A. V. Panov, “Optimal system of subalgebras for sum of two ideals $\mathfrak{aff}(\mathbb{R})\oplus \mathfrak{sl}(2,\mathbb{R})$”, Vestn. Novosib. Gos. Univ., Ser. Mat. Mekh. Inform., 2015, Volume 15, Issue 2,Pages <nobr>90

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Optimal system of subalgebras for sum of two ideals $\mathfrak{aff}(\mathbb{R})\oplus \mathfrak{sl}(2,\mathbb{R})$

A. V. Panov

Chelyabinsk State University

Abstract: 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, optimal system of subalgebras, invariant solutions.

UDC: 517.9

Received: 16.11.2014

DOI: 10.17377/PAM.2015.15.207