Sub-ODE's New Solutions and Their Applications to Two Nonlinear Partial Differential Equations with Higher-Order Nonlinear Terms

摘要

In the present paper,with the aid of symbolic computation,families of new nontrivial solutions of thefirst-order sub-ODE F′~2=AF^2+BF^(2+p)+CF^(2+2p)(where F'=dF/dξ,p>0)are obtained.To our best knowledge,these nontrivial solutions have not been found in[X.Z.Li and M.L.Wang,Phys.Lett.A 361(2007)115]and[S.Zhang,W.Wang,and J.L.Tong,Phys.Lett.A 372(2008)3808]and other existent papers until now.Using thesenontrivial solutions,the sub-ODE method is described to construct several kinds of exact travelling wave solutions for thegeneralized KdV-mKdV equation with higher-order nonlinear terms and the generalized ZK equation with higher-ordernonlinear terms.By means of this method,many other physically important nonlinear partial differential equations withnonlinear terms of any order can be investigated and new nontrivial solutions can be explicitly obtained with the helpof symbolic computation system Maple or Mathematica.