Order Reduction, μ-Symmetry and μ-Conservation Law of The Generalized mKdV Equation with Constant-coeffcients and Variable-coeffcients.

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