Soliton Solution of Generalized 2D Boussinesq Equation with Quadratic and Cubic Nonlinearity

Abstract

The soliton solution of the Kadomtsev-Petviashvili and two-dimensional Boussinesq equations with quadratic and cubic nonlinearity is studied using the Hirota bilinear method. It is shown that the former has only a two-soliton solution propagating in parallel, but the latter has a two-soliton solution propagating in different directions under a certain condition. The Bäcklund transformation for the latter equation is also presented.