https://doi.org/10.1140/epjp/s13360-024-05131-0
Regular Article
Lie symmetry analysis, optimal system and exact solutions for a NLPDE from the reduced quasi-classical self-dual Yang–Mills equation
School of Mathematics and Statistics, Ningbo University, 315211, Ningbo, China
Received:
16
January
2024
Accepted:
23
March
2024
Published online:
15
April
2024
In this paper, the classical Lie group method is employed to obtain exact solutions for a nonlinear partial differential equation (NLPDE) derived from the reduced quasi-classical self-dual Yang–Mills equation. An infinite-dimensional Lie algebra is obtained, and by utilizing a seven-dimensional subspace of this algebra, the commutator table and adjoint representation table are constructed. These tables facilitate the construction of the optimal system for the equation, leading to precise solutions. The obtained solutions are presented graphically, accompanied by a suitable analysis.
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© The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2024. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
