Manuscript Topics

Most of the models appearing in applied sciences, such as biology, physics, medicine can be described by nonlinear partial differential equations (PDEs). The most powerful methods for constructing exact solutions of nonlinear PDEs are symmetry-based methods. These methods were developed by the Norwegian mathematician Sophus Lie in the 19th century and were essentially developed using modern mathematical language. The Lie methods still attracts the attention of many researchers and many of their generalizations have been developed. Moreover, many direct methods have been developed to derive exact solutions of nonlinear PDEs whit physical and biomedical applications.

It is well known that the integrability of differential equations is strongly related to the existence of conservation laws. Conservation laws are used for existence, uniqueness and stability analysis and for the development of numerical methods. Recently, they have been applied to find exact solutions of certain partial differential equations.

The main aim of this Special Issue is to focus on some recent developments in finding solutions of partial differential equations including methods and applications of conservation laws and symmetries of differential equations. Articles and reviews devoted to the theoretical foundations of symmetry-based methods and their applications as well as direct method for solving nonlinear differential equations and nonlinear models (including for biomedical applications) are welcome.

Keywords: Mathematical models, reaction diffusion, Symmetries, conservation laws, reductions, exact solutions

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