Symmetries, Traveling Wave Solutions, and Conservation Laws of a (3+1)-Dimensional Boussinesq Equation

Abstract

We analyze the (3+1)-dimensional Boussinesq equation, which has applications in fluid mechanics. We find exact solutions of the (3+1)-dimensional Boussinesq equation by utilizing the Lie symmetry method along with the simplest equation method. The solutions obtained are traveling wave solutions. Moreover, we construct the conservation laws of the (3+1)-dimensional Boussinesq equation using the new conservation theorem, which is due to Ibragimov.