Symmetry Reductions, Exact Solutions and Conservation Laws of the (3 + 1)-dimensional Nonlinear Evolution Equation

Abstract

Using the modified CK's direct method, we build the relationship between new solutions and old ones and the (3+1)-dimensional nonlinear evolution equation. Based on the invariant group theory, Lie symmetries of the (3+1)-dimensional nonlinear evolution equation are obtained. In addition, applying the given Lie symmetry, we obtain the similarity reduction and new exact solutions, At last, we give the conservation laws of the (3+1)-dimensional nonlinear evolution equation.