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) | Viewed by 695
Special Issue Editors
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
Interests: symmetry methods; applications for differential equations
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
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Keywords
- 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
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