Searching for traveling wave solutions of nonlinear evolution equations in mathematical physics

Abstract

Abstract This paper deals with the analytical solutions for two models of special interest in mathematical physics, namely the ( 2 + 1 ) $(2+1)$ -dimensional generalized Calogero-Bogoyavlenskii-Schiff equation and the ( 3 + 1 ) $(3+1)$ -dimensional generalized Boiti-Leon-Manna-Pempinelli equation. Using a modified version of the Fan sub-equation method, more new exact traveling wave solutions including triangular solutions, hyperbolic function solutions, Jacobi and Weierstrass elliptic function solutions have been obtained by taking full advantage of the extended solutions of the general elliptic equation, showing that the modified Fan sub-equation method is an effective and useful tool to search for analytical solutions of high-dimensional nonlinear partial differential equations.

Keywords

• mathematical physics
• traveling wave solutions
• Fan sub-equation method
• evolution equations