Manuscript Topics

At end of the last century the study and analysis of biological phenomena and life science events received a big impulse from the use of mathematical models. New models have been proposed for describing population dynamics, the evolution of cancer in tissues, cellular developments, chemotaxis, as well as for modeling epidemics such as malaria and dengue, to name a few. On the other hand, mathematical models have also been useful in studies related to finance, psychology, anorexia, depression, love affairs, among others.

The mathematical tools for the investigation of biology problems and their aid to daily problems that life is offering us are crucial.  Their growth and progress in the last decades make the study of mathematical models critical in the quick advancement of natural, biological, physical, life and social sciences. Many of those models are governed by systems of differential equations, both ODEs and PDE, whose solutions give news about features of the models they are describing. Therefore, the search for their exact, explicit and numerical solutions plays an important role in these studies. A powerful and methodological way to derive solutions of differential equations is offered by the symmetry (invariant transformation) methods. At end of XIX century Sophus Lie applied the symmetry groups and equivalence transformations to differential equations originating a field of research devoted to several applications of these methods to differential equations.

In this Special Issue we hope to bring together original and review papers devoted to applications and theoretical developments of symmetry methods to classical or recent linear and nonlinear models in applied sciences.

Potential topics include but are not limited to:
• Group classification problems and modeling in biological and life sciences.
• Symmetry reductions
• Non classical reductions
• Potential symmetries
• Symmetries of difference equations
• Equivalence transformations
• Exact solutions
• Differential invariants
• Linearization
• Diffusion and transport systems
• Reaction diffusion systems
• Balance equations
• Conservation laws

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