On the solution of the Generalized Bretherton Equation by the Homogeneous Balance Method

In this paper, we try to find exact travelling wave solutions of the generalized Bretherton equation for integer, greater than one, values of the exponent $m$ of the nonlinear term. We will use the homogeneous balance method (HBM) to solve the Riccati equation and the reduced nonlinear ordinary differential equation to obtain solutions of the generalized Bretherton equation.