Solitons and other exact solutions for variant nonlinear Boussinesq equations

Abstract

In this article, some integration tools, namely the modified simple equation method, the general Expa-function method, the Jacobi elliptic equation expansion method, the Riccati equation expansion method and the G′/G-expansion method are used to construct exact solutions with parameters and the Jacobi elliptic function solutions for variant nonlinear Boussinesq equations. When these parameters are taken to be special values, the soliton solutions, the singular soliton solutions and trigonometric function solutions are derived from the exact solutions and the Jacobi elliptic function solutions. The obtained results confirm that the proposed methods are efficient techniques for analytic treatment of a wide variety of nonlinear partial differential equations in mathematical physics. We compare the results yielding from these integration tools. Also, a comparison between our results in this article and the well-known results are given.