Special Issue "Symmetry and Equivalence Transformations:Theory and Their Applications to Real Phenomena Modeling"

A special issue of Symmetry (ISSN 2073-8994).

Deadline for manuscript submissions: closed (30 September 2019).

Special Issue Editors

Prof. Dr. Mariano Torrisi
E-Mail Website
Guest Editor
Dipartimento di Matematica e Informatica, University of Catania, 95128 Catania, Italy
Interests: group methods for nonlinear differential equations (both ODEs and PDEs); reduction techniques for the search of exact solutions of PDEs; applications of the group methods to reaction diffusion models, such as nonlinear governing equations modeling population dynamics and biomathematical problems; nonlinear diffusion and propagation of heat
Special Issues, Collections and Topics in MDPI journals
Prof. Dr. Rita Tracinà
E-Mail Website
Guest Editor
Department of Mathematics and Computer Science, Catania University, Catania, Italy
Interests: equivalence transformations and their differential invariants; symmetry classifications and exact solutions of PDEs; application of the group methods to diffusion models; conservation laws
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

Differential equations can be considered one of the most powerful tools to describe real phenomena as those of the natural and life sciences.

The search for their solutions has been an exciting challenge for scientists, in particular for mathematicians. A great impulse of this research was provided by Lie at the end of 19th century. He applied symmetry and equivalence transformations to differential equations originating developments of several methods based on the group transformations that allow often to get solutions for differential equations in a methodological way.

Nowadays, using computer algebra packages (such as MAPLE, MACSYMA, REDUCE, etc.) it is very simple to determine Lie symmetries and, by applying the reduction method, solutions of a specific differential equation.

However, such packages are not so powerful when in differential equations have some arbitrary elements (constitutive functions) or when the equation admits only trivial symmetries, or even no symmetry. For these last cases, other methods for determining reductions (nonclassical or conditional symmetry, weak symmetry, etc.) have been developed.

In the presence of constitutive functions, equivalence transformations and their differential invariants, can be useful to simplify the problem of group classification. Recent developments in biomathematics and in population dynamics bring interesting problems regarding the classification of reaction diffusion systems, for both parabolic and hyperbolic types, with respect to their several constitutive functions. Equivalence transformations are non-degenerate point transformations, which preserve the differential structure of the equation and change only the arbitrary elements. Then, they transform solutions of an equation of the class in solutions of the equivalent equation.

In this Special Issue, original and review papers devoted to group classifications of classical or recent models are welcome, as are those devoted to theoretical developments of group methods and their applications to ordinary and partial differential equations of nonlinear models of real phenomena.

Prof. Dr. Mariano Torrisi
Prof. Dr. Rita Tracinà
Guest Editors

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All papers will be peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Symmetry is an international peer-reviewed open access monthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 1800 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.


  • Group classification problems and modeling
  • Symmetry reductions
  • Non-classical reductions
  • Potential symmetries
  • Equivalence transformations
  • Exact solutions
  • Differential invariants
  • Linearization
  • Diffusion and transport systems
  • Reaction diffusion systems

Published Papers

There is no accepted submissions to this special issue at this moment.
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