A CLASS OF EXACT, PERIODIC-SOLUTIONS OF NONLINEAR ENVELOPE EQUATIONS

A class of periodic solutions of nonlinear envelope equations, e.g., t he nonlinear Schrodinger equation (NLS), is expressed in terms of rati onal functions of elliptic functions. The Hirota bilinear transformati on and theta functions are used to extend and generalize this class of solutions first reported for NLS earlier in the literature. In partic ular a higher order NLS and the Davey-Stewartson (DS) equations are tr eated. Doubly periodic standing waves solutions are obtained for both the DSI and DSII equations. A symbolic manipulation software is used t o confirm the validity of the solutions independently. (C) 1995 Americ an Institute of Physics.