中文摘要：

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modifiedKorteweg-deVries（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一反扭结状结构．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．

英文摘要：

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.