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The nonlinear Schrodinger equation is proved to be consistent-tanh-expansion (CTE) solvable. Some types of dark soliton solutions dressed by cnoidal periodic waves are obtained by means of the CTE method. 相似文献
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Based on the invariant expansion method,some reasonable approximate solutions of coupled Korteweg-de Vries(KdV)equations with diferent linear dispersion relations have been obtained.These solutions contain not only bell type soliton solutions but also periodic wave solutions that expressed by Jacobi elliptic functions.The results also show that if the arbitrary constants are selected suitably,the approximate solutions may become the exact ones. 相似文献
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Riccati-type Bcklund transformations of nonisospectral and generalized variable-coefficient KdV equations 下载免费PDF全文
We extend the method of constructing Bcklund transformations for integrable equations through Riccati equations to the nonisospectral and the variable-coefficient equations. By taking nonisospectral and generalized variable-coefficient Korteweg–de Vries(KdV) equations as examples, their B¨acklund transformations are obtained under a more generalized constrain condition. In addition, the Lax pairs and infinite numbers of conservation laws of these equations are given. Especially, some classical equations such as the cylindrical KdV equation are just the special cases of the constrain condition. 相似文献
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程雪苹 《宁波大学学报(理工版)》2020,33(5):68-76
非局域对称作为对称理论重要组成部分, 近年来逐渐引起人们关注. 本文以势Korteweg-de Vries (KdV)方程、修正Korteweg-de Vries (mKdV)方程和Kadomtsev-Petviashvili (KP)方程为例, 分别介绍了对应非线性系统与B?cklund变换相关的非局域对称、非局域留数对称与Darboux变换相关的非局域对称. 通过引入3个辅助变量, 将KP方程与Darboux变换相关的非局域对称局域化为Lie点对称. 运用对称约化方法简单概述了KP方程的相似约化解, 其中包括孤立子和Boussinesq波相互作用解、孤立子和KdV型波相互作用解以及非均匀背景下的单孤立波解. 相似文献
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In this paper Lou's direct perturbation method is applied to the perturbed coupled nonlinear Schrodinger equations to obtain their asymptotical solutions, which include not only the zero-order solutions but also the first-order modifications. Based on the asymptotical solutions, the effects of perturbations on soliton parameters and the collision between two solitons are then discussed in brief. Furthermore, we directly simulate the perturbed coupled nonlinear SchrSdinger equations by split-step Fourier method to check the validity of the direct perturbation method. It turns out that our analytical results are well supported by the numerical calculations. 相似文献
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