Proceedings of the International Geometry Center

ISSN-print: 2072-9812
ISSN-online: 2409-8906
ISO: 26324:2012
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On symmetry reduction and some classes of invariant solutions of the (1+3)-dimensional homogeneous Monge-Ampère equation

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Vasyl Fedorchuk
Volodymyr Fedorchuk

Abstract

We study the relationship between structural properties of the two-dimensional nonconjugate subalgebras of the same rank of the Lie algebra of the Poincaré group P(1,4) and the properties of reduced equations for the (1+3)-dimensional homogeneous Monge-Ampère equation. In this paper, we present some of the results obtained concerning symmetry reduction of the equation under investigation to identities. Some classes of the invariant solutions (with arbitrary smooth functions) are presented.

Keywords:
symmetry reduction, invariant solutions, classification of Lie algebras, nonconjugate subalgebras, Poincare group P(1,4), Monge-Ampère equation

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How to Cite
Fedorchuk, V., & Fedorchuk, V. (2021). On symmetry reduction and some classes of invariant solutions of the (1+3)-dimensional homogeneous Monge-Ampère equation. Proceedings of the International Geometry Center, 14(3), 206-218. https://doi.org/10.15673/tmgc.v14i3.2078
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Papers
Author Biographies

Vasyl Fedorchuk, Pidstryhach Institute for Applied Problems of Mechanics and Mathematics of NAS of Ukraine

Pidstryhach Institute for Applied Problems of Mechanics and Mathematics of NAS of Ukraine, 79060, 3-b Naukova St., Lviv, Ukraine

Volodymyr Fedorchuk, Pidstryhach Institute for Applied Problems of Mechanics and Mathematics of NAS of Ukraine

Pidstryhach Institute for Applied Problems of Mechanics and Mathematics of NAS of Ukraine, 79060, 3-b Naukova St., Lviv, Ukraine