A class of exact, periodic solutions of nonlinear envelope equations

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Abstract
A class of periodic solutions of nonlinear envelope equations, e.g., the nonlinear Schrödinger equation (NLS), is expressed in terms of rational functions of elliptic functions. The Hirota bilinear transformation and theta functions are used to extend and generalize this class of solutions first reported for NLS earlier in the literature. In particular a higher order NLS and the Davey–Stewartson (DS) equations are treated. Doubly periodic standing waves solutions are obtained for both the DSI and DSII equations. A symbolic manipulation software is used to confirm the validity of the solutions independently.