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Stability analysis and multi-wave structures of the ill-posed Boussinesq equation arising in nonlinear physical science

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Abstract

In this manuscript, an analysis is carried out on the dynamic behavior of the ill-posed Boussinesq equation, which arises in nonlinear lattices and shallow water waves. The simplified Hirota method is employed to obtain multi-wave structures, such as one-soliton, two-soliton and three-soliton solutions. Some solutions are visually demonstrated through 3D, 2D and density plots. Furthermore, a comprehensive discussion on the stability analysis of the equation under study is presented. These results are innovative and have not been previously investigated in the context of this equation. These results show that the methodology used is concise, straightforward, and efficient, and as a result, it makes a significant contribution to comprehending the complexity of multi-wave profiles in nonlinear physical science models.

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Authors and Affiliations

  1. School of Mathematics and Statistics, Central South University, Changsha, 410083, China

    Muhammad Naveed Rafiq & Haibo Chen

  2. Department of Mathematics and Statistics, The University of Lahore, Lahore, 54590, Pakistan

    Muhammad Hamza Rafiq

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  1. Muhammad Naveed Rafiq
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  2. Haibo Chen
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Rafiq, M.N., Chen, H. & Rafiq, M.H. Stability analysis and multi-wave structures of the ill-posed Boussinesq equation arising in nonlinear physical science. Opt Quant Electron 55, 1243 (2023). https://doi.org/10.1007/s11082-023-05537-7

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