.     

立方五次方非线性Schrodinger方程的动力学性质研究

采用辛算法数值求解了一维立方五次方非线性Schrödinger方程,研究了不同非线性参数下非线性Schrödinger方程的动力学性质.数值结果表明,随着立方非线性参数的增加,系统经历了拟周期状态、混沌状态和周期状态,且在五次方项的调制下,呼吸子解可以退化为单孤子解. 关键词： 非线性Schrödinger方程 动力学性质 孤子 辛算法     

立方五次方非线性Schrdinger方程的动力学性质研究

采用辛算法数值求解了一维立方五次方非线性Schrdinger方程,研究了不同非线性参数下非线性Schrdinger方程的动力学性质.数值结果表明,随着立方非线性参数的增加,系统经历了拟周期状态、混沌状态和周期状态,且在五次方项的调制下,呼吸子解可以退化为单孤子解.     

非线性Schrdinger方程的动力学行为分析

采用辛算法数值求解非线性Schr dinger方程的周期初值问题,建立不同的相空间来分析其动力学特性.首先比较分析了不同的相空间中立方非线性Schr dinger方程在不同立方非线性参数下的长时间演化的动力学特性,然后讨论了相空间中立方-五次方非线性Schr dinger方程在不同立方和五次方非线性参数下的长时间演化的动力学特性,数值结果显示,对于不同的立方非线性参数,随着五次方非线性参数的增加,动力学行为的演化路径是不一样的.     

非线性Schroedinger方程的动力学行为分析

采用辛算法数值求解非线性Schroedinger方程的周期初值问题，建立不同的相空间来分忻其动力学持性．首先比较分析了不同的相空间中立方非线性Sehroedinger方程在不同立方非线性参数下的长时间演化的动力学特性，然后讨论了相空间中立方一五次方非线性Sehroedinger方程在不同立方和五次方非线性参数下的长时间演化的动力学特性，数值结果显示，对于不同的立方非线性参数，随着五次方非线性参数的增加，动力学行为的演化路径是不一样的．     

抛体运动轨迹的数值分析

现行的多数大学物理教材中只讨论了忽略空气阻力或空气阻力与速度的大小成正比的情况, 没有讨论 空气阻力与速度的高次方成正比的情况. 主要的原因是空气阻力与速度的高次方成正比时, 动力学方程为超越方 程, 无法得到解析解. 本文通过数值求解在空气阻力作用下的抛体运动的动力学方程, 得到了空气阻力与速度的高 次方成正比时的抛体运动轨迹, 并分析了抛体质量、 抛射角、 初速度对运动轨迹的影响     

变系数非线性Schrdinger方程的孤子解及其相互作用

在光孤子通信和Bose-Einstein凝聚体动力学研究中,求解广义非线性Schrdinger方程是一个重要的研究方向.稳定的孤子模式具有潜在的应用,可为实验技术的实现提供依据.本文引进一种相似变换,将变系数非线性Schrdinger方程转化成非线性Schrdinger方程,并利用已知解深入研究变系数非线性Schrdinger方程解的单孤子解、两孤子解和连续波背景下的孤子解.同时通过选择不同的具体参数,给出它们的图像分析和相应的讨论.     

变系数非线性Schrödinger方程的孤子解及其相互作用

在光孤子通信和Bose-Einstein凝聚体动力学研究中,求解广义非线性Schrödinger方程是一个重要的研究方向.稳定的孤子模式具有潜在的应用,可为实验技术的实现提供依据.本文引进一种相似变换,将变系数非线性Schrödinger方程转化成非线性Schrödinger方程,并利用已知解深入研究变系数非线性Schrödinger方程解的单孤子解、两孤子解和连续波背景下的孤子解.同时通过选择不同的具体参数,给出它们的图像分析和相应的讨论. 关键词： 非线性Schrö dinger方程 相似变换 变系数 孤子解     

变系数非线性Schr(o)dinger方程的孤子解及其相互作用

在光孤子通信和Bose-Einstein凝聚体动力学研究中,求解广义非线性Schr(o)dinger方程是一个重要的研究方向.稳定的孤子模式具有潜在的应用,可为实验技术的实现提供依据.本文引进一种相似变换,将变系数非线性Schr(o)dinger方程转化成非线性Schr(o)dinger方程,并利用已知解深入研究变系数非线性Schr(o)dinger方程解的单孤子解、两孤子解和连续波背景下的孤子解.同时通过选择不同的具体参数,给出它们的图像分析和相应的讨论.     

Dynamics of cubic–quintic nonlinear Schr?dinger equation with different parameters

We study the dynamics of the cubic–quintic nonlinear Schr?dinger equation by the symplectic method. The behaviors of the equation are discussed with harmonically modulated initial conditions, and the contributions from the quintic term are discussed. We observe the elliptic orbit, homoclinic orbit crossing, quasirecurrence, and stochastic motion with different nonlinear parameters in this system. Numerical simulations show that the changing processes of the motion of the system and the trajectories in the phase space are various for different cubic nonlinear parameters with the increase of the quintic nonlinear parameter.     

A note on grey solitons of the cubic–quintic Schrödinger equation

Using the soliton solutions of the Boussinesq-like equation as brick materials, the one, two and three grey solitons of the nonlinear cubic–quintic nonlinear Schrödinger equation are constructed. We present the elastic and inelastic interaction of these solutions.     

