Order Reduction, $\mu$-Symmetry and $\mu$-Conservation Law of The Generalized mKdV Equation with Constant-coefficients and Variable-coefficients
محورهای موضوعی : مجله بین المللی ریاضیات صنعتی
1 - Department of Mathematics, Borujerd Branch, Islamic Azad University, Borujerd, Iran.
کلید واژه: Order reduction, $mu$-symmetry, Symmetry, Variational problem, $mu$-conservation law,
چکیده مقاله :
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.
هدف از این مقاله، محاسبه کاهش مرتبه معادله تعمیم یافته mKdV با ضرایب ثابت و متغیر به روش مو-تقارن است. بعلاوه، مو- قانون بقا و لاگرانژین معادله تعمیم یافته mKdV با ضرایب ثابت و متغیر، با استفاده از روش مسئله تغیراتی بدست می آید.
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