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 Chelyab. Fiz.-Mat. Zh., 2016, Volume 1, Issue 1, Pages 93–103 (Mi chfmj10)

Mathematics

Group analysis of a quasilinear equation

V. E. Fedorov, N. V. Filin

Chelyabinsk State University, Chelyabinsk, Russia

Abstract: Symmetry analysis is carried out for a second order quasilinear partial differential equation with a free element depending on the phase function. In the nonlinear case two-dimensional principal groups kernel and free element specifications leading to the third symmetries are found. Invariant solutions or submodels are calculated for non-similar one-dimensional subalgebras of the principal Lie algebras with the specifications that were obtained. Conservation laws for the equations are calculated. The linear case with a constant free element is researched also. It is shown that the investigation results don't depend on the equation type.

Keywords: group analysis, symmetries group, Lie algebra, optimal system of subalgebras, invariant solution, submodel, conservation law.

 Funding Agency Grant Number Ministry of Education and Science of the Russian Federation 14.Z50.31.0020

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UDC: 517.95
Revised: 02.02.2016

Citation: V. E. Fedorov, N. V. Filin, “Group analysis of a quasilinear equation”, Chelyab. Fiz.-Mat. Zh., 1:1 (2016), 93–103

Citation in format AMSBIB
\Bibitem{FedFil16} \by V.~E.~Fedorov, N.~V.~Filin \paper Group analysis of a quasilinear equation \jour Chelyab. Fiz.-Mat. Zh. \yr 2016 \vol 1 \issue 1 \pages 93--103 \mathnet{http://mi.mathnet.ru/chfmj10} \elib{https://elibrary.ru/item.asp?id=27541610}