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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


Full text: PDF file (668 kB)
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UDC: 517.95
Received: 06.09.2014
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}


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