(3+1)维KP-Boussinesq和BKP-Boussinesq方程的精确行波解

Exact Traveling Wave Solutions and Bifurcation for (3+1) Dimensional KP-Boussinesq and BKP-Boussinesq Equations

本文借助平面动力系统分支理论以及Hamilton能量函数研究(3+1)维KP-Boussinesq和BKP-Boussinesq方程。得到了这两类方程行波解的所有分支、相图,同时计算出了所有行波解的精确参数表达式以及参数条件。该文得到这两类方程的行波包括亮、暗孤子、周期波、扭子波以及一些其它类型的波。

In this paper, the (3+1) dimensional KP-Boussinesq and BKP-Boussinesq equations are studied by using the bifurcation theory of planar dynamical systems and Hamilton energy functions. All the branches and phase diagrams of the traveling wave solutions of these two equations are obtained, and the exact parameter expressions and parameter conditions of all the traveling wave solutions are also calculated. In the paper, the traveling wave solutions of these two equations are obtained, including solitary wave solutions, periodic wave solutions and kink wave solutions.