Symmetry reduction and exact solutions of two higher-dimensional nonlinear evolution equations

Abstract

Abstract In this paper, symmetries and symmetry reduction of two higher-dimensional nonlinear evolution equations (NLEEs) are obtained by Lie group method. These NLEEs play an important role in nonlinear sciences. We derive exact solutions to these NLEEs via the exp ( − ϕ ( z ) ) $\exp(-\phi (z))$ -expansion method and complex method. Five types of explicit function solutions are constructed, which are rational, exponential, trigonometric, hyperbolic and elliptic function solutions of the variables in the considered equations.

Keywords

• nonlinear evolution equations
• symmetry
• exp ( − ϕ ( z ) ) $\exp(-\phi(z))$ -expansion method
• complex method
• exact solutions
• meromorphic function