The exact traveling wave solutions to two integrable KdV6 equations

Abstract

The exact explicit traveling solutions to the two completely integrable sixth-order nonlinear equations KdV6 are given by using the method of dynamical systems and Cosgrove’s work. It is proved that these traveling wave solutions correspond to some orbits in the 4-dimensional phase space of two 4-dimensional dynamical systems. These orbits lie in the intersection of two level sets defined by two first integrals.

Keywords

KdV6 equation / Exact traveling wave solution / Solitary wave solution / Quasi-periodic wave solution

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