Explicit and exact traveling wave solutions for generalized Benjamin-Bona-Mahoney-Burgers equation with dual high-order nonlinear terms

Abstract

In recent years, the investigation of exact solutions to nonlinear partial differential equations has played an important role in nonlinear phenomena. Several powerful methods have been proposed to obtain exact solutions of nonlinear partial differential equations, such as the first integral method, tanh-sech method, sine-cosine method, Jacobi elliptic function method, Fexpansion method, exp-function method, expansion method and so on. The first integral method was first proposed by Feng in solving Burgers-KdV equation. It is a direct algebraic method based on the commutative algebra. Recently, it was successfully used for constructing exact solutions to a variety of nonlinear problems. Our interest in the present work is in implementing the first integral method to find the exact solution for generalized Benjamin-Bona-Mahoney-Burgers (BBMB) equation with dual high-order nonlinear terms. Considering the generalized BBMB equation with dual arbitrary power-law nonlinearity ,,