Solitary wave and doubly periodic wave solutions for the Kersten–Krasil’shchik coupled KdV–mKdV system

In this work we devise an algebraic method to uniformly construct solitary wave solutions and doubly periodic wave solutions of physical interest for the Kersten–Krasil’shchik coupled KdV–mKdV system. This system as the classical part of one of superextension of the KdV equation was proposed very recently. The complete integrability, singular analysis and Lax pairs for this system have been found, but its exact solution are still unknown.