Exact Periodic and New Solitary Wave Solutions to the Generalization of Integrable (2+1)-dimensional Dispersive Long Wave Equations

Abstract

A general solution involving three arbitrary functions is first obtained for the generalization of integrable (2+1)-dimensional dispersive long wave equations by means of WTC truncation method. Exact periodic wave solutions are then expressed as rational functions of the Jacobi elliptic functions. For the first time the interaction of Jacobi elliptic waves is studied and found to be nonelastic! Limit cases are studied and some interesting, new solitary structures are revealed. The interactions of between two dromions, between dromion and solitoff and between y -periodic solitons are all nonelastic, and x -periodic solitons can propagate steadily. It is shown that the Jacobi elliptic wave solutions can be viewed as the generalization of dromion, dromion-solitoff and periodic solitons.