共查询到20条相似文献,搜索用时 109 毫秒
1.
为了构造非线性发展方程的无穷序列复合型类孤子新解, 进一步研究了G'(ξ)/G(ξ) 展开法. 首先, 给出一种函数变换, 把常系数二阶齐次线性常微分方程的求解问题转化为一元二次方程和Riccati方程的求解问题. 然后, 利用Riccati方程解的非线性叠加公式, 获得了常系数二阶齐次线性常微分方程的无穷序列复合型新解. 在此基础上, 借助符号计算系统Mathematica, 构造了改进的(2+1)维色散水波系统和(2+1)维色散长波方程的无穷序列复合型类孤子新精确解.
关键词:
G'(ξ)/G(ξ)展开法')" href="#">G'(ξ)/G(ξ)展开法
非线性叠加公式
非线性发展方程
复合型类孤子新解 相似文献
2.
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Ostrovsky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.
关键词:
非线性波方程
尖峰孤子解
待定系数法 相似文献
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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. 相似文献
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采用行波法约化方程,建立一种变换关系,把求解(3+1)维NizhnikNovikovVeselov(NNV)方程的解转化为求解一维非线性KleinGordon方程的解,从而得到了(3+1)维NNV方程的孤子解和周期解.
关键词:
(3+1)维Nizhnik-Novikov-Veselov方程
非线性Klein-Gordon方程
孤子解
周期解 相似文献
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采用分步确定拟解的原则, 对齐次平衡法求非线性发展方程孤子解的关键步骤作了进一步改 进. 以广义Boussinesq方程和bidirectional Kaup-Kupershmidt方程为应用实例, 说明使用 该方法可有效避免“中间表达式膨胀”的问题, 除获得标准Hirota形式的孤子解外, 还能获 得其他形式的孤子解.
关键词:
齐次平衡法
孤子解
孤波解
广义Boussinesq方程
bidirectional Kaup-Kupershmi dt方程 相似文献
9.
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Schrdinger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Schrdinger方程转化成非线性Schrdinger方程,并利用已知解深入研究变系数非线性Schrdinger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. 相似文献
10.
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 相似文献
11.
Bifurcations and Single Peak Solitary Wave Solutions of an Integrable Nonlinear Wave Equation 下载免费PDF全文
Wei Wang Chunhai Li & Wenjing Zhu 《advances in applied mathematics and mechanics.》2016,8(6):1084-1098
Dynamical system theory is applied to the integrable nonlinear wave equation $u_t±(u^3−u^2)x+(u^3)xxx=0$. We obtain the single peak solitary wave solutions and
compacton solutions of the equation. Regular compacton solution of the equation corresponds to the case of wave speed $c$=0. In the case of $c^6$≠0, we find smooth soliton
solutions. The influence of parameters of the traveling wave solutions is explored by
using the phase portrait analytical technique. Asymptotic analysis and numerical simulations
are provided for these soliton solutions of the nonlinear wave equation. 相似文献
12.
《Physics letters. A》2001,291(6):376-380
Making use of a extended tanh method with symbolic computation, we find a new complex line soliton for the two-dimensional (2D) KdV–Burgers equation. Its real part is the sum of the shock wave solution of a 2D Burgers equation and the solitary wave solution of a 2D KdV (KP) equation, and its imaginary part is the product of the shock wave solution of a 2D Burgers equation and the solitary wave solution of a 2D MKdV (MKP) equation. 相似文献
13.
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. 相似文献
14.
Hirota method is used to directly construct quasi-periodic wave solutions for the nonisospectral soliton equation.One and two quasi-periodic wave solutions for the variable-coefficient KdV equation are studied.The well known one-soliton solution can be reduced from the one quasi-periodic wave solution. 相似文献
15.
The D’Alembert solution is an important basic formula in linear partial differential theory due to that it can be considered as a general solution of the wave motion equation. However, the study of the D’Alembert wave is few works in nonlinear partial differential systems. In this paper, one construct the D’Alembert solution of a (2+1)-dimensional generalized breaking soliton equation which possesses the nonlinear terms. This D’Alembert wave has one arbitrary function in the traveling wave variable. We investigate the dynamics of the three soliton molecule, the soliton molecule by bound as an asymmetry soliton and one-soliton, the interaction between the half periodic wave and two-kink, and the interaction among the half periodic wave, one-kink and a kink soliton molecule of the (2+1)-dimensional generalized breaking soliton equation by selecting the appropriate parameters. 相似文献
16.
We study the moving bright solitons in the weak attractive Bose–Einstein condensate with a spin–orbit interaction. By solving the coupled nonlinear Schr ?dinger equation with the variational method and the imaginary time evolution method,two kinds of solitons(plane wave soliton and stripe solitons) are found in different parameter regions. It is shown that the soliton speed dominates its structure. The detuning between the Raman beam and energy states of the atoms decides the spin polarization strength of the system. The soliton dynamics is also studied for various moving speed and we find that the shape of individual components can be kept when the speed of soliton is low. 相似文献
17.
利用Hirota方法及Riemann theta函数得到了一个(3+1)维孤子方程的周期解.在极限情况下,该周期解退化为孤子解.另外,利用计算机技术和Mathematica绘制了解的三维曲面图. 相似文献
18.
Variable Separation Solution for (1+1)-Dimensional Nonlinear Models Related to Schroedinger Equation
XUChang-Zhi ZHANGJie-Fang 《理论物理通讯》2004,42(4):568-572
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. 相似文献
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20.
The extended homoclinic test function method is a kind of classic, efficient and well-developed method to solve nonlinear evolution equations. In this paper, with the help of this approach, we obtain new exact solutions (including kinky periodic solitary-wave solutions, periodic soliton solutions, and cross kink-wave solutions) for the new (2+1)-dimensional KdV equation. These results enrich the variety of the dynamics of higher-dimensionai nonlinear wave field. 相似文献