https://doi.org/10.1140/epjp/s13360-023-03818-4
Regular Article
An optimal system, invariant solutions, conservation laws, and complete classification of Lie group symmetries for a generalized (2+1)-dimensional Davey–Stewartson system of equations for the wave propagation in water of finite depth
Department of Mathematics, Faculty of Mathematical Sciences, University of Delhi, 110007, Delhi, India
a
dhimans600@gmail.com
b
sachinambariya@gmail.com
Received:
10
September
2022
Accepted:
14
February
2023
Published online:
2
March
2023
The nonlinear Schrödinger equation has had several applications in the mean-field regime, including planar waveguides, nonlinear optical fibers, and Bose-Einstein condensates contained in highly anisotropic cigar-shaped traps. We investigate wave propagation dynamics in water of finite depth using the generalized Davey–Stewartson system of equations due to gravity force and surface tension. Finally, we study the governing model with full nonlinearity using the Lie symmetry approach. The generalized Davey–Stewartson equations are used in this work to obtain a variety of closed-form invariant solutions. Two stages of Lie symmetry reduction were used to produce the desired analytical solutions. Moreover, we will derive Lie symmetry generators and Lie symmetry groups, followed by a derivation of the one-dimensional optimal system for subalgebras. This optimal system leads to specific symmetry reductions. By means of these symmetry reductions, we can get analytical solutions, such as rational solutions, soliton solutions, and solutions based on arbitrary independent functional parameters. In addition, using the new conservation theorem and Noether operators, we derive conservation laws for the DS system of equations as well. A differential equation can be analyzed using these conservation laws to determine its internal properties, existence, and uniqueness. Symbolic computations are carried out using Mathematica and Maple software packages.
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© The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2023. 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.
