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Auto-Bäcklund Transformation with the Solitons and Similarity Reductions for a Generalized Nonlinear Shallow Water Wave Equation

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Abstract

Studies on the shallow water waves belong to the cutting-edge issues in sciences and engineering. In this paper, introducing symbolic computation, for a generalized nonlinear shallow water wave equation, with respect to the displacement and velocity of the water, we establish an auto-Bäcklund transformation with some solitonic solutions, as well as a set of the similarity reductions, the latter of which ought to be focused towards a known ordinary differential equation. Our results are seen to tie to the gravitational force and wave height.

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Notes

  1. Such a difference comes from the distinction between Assumption (3) in Ref. [11] and Assumption (16) in this paper.

  2. similar to those in Refs. [49,50,51,52]

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The author expresses sincere thanks to the Editors and Reviewers for their valuable comments.

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  1. College of Science, and Bei**g Key Laboratory on Integration and Analysis of Large-Scale Stream Data, North China University of Technology, Bei**g, 100144, China

    **n-Yi Gao

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Gao, XY. Auto-Bäcklund Transformation with the Solitons and Similarity Reductions for a Generalized Nonlinear Shallow Water Wave Equation. Qual. Theory Dyn. Syst. 23, 181 (2024). https://doi.org/10.1007/s12346-024-01034-8

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