Application of Exterior Differential Systems to Nonlinear Evolution Equations

Abstract

We investigate nonlinear evolution equations with Lax integrability using the tool of differential forms and exterior differential systems. We restate the Lax equations of the nonlinear evolution equation in the form of an exterior differential system. Therefore, we embark on an attempt to apply the method of Estabrook-Wahlquist EW prolongation structure, which has reviewed and developed the new and extended EW technique. We also extended our analysis to a study of differential systems which defined equations that include the Camassa-Holm and Degasperis-Procesi equations as specific cases.