Order Reduction, $mu$-Symmetry and $mu$-Conservation Law of The Generalized mKdV Equation with Constant-coefficients and Variable-‎coefficients‎

The goal of this paper is to calculate the order reduction of the generalized mKdV equation with constant coefficients (gmKdVcc) and the generalized mKdV equation with variable-coefficients (gmKdVvc) using the mu-symmetry method. Moreover we obtain Lagrangian and mu-conservation law of the gmKdVcc equation and the gmKdVvc equation using the variational problem method.