Truncated series solutions to the (2+1)-dimensional perturbed Boussinesq equation by using the approximate symmetry method**Project supported by the National Natural Science Foundation of China (Grant No. 11505094) and the Natural Science Foundation of Jiangsu Province, China (Grant No. BK20150984).

Abstract

In this paper, the (2+1)-dimensional perturbed Boussinesq equation is transformed into a series of two-dimensional (2D) similarity reduction equations by using the approximate symmetry method. A step-by-step procedure is used to acquire Jacobi elliptic function solutions to these similarity equations, which generate the truncated series solutions to the original perturbed Boussinesq equation. Aside from some singular area, the series solutions are convergent when the perturbation parameter is diminished.