Recent Advances and Applications of Lie Symmetry Techniques

A special issue of Symmetry (ISSN 2073-8994). This special issue belongs to the section "Mathematics".

Deadline for manuscript submissions: closed (31 December 2022) | Viewed by 2175

Special Issue Editors


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Guest Editor
School of Computer Science and Applied Mathematics, University of the Witwatersrand, Private Bag 3, WITS 2050, South Africa
Interests: solute transport in soils; population dynamics; heat transfer; Lie symmetry techniques; differential equations

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Guest Editor
UniSA STEM, University of South Australia, Mawson Lakes, Adelaide, SA 5095, Australia
Interests: nonlinear partial differential equations; lie symmetry techniques; reaction-diffusion problems; biological invasions

Special Issue Information

Dear Colleagues,

The search for exact solutions of differential equations continues unabated. Perhaps this is because when constructed, exact solutions may be used to benchmark numerical schemes, and in addition, these solutions can give insight into real-world processes or phenomena. Lie symmetry techniques provide a systematic tool that can be used to construct invariant (exact) solutions. This Special Issue is devoted to the analysis of applied linear and nonlinear differential equations arising in different physical phenomena. Papers in the applications of, but not limited to, point symmetries, nonclassical symmetries, conservations laws, Noether symmetries, and group classification will be considered for publication in this Special Issue. 

Prof. Dr. Raseelo J. Moitsheki
Dr. Bronwyn Hajek
Guest Editors

Manuscript Submission Information

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Keywords

  • lie point symmetries
  • conservation laws
  • Noether symmetries
  • group classification
  • differential equations
  • group invariant solutions
  • first integrals
  • nonclassical (or Q-conditional) symmetries

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Published Papers (1 paper)

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Research

14 pages, 540 KiB  
Article
Symmetries and Solvability of a Class of Higher Order Systems of Ordinary Difference Equations
by Kgatliso Mkhwanazi and Mensah Folly-Gbetoula
Symmetry 2022, 14(1), 108; https://doi.org/10.3390/sym14010108 - 8 Jan 2022
Cited by 1 | Viewed by 1594
Abstract
We perform Lie analysis for a system of higher order difference equations with variable coefficients and derive non-trivial symmetries. We use these symmetries to find exact formulas for the solutions in terms of k. Furthermore, a detailed study for a specific value [...] Read more.
We perform Lie analysis for a system of higher order difference equations with variable coefficients and derive non-trivial symmetries. We use these symmetries to find exact formulas for the solutions in terms of k. Furthermore, a detailed study for a specific value of k is presented. Our findings generalize some results in the literature. Full article
(This article belongs to the Special Issue Recent Advances and Applications of Lie Symmetry Techniques)
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