Exact and explicit traveling wave solutions to the generalized Gardner and BBMB equations with dual high-order nonlinear terms

Abstract

In this paper, the first integral method is used to solve the generalized Gardner and Benjamin–Bona–Mahoney–Burgers (BBMB) equations with dual high-order nonlinear terms. Consequently, the exact and explicit traveling wave solutions are obtained. For some specific choice of parameters, obtained solutions are reduced to the solutions of classical Gardner and BBM equations. Comparisons between our results and the well-known results are given. In addition, 3-D and 2-D graphical representations of the exact solutions are depicted. • The first integral method is utilized to find the exact traveling wave solutions for generalized Gardner and BBMB equations. • For some specific choice of parameters, the exact solutions are reduced to the solutions of classical Gardner and BBM equations. • The obtained exact solutions are compared with the other existing results.