The Repeated Homogeneous Balance Method to Construct the Traveling Wave Solutions of Nonlinear Partial Differential Equations

摘要

A repeated homogeneous balance method is proposed to construct the travelling wave solutions of nonlinear partial differential equations. The key procedure is that the homogeneous balance method is used to solve the ansatz equation the Riccati equation. It surmounts the difficulty of solving the Riccati equation. As an illustrative equation, the KdV equation is investigated by the repeated homogeneous balance method and then its more new exact travelling wave solutions are obtained.