广义b方程的孤立波解及周期波解

Solitary and Periodic Solutions of the Generalized b-equation

对于广义b方程的研究主要集中在b≥0的情况,该文利用分支方法研究了b=−3这类特殊广义b方程的分支、非线性波解及动力学特征.在一定参数条件下,得到了该方程的分支相图,还发现了不同于b>0情况的新现象,在行波系统中有无限多周期轨穿过奇异直线φ=c.同时,给出了光滑孤立波解和光滑周期波解的存在性及其精确表达式,共获得了15个非线性波解的显式表达式.

The research of generalized b-equation mainly focuses on the case of b≥0.This paper uses the bifurcation method to investigate the bifurcation,nonlinear wave solutions and dynamical characteristics of generalized b-equation with b=−3.Under certain parameter conditions,one obtains the bifurcation phase diagram of the equation.Meanwhile,a new phenomenon is found different from the case of b>0,in which an infinite number of periodic trajectories in the traveling wave system cross the singular lineφ=c.The existence of solitary and periodic solutions is given,and the 15 exact expressions for nonlinear wave solutions are obtained.