The objective of this paper is to investigate the Davey-Stewartson equation in -dimensional space. All explicit expressions of the bounded traveling wave solutions for the equation are obtained by using the bifurcation method and qualitative theory of dynamical systems. Moreover, for some special selections of the energy level h, it is shown that the exact periodic solutions evolute into solitary wave solution. The approach we used is reliable and also effective to study the traveling wave solutions of some other nonlinear equations.

Davey-Stewartson equation, bifurcation, phase portraits, traveling wave solutions.