Geodesic
Optimal system of subalgebras for sum of two ideals $\mathfrak{aff}(\mathbb{R})\oplus \mathfrak{sl}(2,\mathbb{R})$
Sibirskij žurnal čistoj i prikladnoj matematiki, Tome 15 (2015) no. 2, pp. 90-96

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Optimal system of subalgebras for one algebra Lie is constructed. This algebra Lie is direct sum of algebra of affine transformations group $Aff(\mathbb{R})$ and algebra of projective transformations group $SL(2,\mathbb{R})$. Some invariant solutions for one nonlinear partial differential equation are found.
Keywords: symmetry group, Lie algebra
Mots-clés : optimal system of subalgebras, invariant solutions. 
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     author = {A. V. Panov},
     title = {Optimal system of subalgebras for sum of two ideals $\mathfrak{aff}(\mathbb{R})\oplus \mathfrak{sl}(2,\mathbb{R})$},
     journal = {Sibirskij \v{z}urnal \v{c}istoj i prikladnoj matematiki},
     pages = {90--96},
     publisher = {mathdoc},
     volume = {15},
     number = {2},
     year = {2015},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VNGU_2015_15_2_a6/}
}
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A. V. Panov. Optimal system of subalgebras for sum of two ideals $\mathfrak{aff}(\mathbb{R})\oplus \mathfrak{sl}(2,\mathbb{R})$. Sibirskij žurnal čistoj i prikladnoj matematiki, Tome 15 (2015) no. 2, pp. 90-96. http://geodesic.mathdoc.fr/item/VNGU_2015_15_2_a6/