mKdV和mBBM方程的新型孤子解  

New type soliton solutions to mKdV and mBBM equations

作　　者：刘煜[1] 刘伟庆[2] 吕卫东[2] 

机构地区：[1]河南电力试验研究院情报所,河南郑州450052 [2]河南科技大学数学与统计学院,河南洛阳471003

出　　处：《安徽大学学报（自然科学版）》2012年第4期37-42,共6页Journal of Anhui University(Natural Science Edition)

基　　金：河南电力试验研究院科研基金资助项目

摘　　要：尖峰孤子解和紧孤子解是非线性方程的新型孤子解.利用相关文献提出的方法分别研究修正的KdV方程(mKdV)和修正的BBM方程(mBBM),得到3种形式的孤子解:尖峰孤子解、双峰孤子解和尖峰紧孤子解.通过数值模拟得到解的图像,其中之一为双峰形的孤立波.这些结果进一步丰富了这2个非线性波方程的精确解的形式和内容.该文提出的3个拟解之一还可以用于其他多个非线性波方程,如:Klein-Gordon方程、Ф4方程、Sine-Gordon方程和Landau-Ginzburg-Higgs方程.Peakon solution and compacton solution are new type soliton solutions to nonlinear wave equations. In this paper, we researched two nonlinear wave equations- modified Korteweg-de Vries （mKdV） equation and modified Benjamin-Bona-Mahony（mBBM） equation ,respectively, and obtained three kinds of new type soliton solutions： peakon solutions, double-peak soliton solutions and peaked compacton solution. These results further enriched the patterns of explicit and exact solutions to mKdV and mBBM equations. The graphs of these solutions were given through numerical simulation, one of which was a double-peak solitary wave. One of three ansatz solutions proposed could also be used in many other nonlinear wave equations such as Klein- Gordon equation, Ф4equation, Sine-Gordon equation and Landau-Ginzburg-Higgs equation.

关 键 词：MKDV方程 MBBM方程 尖峰孤子解 双峰孤子解 尖峰紧孤子解 

分 类 号：O411.1[理学—理论物理]