Geodesic
Group analysis of a quasilinear equation
Čelâbinskij fiziko-matematičeskij žurnal, Tome 1 (2016) no. 1, pp. 93-103

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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. 
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     author = {V. E. Fedorov and N. V. Filin},
     title = {Group analysis of a quasilinear equation},
     journal = {\v{C}el\^abinskij fiziko-matemati\v{c}eskij \v{z}urnal},
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     volume = {1},
     number = {1},
     year = {2016},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/CHFMJ_2016_1_1_a9/}
}
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V. E. Fedorov; N. V. Filin. Group analysis of a quasilinear equation. Čelâbinskij fiziko-matematičeskij žurnal, Tome 1 (2016) no. 1, pp. 93-103. http://geodesic.mathdoc.fr/item/CHFMJ_2016_1_1_a9/