Document Type : Original Article
Department of Mathematics, Broujerd Branch, Islamic Azad University, Broujerd, Iran
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.