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

Subject Areas : International Journal of Industrial Mathematics

خدایار گودرزی ¹ ( Department of Mathematics, Borujerd Branch, Islamic Azad University, Borujerd, Iran. )

Received: 2021-10-29 Accepted : 2022-06-25 Published : 2022-09-01

Keywords: Order ‎reduction‎, $mu$-symmetry, S‎ymmetry, Variational problem, $mu$-conservation law,

Abstract :

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.

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