Qualitative analysis and explicit traveling wave solutions for the Davey-Stewartson equation

摘要

In this paper, we use the bifurcation method of dynamical systems to study the traveling wave solutions for the Davey-Stewartson equation. A number of traveling wave solutions are obtained. Those solutions contain explicit periodic wave solutions, periodic blow-up wave solutions, unbounded wave solutions, kink profile solitary wave solutions, and solitary wave solutions. Relations of the traveling wave solutions are given. Some previous results are extended.