Variational problem, Lagrangian and $\mu$-conservation law of the generalized Rosenau-type equation

Abstract

The goal of this article is to compute conservation law, Lagrangian and $\mu$-conservation law of the generalized Rosenau-type equation using the homotopy operator, the $\mu$-symmetry method and the variational problem method. The generalized Rosenau-type equation includes the generalized Rosenau equation, the generalized Rosenau-RLW equation and the generalized Rosenau-KdV equation, which admits the third-order Lagrangian. The article also compares the conservation law and the $\mu$-conservation law of these three equation.

Keywords

• $\mu$-symmetry
• conservation law
• $\mu$-conservation law
• lagrangian
• variational problem