Classification of differential equations with respect to their symmetry properties
According to the materials of scientific report at the meeting of the Presidium of NAS of Ukraine, July 5, 2017
DOI:
https://doi.org/10.15407/visn2017.09.033Keywords:
Lie symmetry, group classification, equivalence group, method of mappings between classes, Kawahara equation, reaction-diffusion equation, exact solutionsAbstract
The report is devoted to the problem of Lie symmetry classification for classes of nonlinear partial differential equations. Such symmetries allow one, in particular, to select equations of potential physical interest and to construct their exact solutions. For many classes of partial differential equations which are important for applications classical methods of group analysis do not result in exhaustive group classification. Such complicated group classification problems require new tools to be solved completely. Majority of the modern approaches are based on the usage of nondegenerate point transformations. Using the group classifications of variable coefficient generalized Kawahara equations and quasilinear reaction–diffusion equations as illustrative examples, we show the effectiveness of the recently developed approaches. These approaches include, in particular, the construction of the widest possible equivalence groups and the method of mapping between classes.
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