广义(N＋1)维Boussinesq方程的有界行波解

Bounded Travelling Wave Solutions of an(N+1)-dimensional Generalized Boussinesq Equation

利用推广的Fan子方程法,借助于符号计算软件Maple求解广义(N+1)维Boussinesq方程,利用动力系统分支理论方法研究子方程,获得了其在所有参数条件下的相图分支及有界解的显式表达式,从而得到原方程更为丰富的有界解,其中包括三角函数解、双曲函数解以及双周期Jacobi椭圆函数解.

In this paper, we study an （ N ＋ 1 ） - dimensional generalized Boussinesq equation by using the improved Fan sub-equa- tion method with the aid of symbolic computation software maple. By making use of bifurcation theory of dynamical systems to investi- gate the sub-equation, we obtain the explicit expressions of bounded solutions and the bifurcations and phase portraits under all possible parametric conditions, therefore, more bounded travelling wave solutions to the original equation are acquired which include triangular function solutions, hyperbolic function solutions and Jacobi elliptic function solutions with double periodic.