https://doi.org/10.1140/epjp/s13360-025-06302-3
Regular Article
Derivation, nonlocal symmetry analysis, and exact solutions of modified Broer-Kaup equations
School of Mathematical Sciences, Inner Mongolia University, 010021, Hohhot, China
Received:
11
November
2024
Accepted:
6
April
2025
Published online:
5
May
2025
Throughout this work, the conservation laws of the (1+1)-dimensional Broer-Kaup (BK) equations are constructed using the multiplier method. These conservation laws are then used to derive higher dimensional BK equations. By introducing constraint conditions, the higher dimensional equation is reduced to a (1+1)-dimensional modified Broer-Kaup (mBK) equations. Subsequently, the mBK equations are researched through the nonlocal symmetry method. A new closed system, which is nonlocally symmetric, is constructed using the Lax pair and the introduction of a potential function. By applying finite symmetry transformations and symmetry reductions to the closed system, the exact solutions of the mBK equations are obtained. By selecting different parameters, a set of knot solutions and dark soliton solutions are derived, and their dynamical behavior is analyzed.
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© The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2025
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.