Nonlinear Schrödinger equation for optical media with quintic nonlinearity

A nonlinear quintic Schrödinger equation (NLQSE) is developed and studied in detail. It is found that the NLQSE has soliton solutions, the stability of which is analysed using variational method. It is also found that the soliton pulse width in the materials supporting NLQSE is small compared to soliton pulse width of the commonly studied nonlinear cubic Schrödinger equation (NLCSE).     

Dynamics of NLS solitons described by the cubic-quintic Ginzburg-Landau equation

The generalized moment method is applied to average the Ginzburg-Landau equation with quintic nonlinearity in the neighborhood of a soliton solution to the nonlinear Schrödinger equation. A qualitative analysis of the resulting dynamical system is presented. New soliton solutions bifurcating from a known exact soliton solution are obtained. The results of the qualitative analysis are compared with those obtained by direct numerical solution of the Ginzburg-Landau equation.     

Traveling-waves and solitons in a generalized time-variable coefficients nonlinear Schrödinger equation with higher-order terms

In this work, we study exact solutions of a generalized nonautonomous cubic–quintic nonlinear Schrödinger equation with higher-order terms, and the dispersion and the nonlinear coefficients engendering temporal dependency. Similarity transformations are used to convert the nonautonomous equation into autonomous one and then we present solutions in a general way. These solutions are obtained for the first class by using the F-expansion method and for the second class constituted by most general bright, dark and front by a direct substitution. We also generalize the external potential which traps the system and the nonlinearities. Finally, the stability of the soliton solutions under slight disturbance of the constraint conditions and initial perturbation of white noise is discussed analytically and numerically. The results reveal that solitons can propagate in a stable way under slight disturbance of the constraint conditions and initial perturbation of a 10% white noise.     

Nonlinear theory of transverse perturbations of quasi-one-dimensional solitons

An averaged variational principle is applied to analyze the nonlinear effect of transverse perturbations (including diffraction) on quasi-one-dimensional soliton propagation governed by various wave equations. It is shown that parameters of the spatiotemporal solitons described by the cubic Schrödinger equation and the Yajima-Oikawa model of interaction between long-and short-wavelength waves satisfy the spatial quintic nonlinear Schrödinger equation for a complex-valued function composed of the amplitude and eikonal of the soliton. Three-dimensional solutions are found for two-component “bullets” having long-and short-wavelength components. Vortex and hole-vortex structures are found for envelope solitons and for two-component solitons in the regime of resonant long/short-wave coupling. Weakly nonlinear behavior of transverse perturbations of one-dimensional soliton solutions in a self-defocusing medium is described by the Kadomtsev-Petviashvili equation. The corresponding rationally localized “lump” solutions can be considered as secondary solitons propagating along the phase fronts of the primary solitons. This conclusion holds for primary solitons described by a broad class of nonlinear wave equations.     

Two-dimensional matter-wave solitons and vortices in competing cubic-quintic nonlinear lattices

The nonlinear lattice — a new and nonlinear class of periodic potentials — was recently introduced to generate various nonlinear localized modes. Several attempts failed to stabilize two-dimensional (2D) solitons against their intrinsic critical collapse in Kerr media. Here, we provide a possibility for supporting 2D matter-wave solitons and vortices in an extended setting — the cubic and quintic model — by introducing another nonlinear lattice whose period is controllable and can be different from its cubic counterpart, to its quintic nonlinearity, therefore making a fully “nonlinear quasi-crystal”.A variational approximation based on Gaussian ansatz is developed for the fundamental solitons and in particular, their stability exactly follows the inverted Vakhitov–Kolokolov stability criterion, whereas the vortex solitons are only studied by means of numerical methods. Stability regions for two types of localized mode — the fundamental and vortex solitons — are provided. A noteworthy feature of the localized solutions is that the vortex solitons are stable only when the period of the quintic nonlinear lattice is the same as the cubic one or when the quintic nonlinearity is constant, while the stable fundamental solitons can be created under looser conditions. Our physical setting (cubic-quintic model) is in the framework of the Gross–Pitaevskii equation or nonlinear Schrödinger equation, the predicted localized modes thus may be implemented in Bose–Einstein condensates and nonlinear optical media with tunable cubic and quintic nonlinearities.     

Rogue wave solutions for the coupled cubic–quintic nonlinear Schrödinger equations in nonlinear optics

A generalized Darboux transformation for the coupled cubic–quintic nonlinear Schrödinger equation is constructed by the Darboux matrix method. As applications, the Nth-order rogue wave solutions of the coupled cubic–quintic nonlinear Schrödinger equation have been obtained. In particular, the dynamics of the general first- and second-order rogue waves are discussed and illustrated through some figures.     

Optical solitons for non-Kerr law nonlinear Schrödinger equation with third and fourth order dispersions

In this paper, we obtain optical soliton solutions for non-Kerr law nonlinear Schrödinger equation (NLSE) with third order (3OD) and fourth order dispersions (4OD). We will use two integration schemes, namely sin-cosine method and Bernoulli’s equation approach with five laws of nonlinearities. Sine-cosine method is applicable to Kerr, power and anti-cubic laws, this method provides bright soliton solutions. The second method is applicable to parabolic and cubic quintic laws, this method generates dark soliton. The results may be used in discussing the propagation of optical solitons in highly dispersive media with Kerr, power, anti-cubic, parabolic and cubic quintic law nonlinearities.