Group analysis of a quasilinear equation
V. E. Fedorov, N. V. Filin
Chelyabinsk State University, Chelyabinsk, Russia
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.
group analysis, symmetries group, Lie algebra, optimal system of subalgebras, invariant solution, submodel, conservation law.
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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
\by V.~E.~Fedorov, N.~V.~Filin
\paper Group analysis of a quasilinear equation
\jour Chelyab. Fiz.-Mat. Zh.
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