离散差分微分方程的双扭结孤立波及其稳定性

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 rnKdV 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.