mBBM方程的双扭结孤立波及其动力学稳定性

计算物理 ›› 2016, Vol. 33 ›› Issue (2): 212-220.

mBBM方程的双扭结孤立波及其动力学稳定性

王林雪¹, 宗谨^1,2, 王雪玲¹, 石玉仁¹

1. 西北师范大学物理与电子信息工程学院, 兰州 730070;
2. 甘肃民族师范学院物理与水电工程系, 合作 747000

收稿日期:2015-01-20 修回日期:2015-05-30 出版日期:2016-03-25 发布日期:2016-03-25
通讯作者: 石玉仁,E-mail:shiyr@nwnu.edu.cn
作者简介:王林雪(1991-),女,辽宁朝阳,硕士生,研究方向:非线性物理,E-mail:wlx0123@126.com
基金资助:
国家自然科学基金（11047010，11565021）资助项目

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

WANG Linxue¹, ZONG Jin^1，2, WANG Xueling¹, SHI Yuren¹

1. College of Physics and Electronic Engineering, Northwest Normal University, Lanzhou 730070, China;
2. College of Physics and Hydropower Engineering, Gansu Normal University For Nationalitles, Hezuo 747000, China

Received:2015-01-20 Revised:2015-05-30 Online:2016-03-25 Published:2016-03-25

摘要/Abstract

摘要： 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.

关键词: mBBM方程, 双扭结孤立波, 有限差分格式, 动力学稳定性

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

中图分类号:

O411.1

王林雪, 宗谨, 王雪玲, 石玉仁. mBBM方程的双扭结孤立波及其动力学稳定性[J]. 计算物理, 2016, 33(2): 212-220.

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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