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New Analytic Solutions for Fluid Flow Equations in Higher Dimensions Around an Offshore Structure Describing Bidirectional Wave Surfaces

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Abstract

Offshore structures are utilized in several fields, including marine engineering, the oil and gas industries, energy harvesting systems, transportation, aquaculture, and more. The exact solution of nonlinear evolution equations shows the various physical behavior of these equations. In this order, this article aims to examine the \((2+1)\) and \((3+1)\)-dimensional Kadomtsev–Petviashvili–Benjamin–Bona–Mahony equations for the fluid flows around an offshore structure. The Paul–Painlevé approach method has been adopted for the first time to solve these nonlinear evolution equations analytically. By employing this method, abundant multiple exact solutions have been derived. All the obtained solutions are verified by using the software MATHEMATICA. All the results have been expressed by the 3D graphs. These graphs depict the solitary wave solutions in the form of singular, bright, dark and singular periodic-soliton solutions. By carefully selecting the parameters used in numerical simulation and physical explanations, we can demonstrate the importance of the findings. The obtained results depict the bidirectional wave surfaces around an offshore structure in fluid dynamics. It is suggested that the provided approach can be used to facilitate nonlinear dynamical models that can be used in a wide range of physical applications. We believe that many professionals in the field of nonlinear physics and engineering models will gain knowledge from this study.

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  1. Department of Mathematics, National Institute of Technology, Rourkela, 769008, India

    Shailendra Singh & Santanu Saha Ray

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  1. Shailendra Singh
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Singh, S., Saha Ray, S. New Analytic Solutions for Fluid Flow Equations in Higher Dimensions Around an Offshore Structure Describing Bidirectional Wave Surfaces. Qual. Theory Dyn. Syst. 22, 123 (2023). https://doi.org/10.1007/s12346-023-00823-x

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