The improved sub-ODE method for a generalized KdV–mKdV equation with nonlinear terms of any order

In this Letter, Li and Wang's sub-ODE method [X.Z. Li, M.L. Wang, Phys. Lett. A 361 (2007) 115] is improved and applied to the generalized KdV–mKdV equation with nonlinear terms of any order. As a result, more travelling wave solutions are obtained including not only all the known solutions found by Li and Wang but also other formal solutions. This improved sub-ODE method can be used for solving other nonlinear partial differential equations with nonlinear terms of any order in mathematical physics.