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Fourth-order pattern forming PDEs: partial and approximate symmetries

Authors
  • Jamal, Sameerah
  • Johnpillai, Andrew G.
Publication Date
Mar 18, 2020
Source
VGTU
Keywords
Language
English
License
Green
External links

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.

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