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Article

Symmetries and Invariant Solutions of Higher-Order Evolution Systems

Department of Mathematics and Computer Science, University of Catania, Viale Andrea Doria, 6, 95125 Catania, Italy
Symmetry 2024, 16(8), 1023; https://doi.org/10.3390/sym16081023
Submission received: 18 July 2024 / Revised: 3 August 2024 / Accepted: 8 August 2024 / Published: 10 August 2024
(This article belongs to the Special Issue Application of Symmetry in Equations)

Abstract

In this paper, we investigate evolution systems in two components, characterized by higher-order spatial derivatives and the presence of two arbitrary functions. Our study begins with an analysis of a fourth-order system. We perform a detailed group classification and identify specific forms of the constitutive functions that allow the system to exhibit additional symmetries in addition to spatial and temporal translations. We extend these results to nth-order systems. Moreover, we derive invariant solutions for these systems. Finally, for each order n, we are able to find non-negative solutions.
Keywords: higher-order evolution systems; Lie symmetries; exact solutions higher-order evolution systems; Lie symmetries; exact solutions

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MDPI and ACS Style

Tracinà, R. Symmetries and Invariant Solutions of Higher-Order Evolution Systems. Symmetry 2024, 16, 1023. https://doi.org/10.3390/sym16081023

AMA Style

Tracinà R. Symmetries and Invariant Solutions of Higher-Order Evolution Systems. Symmetry. 2024; 16(8):1023. https://doi.org/10.3390/sym16081023

Chicago/Turabian Style

Tracinà, Rita. 2024. "Symmetries and Invariant Solutions of Higher-Order Evolution Systems" Symmetry 16, no. 8: 1023. https://doi.org/10.3390/sym16081023

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