The improved sub-ODE method for a generalized KdV-mKdV equation with nonlinear terms of any order. (English) Zbl 1220.35157
Summary: In this Letter, Li and Wang’s sub-ODE method [X.Z. Li and M.L. Wang, ibid. 361, No. 1–2, 115–118 (2007; Zbl 1170.35085)] 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.
MSC:
| 35Q53 | KdV equations (Korteweg-de Vries equations) |
| 35C07 | Traveling wave solutions |
| 35C20 | Asymptotic expansions of solutions to PDEs |
| 83C15 | Exact solutions to problems in general relativity and gravitational theory |
Citations:
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