Applications of dispersive analytical wave solutions of nonlinear seventh order Lax and Kaup-Kupershmidt dynamical wave equations

Abstract

In this article, new travelling wave solutions are constructed for two applications of the seventh order KdV equations, the seventh order Lax-equation and the seventh order Kaup-Kupershmidt equation. Using the modified auxiliary equation of direct algebraic method, we study the considered nonlinear PDEs analytically. As a result, we found several stable and analytical solutions.