Analytic solutions for a new model of the(3+1)-Boussinesq equation

Abstract

In this paper, we have applied the mapping method to solve the (3+1)-dimensional Boussinenesq equation where we have obtained exact solutions for evolution equation to construct exact periodic and soliton solutions of nonlinear partial differential evolution equation. Many have obtained new families of exact traveling wave solutions, but the Boussinesq equation is successfully. These solutions may be significantly important for the explanation of some practical physical problems. New exact travelling wave solutions are obtained and expressed in terms of hyperbolic functions, trigonometric functions, rational functions and elliptic functions. It is shown that the mapping method provides a powerful mathematical tool for solving a great many nonlinear partial differential equations in mathematical physics.