Bilinear form and exact solutions for a new extended (2+1)-dimensional Boussinesq equation

Abstract

In this article, a new extended (2+1)-dimensional Boussinesq equation which can be used to describe the propagation of shallow water waves, was investigated. By using the bilinear bell polynomial theorem, the Hirota bilinear form of this considered equation can be obtained. Then, on the basis of the Hirota bilinear form, some new exact solutions through the extended homoclinic test approach with an arbitrary constant solution u0 were yielded. These exact solutions show the evolution of periodic characteristics as can be seen from the three-dimensional figures. The results shown new mechanical structures and reveal different characteristics for this evolution equation.