BKK方程的分支现象与非线性波解

Bifurcation phenomena and nonlinear wave solutions of BKK equation

研究Broer-Kaup-Kupershmidt(BKK)方程的分支现象与非线性波解。首先,通过行波变换,求得BKK方程的首次积分与奇点,接着运用动力系统定性理论和分支方法给出BKK方程在各区域中的相图,并获得方程的一些非线性波解;进一步,扭波的三种分支现象被揭示;最后,利用Maple软件对这些分支现象进行模拟。

The bifurcation phenomena and nonlinear wave solutions of Broer-Kaup-Kupershmidt(BKK)equation are studied.Firstly,the first integral and singularities of the BKK equation are obtained by travelling wave transformation.Then the bifurcation phase portraits of the BKK equation in each region are presented by using the bifurcation method and qualitative theory of dynamical systems,and some nonlinear wave solutions of the equation are obtained.Furthermore,three bifurcation phenomena of kink wave are revealed.Finally,Maple software is used to simulate these bifurcation phenomena.