Classification of Lie reductions of generalized Kawahara equations with variable coefficients
DOI:
https://doi.org/10.15407/dopovidi2022.06.003Keywords:
Lie symmetries, reduction method, Kawahara equations, group classification, exact solutionsAbstract
A class of generalized Kawahara equations with time-dependent coefficients is studied from Lie symmetry point of view. A classification of Lie reductions of equations from this class has been carried out. For each case of Lie symmetry extension, the type of the maximal invariance algebra of the corresponding Kawahara equation is determined, and the respective optimal system of one-dimensional subalgebras is found, which are further used to construct Lie ansatzes. Lie reductions of Kawahara equations to ordinary differential equations are performed, some exact Lie invariant solutions are also constructed.
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