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Information × Registration Number 0219U100022, 0118U003803 , R & D reports Title Symmetry classification and exact solutions of nonlinear models of physical and biological processes popup.stage_title Head Vаnieievа Olenа O., Кандидат фізико-математичних наук Registration Date 04-01-2019 Organization The Institute of Mathematics of NASU popup.description2 Key words: Lie symmetry, reduction operator, group classification, equivalence groupoid, Newel-Whitehead-Segel equation, reaction-diffusion equation, exact solutions. Object of research: nonlinear models of mathematical physics and biology. Purpose: to study with the symmetry point of view and to find exact solutions of equations that model real physical and biological processes, in particular of the Newell-Whitehead-Segel equations and diffusion reactions with variable coefficients. Research methods: modern methods of group analysis, in particular, the usage of the equivalence groupoid, the method of mappings between classes of differential equations, the partition of a class, that is not normalized, into normalized subclasses, also the classical Lie-Ovsyannikov method, Lie reduction method, the direct method for finding admissible transformations. The main results obtained in this work are exhaustive group classifications (Lie symmetry classifications) of several classes of reaction-diffusion equations with variable coefficients depending on spatial or temporal variables, as well as the classification of regular nonclassical symmetry operators for the class of the Newell-Whitehead-Segel equations. As a result, model equations with non-trivial symmetric properties are singled out, which are potentially more interesting for applications. Exact solutions have been constructed that allow us to study the nature of diffusion. An important task of finding equivalence groupoids for equations that are interesting for applications is also solved, and the respective classes are investigated for their normalization property. These results are useful, in particular, for the problems of classification of different types of symmetries, local conservation laws and construction of exact solutions, as well as in the study of integrability of nonlinear evolution equations. Product Description popup.authors popup.nrat_date 2020-04-02 Close