(2+1) Dimensional Wave Patterns of the Davey–Stewartson System

Abstract

(2+1) (2 spatial and 1 temporal) dimensional patterns of standing waves are calculated theoretically for the Davey–Stewartson equations (DS). DS are relevant in hydrodynamic free surface waves of finite depth, and constitute a system of evolution equations with rich structure. The Hirota bilinear method, theta and Jacobi elliptic functions are employed. The wave patterns will be periodic in two mutually perpendicular spatial directions. The long wave limit can be taken by letting one of the spatial periods to become large. Special bright or dark solitons will result. The validity of all these solutions is verified independently by direct differentiation with the software MATHEMATICA.