A new expansion method of first order nonlinear ordinary differential equation with at most a sixth-degree nonlinear term and its application to mBBM model

Abstract

Based on a first order nonlinear ordinary differential equation with at most a sixth-degree nonlinear term which is extended from a type of elliptic equation, and by converting it into a new expansion form, this paper proposes a new algebraic method to construct exact solutions for nonlinear evolution equations. Being concise and straightforward, the method is applied to modified Benjamin–Bona–Mahony (mBBM) model, and some new exact solutions to the system are obtained. The algorithm is of important significance in exploring exact solutions for other nonlinear evolution equations.