Mathematical Physics
[Submitted on 23 Apr 2018 (v1), last revised 3 Dec 2019 (this version, v3)]
Title:Enhanced group classification of nonlinear diffusion-reaction equations with gradient-dependent diffusion
View PDFAbstract:We carry out the enhanced group classification of a class of (1+1)-dimensional nonlinear diffusion-reaction equations with gradient-dependent diffusivity using the two-step version of the method of furcate splitting. For simultaneously finding the equivalence groups of an unnormalized class of differential equations and a collection of its subclasses, we suggest an optimized version of the direct method. The optimization includes the preliminary study of admissible transformations within the entire class and the successive splitting of the corresponding determining equations with respect to arbitrary elements and their derivatives depending on auxiliary constraints associated with each of required subclasses. In the course of applying the suggested technique to subclasses of the class under consideration, we construct, for the first time, a nontrivial example of finite-dimensional effective generalized equivalence group. Using the method of Lie reduction and the generalized separation of variables, exact solutions of some equations under consideration are found.
Submission history
From: Roman Popovych [view email][v1] Mon, 23 Apr 2018 23:12:09 UTC (36 KB)
[v2] Wed, 26 Dec 2018 23:47:34 UTC (41 KB)
[v3] Tue, 3 Dec 2019 01:07:45 UTC (41 KB)
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