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

Abstract

Abstract: 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.

Key words: mBBM equation, solitary wave with double kinks, finite difference scheme, dynamical stability

CLC Number:

O411.1

WANG Linxue, ZONG Jin, WANG Xueling, SHI Yuren. Solitary Waves with Double Kinks of mBBM Equation and Their Dynamical Stabilities[J]. CHINESE JOURNAL OF COMPUTATIONAL PHYSICS, 2016, 33(2): 212-220.

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