Open AccessOn symmetry reduction and some classes of invariant solutions of the (1+3)-dimensional homogeneous Monge-Ampère equation
Author(s) -
В. І. Федорчук,
В. М. Федорчук
Publication year - 2021
Publication title -
trudy meždunarodnogo geometričeskogo centra/pracì mìžnarodnogo geometričnogo centru
Language(s) - English
Resource type - Journals
eISSN - 2409-8906
pISSN - 2072-9812
DOI - 10.15673/tmgc.v14i3.2078
Subject(s) - mathematics , invariant (physics) , homogeneous , rank (graph theory) , symmetry (geometry) , symmetry group , pure mathematics , lie group , reduction (mathematics) , lie algebra , mathematical analysis , mathematical physics , algebra over a field , combinatorics , geometry
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.