On the Periodic Solutions of the Davey-Stewartson Systems

Abstract

The periodic, traveling wave solutions of all four versions of the Davey-Stewartson system (namely the focusing and the defocusing cases of both the Davey-Stewartson I and the Davey-Stewartson II equations) are derived and classified. For all four versions, these solutions are described in terms of elliptic functions. Special reductions and limiting cases, including harmonic limits, soliton limits, and one-dimensional solutions, are also explicitly discussed.