Rosenau-KdV equation coupling with the Rosenau-RLW equation: conservation laws and exact solutions

Abstract

We compute the conservation laws for the Rosenau-Kortweg de Vries equation coupling with the Regularized Long-Wave equation using Noether's approach through a remarkable method of increasing the order of the Rosenau-KdV-RLW equation. Furthermore, exact solutions for the Rosenau- KdV-RLW equation are acquired by employing the Kudryashov method.