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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

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Abstract

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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Acknowledgements

The authors wish to acknowledge the Editor and referees for their supportive and constructive comments. The author, Sachin Kumar, is grateful for the financial support provided by “SERB-DST”, New Delhi, India under the EEQ scheme with reference number EEQ/2020/000238.

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  1. Department of Mathematics, Faculty of Mathematical Sciences, University of Delhi, Delhi, 110007, India

    Shubham Kumar Dhiman & Sachin Kumar

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  1. Shubham Kumar Dhiman
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  2. Sachin Kumar
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Correspondence to Shubham Kumar Dhiman or Sachin Kumar.

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Dhiman, S.K., Kumar, S. 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. Eur. Phys. J. Plus 138, 195 (2023). https://doi.org/10.1140/epjp/s13360-023-03818-4

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