Special solutions from the variable separation approach: the Davey - Stewartson equation

Abstract

A variable separation procedure for the Davey - Stewartson (DS) equation is proposed by using a prior ansatz to its bilinear form. The reduced equations for two variable separated fields have the same trilinear form although they possess different independent variables. The trilinear equation can be changed to a spacetime symmetric form and can be solved by means of a Boussinesq-type equation system. Whenever a pair of solutions of the reduced fields are obtained, a corresponding solution of the DS equation can be obtained algebraically. The single dromion solution and some kinds of positon solutions are obtained explicitly.