Multiple Soliton-like and Periodic-like Solutions to the Generalization of Integrable (2+1)-Dimensional Dispersive Long-Wave Equations

Abstract

In this paper, the generalization of integrable (2+1)-dimensional dispersive long-wave equations (GIDLWE) introduced by Boiti et al. is investigated. The idea of the homogeneous balance method, which is very concise and primary, is extended and applied to GIDLWE. As a result, multiple soliton-like solutions, which contain the single soliton-like solutions, double soliton-like solutions and periodic-like solutions are constructed for the GIDLWE. In addition, by using a transformations we find that the GIDLWE can be reduced to be the Burgers equation with the external force which can be used to search for more exact solutions of GIDLWE. This approach is also extended to other nonlinear evolution equations in mathematical physics.