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Fourth-order pattern forming PDEs: partial and approximate symmetries

Abstract

This paper considers pattern forming nonlinear models arising in the study of thermal convection and continuous media. A primary method for the derivation of symmetries and conservation laws is Noether’s theorem. However, in the absence of a Lagrangian for the equations investigated, we propose the use of partial Lagrangians within the framework of calculating conservation laws. Additionally, a nonlinear Kuramoto-Sivashinsky equation is recast into an equation possessing a perturbation term. To achieve this, the knowledge of approximate transformations on the admissible coefficient parameters is required. A perturbation parameter is suitably chosen to allow for the construction of nontrivial approximate symmetries. It is demonstrated that this selection provides approximate solutions.

Keyword : pattern formation, optimal system of one-dimensional subalgebras, Lie symmetries, exact solutions

How to Cite
Jamal, S., & Johnpillai, A. , G. (2020). Fourth-order pattern forming PDEs: partial and approximate symmetries. Mathematical Modelling and Analysis, 25(2), 198-207. https://doi.org/10.3846/mma.2020.10115
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Mar 18, 2020
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