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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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基于推广的立方非线性Klein—Gordon方程对一般形式的变系数非线性Schrodinger方程进行研究,讨论了无啁啾情形的孤子解,发现了包括亮、暗孤子解和类孤子解在内的一些新的精确解.同时对基本孤子的色散控制方法进行了简单讨论.作为特例,常系数非线性Schrodinger方程和两类特殊的变系数非线性Schrodinger方程的结果和已知的形式一致.此外,还研究了一个周期增益或损耗的光纤系统,得到了有意义的结果. 相似文献
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基于推广的立方非线性Klein-Gordon方程对一般形式的变系数非线性Schr(o)dinger方程进行研究,讨论了无啁啾情形的孤子解,发现了包括亮、暗孤子解和类孤子解在内的一些新的精确解.
同时对基本孤子的色散控制方法进行了简单讨论. 作为特例,常系数非线性Schr(o)dinger方程和两类特殊的变系数非线性Schr(o)dinger方程的结果和已知的形式一致.此外,还研究了一个周期增益或损耗的光纤系统,得到了有意义的结果. 相似文献
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孤子运动的Miles方程是一个具特征的非线性Schrdinger型方程.借求孤子解的微扰法,导出所遵循的矩阵方程,和孤子解的修正量δu(x,λ).并据双孤子解,计算了它的周期互作用状态
关键词:
Miles方程 微扰双孤子解 相似文献
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利用双参数假设给出了一类非线性耦合方程的若干孤子解公式,使物理上许多著名的方程作为该方程的特殊情形得到相应的孤子解,指正了一些文献的错误.
关键词:
非线性发展方程
双参数假设
孤子解 相似文献
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Some exact solutions to the inhomogeneous higher-order nonlinear Schrdinger equation by a direct method 下载免费PDF全文
By symbolic computation and a direct method, this paper
presents some exact analytical solutions of the one-dimensional
generalized inhomogeneous higher-order nonlinear Schr?dinger
equation with variable coefficients, which include bright solitons,
dark solitons, combined solitary wave solutions, dromions,
dispersion-managed solitons, etc. The abundant structure of these
solutions are shown by some interesting figures with computer
simulation. 相似文献
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高阶非线性薛定谔方程的精确周期解和孤波解 总被引:1,自引:1,他引:0
本文利用行波约化方法,研究了用于描述飞秒光脉冲传输的高阶非线性薛定谔方程,得到了它的包络型Jacobian椭圆函数双周期解和孤波解.分析结果表明亮孤子的存在依赖于负三阶色散效应,暗孤子的存在依赖于正三阶色散效应. 相似文献
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By using the solutions of an auxiliary Lam\'e equation, a direct algebraic method is
proposed to construct the exact solutions of $N$-coupled nonlinear Schr\"{o}dinger
equations. The abundant higher-order exact periodic solutions of a family of
$N$-coupled nonlinear Schr\"{o}dinger equations are explicitly obtained with the aid
of symbolic computation and they include corresponding envelope solitary and shock
wave solutions. 相似文献
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With the aid of a class of nonlinear ordinary differential equation (ODE) and its various positive solutions, four types of exact solutions of the generalized derivative nonlinear Schrödinger equation (GDNLSE) have been found out, which are the bell-type solitary wave solution, the algebraic solitary wave solution, the kink-type solitary wave solution and the sinusoidal traveling wave solution, provided that the coefficients of GDNLSE satisfy certain constraint conditions. For more general GDNLSE, the similar results are also given. 相似文献
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Two-dimensional accessible solitary wave families of the
generalized nonlocal nonlinear Schr?dinger equation are obtained by
utilizing superpositions of various single accessible solitary solutions.
Specific values of soliton parameters are selected as initial conditions and
the superposition of known single solitary solutions in the highly nonlocal
regime are launched into the nonlocal nonlinear medium with a Gaussian
response function, to obtain novel numerical solitary solutions of improved
stability. Our results reveal that in nonlocal media with the Gaussian
response the higher-order spatial accessible solitary families can exist in
various forms, such as asymmetric necklace, asymmetric fractional, and
symmetric multipolar necklace solitons. 相似文献
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By using the extended F-expansion method, the exact solutions,including periodic wave solutions expressed by Jacobi elliptic functions, for (2+1)-dimensional nonlinear Schrǒdinger equation are derived. In the limit cases, the solitary wave solutions and the other type of traveling wave solutions for the system are obtained. 相似文献
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立方非线性Schr?dinger方程的Jacobi椭圆函数周期解 总被引:4,自引:2,他引:2
本文利用F-展开法,求出了立方非线性Schrodinger方程的由Jacobi椭圆函数表示的行波解;并且在极限情况下,得到了方程的孤波解. 相似文献