Symmetry reduction, exact solutions and conservation laws of the Bogoyavlenskii equation

摘要

In this paper, by applying the direct symmetry method, we obtain the symmetry reductions, group invariant solutions and some new exact solutions of the Bogoyavlenskii equation, which include hyperbolic function solutions, trigonometric function solutions and power series solutions. We also give the conservation laws of the Bogoyavlenskii equation.