An improved algebra method and its applications in nonlinear wave equations
An improved algebra method and its applications in nonlinear wave equations
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DOI：
10.1016/j.chaos.2003.12.042
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发表时间：
2004-08
影响因子：
7.8
通讯作者：
Zhenya Yan
中科院分区：
文献类型：
--
作者：
Zhenya Yan
本文进一步研究了一阶非线性常微分方程的其他类型的精确解，包括代数方法。利用该方程的解，给出了耦合KdV方程、非线性色散mK(m,n,k)方程、变浅水波浪方程、非线性耗散方程和高阶非线性薛定谔方程的几类解。这些解包括康密顿解、孤立模式解、孤立波解、Weierstrass椭圆函数解，它们可能有助于解释一些现象。
In this paper, other types of exact solution of a first-order nonlinear ordinary differential equation, which is including the algebraic method, is further investigated. By using the solutions of this equation, we give some types of solutions of the coupled KdV equation, nonlinear dispersion mK(m,n,k) equation, the variant shallow water wave equation, nonlinear dissipative equation and the higher-order nonlinear Schrodinger equation. These solutions includes compacton solutions, solitary pattern solutions, solitary wave solutions, Weierstrass elliptic function solutions, which may be useful to explain some phenomena.