Many scholars have studied the exact solutions of the generalized Benney equation and the generalized fifth order KdV equation,but most of them focus on finding meromorphic solutions of integrable differential equations.In this paper,by using Painlevé transformation method and polynomial principle,exact solutions without meromorphic solution structure of the above nonlinear integrable PDEs are constructed,and it is proved that the solutions are kink solutions.Furthermore,it is explained that this method can be extended to find kink solutions for other higher-order nonlinear nonintegrable differential equations.
关键词
Benney方程/五阶KdV方程/Painlevé变换法/扭波解
Key words
Benney equation/fifth order KdV equation/Painlevé transformation method/kink solution
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