10.71932/ijm.2023.1081402
High-Order Noether’s Transformation and New Densities for BBM Equation via Contact Symmetries
- Mehdi Jafari*
1 - Mojtaba Farazi1
- Payame Noor University (PNU), Department of Mathematics, P.O. Box 19395-4697, Tehran, Iran.
Received: 01-10-2023
Accepted: 25-12-2023
Published in Issue 15-11-2024
Copyright (c) 2024 International Journal of Mathematical Modeling & Computations
This work is licensed under a Creative Commons Attribution 4.0 International License.
How to Cite
Abstract
Noether's first theorem shows how symmetry groups of one-parameter transformations lead to the generation of conservation laws for the Euler-Lagrange equations. She states in her second theorem that there is a relationship between Euler's basic equation and Lagrange's basic equation. This one-to-one correspondence leads to a type of symmetry called generalized symmetry. According to these materials, in this paper, we want to obtain these types of symmetries for the Benjamin-Bona-Mahony (BBM) equation and show that each symmetry is connected to a specific conservation law. For this purpose, we obtain the symmetries of this equation using the Lie symmetry method, and then using the adjoint operator, we provide a classification on the group invariant solutions of this equation. Then, by applying Noether's method, we obtain a new conservation law for each symmetry.
Keywords
- BBM equation,
- Generalized symmetries,
- Multiplier method,
- Contact symmetries,
- Conservation laws.
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