mBBM方程的双扭结孤立波及其动力学稳定性

采用双曲函数展开法得到Modified Benjamin-Bona-Mahony（mBBM）方程的一类扭结-反扭结状的双扭结孤立波解，在不同的极限情况下，此孤立波分别退化为mBBM方程的扭结状和钟状孤立波解.对双扭结型单孤子的结构特征进行分析，构造有限差分格式对其动力学稳定性进行数值研究.有限差分格式为两层隐式格式，在线性化意义下无条件稳定.数值结果表明mBBM方程的双扭结型单孤子在不同类型的扰动下均具有很强的稳定性.对双孤立波的碰撞进行数值模拟，发现既存在弹性碰撞也存在非弹性碰撞.

Solitary Waves with Double Kinks of mBBM Equation and Their Dynamical Stabilities

We obtained a class of solitary wave solutions of modified Benjamin-Bona-Mahony (mBBM) equation with kink-antikink structure by using hybolic-function expansion method. Solitary wave solution reduces to a kink-like solution or bell-like solution under different limitations. We analyzed structures of solitary wave with double kinks. Dynamical stability is investigated numerically with a finite difference scheme. The scheme is implicit and it is absolutely stable in linearization sense. It indicates that single soliton with double kinks is stable under different disturbances. Meanwhile,collision of two solitary waves is numerically simulated. It was found that collision between two solitary waves can be either elastic or inelastic.