摘要
改进了双曲正切函数展开法,使其可用于离散型差分微分方程的求解,并以离散modified Korteweg-de Vries(mKdV)方程为例说明了该方法,得到了该方程的3类精确行波解,其中一类解具有扭结-反扭结状结构.在不同参数情况下,该解分别为离散mKdV方程的扭结状或钟状孤波解.采用四阶Runge-Kutta法对该类孤立波解的稳定性进行了数值研究,结果表明在简谐波扰动和随机扰动下,该孤子均具有很强的稳定性.
The hyperbola function expansion method is improved to solve discrete difference-differential equations and the method is illustrated by the discrete modified Kortewdg-de Vries （mKdV） equation. Some analytical solutions of the discrete mKdV equation are obtained. One of the single soliton solutions has a kink-antikink structure and it reduces to a kink-like solution and bell-like solution under different limitations. The stability of the single soliton solution with double kinks is investigated numerically by the fourth-order Runge-Kutta method. The results indicate that the soliton is stable under different disturbances.
出处
《西北师范大学学报（自然科学版）》
CAS
北大核心
2013年第4期38-42,56,共6页
Journal of Northwest Normal University(Natural Science)
基金
国家自然科学基金资助项目(11047010)
关键词
离散mKdV方程
双扭结单孤子
稳定性
discrete mKdV equation single soliton solution with double kinks stability
