SPECIAL SOLUTIONS FROM THE VARIABLE SEPARATION APPROACH - THE DAVEY-STEWARTSON EQUATION

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 f orm although they possess different independent variables. The triline ar equation can be changed to a spacetime symmetric form and can be so lved by means of a Boussinesq-type equation system. Whenever a pair of solutions of the reduced fields are obtained, a corresponding solutio n of the DS equation can be obtained algebraically. The single dromion solution and some kinds of positon solutions are obtained explicitly.