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Dispersive soliton solutions to the (4+1)-dimensional Boiti–Leon–Manna–Pempinelli equation via an analytical method

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Abstract

The primary objective of this study is to extract nonlinear wave patterns from the (4+1)-dimensional Boiti–Leon–Manna–Pempinelli (4D-BLMP) equation, considering both constant and time-dependent coefficients, which is used widely to describe the incompressible fluid. By employing the amended extended tanh-function method, we successfully obtained innovative solutions in the form of combo dark bright, hyperbolic or lumps, periodic, and singular mix solitons solutions, and others. To ensure the utmost precision and reliability of our findings, we rigorously confirm them using the robust Mathematica software. These solutions hold paramount importance in the domains of in the study of incompressible fluids and acoustic waves, enriching our understanding of the foundational physical principles embedded within the equation. The study visually presents the computed wave solutions using 2D, 3D, and contour plots, effectively representing the internal structure of the phenomenon. This study proves that the computational method used is efficient, brief, and widely applicable, making it valuable to engineers who work with engineering models and dynamical models. This research can help to better understand physical phenomena in many areas of applied physics, particularly in the study of incompressible fluids and acoustic waves.

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Acknowledgements

The author (Taseer Muhammad) thanks the KKU research unit for the financial and administrative support under grant number 521 for year 44.

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Authors and Affiliations

  1. Department of Mathematics, Faculty of Science, University of Gujrat, Gujrat, 50700, Pakistan

    Jamshad Ahmad & Sobia Rani

  2. Department of Mathematics, College of Sciences, King Khalid University, 61413, Abha, Saudi Arabia

    Taseer Muhammad & Shafqat Ur Rehman

  3. Department of Mathematics, Grand Asian University, 7KM, Pasrur Road, Sialkot, 51310, Pakistan

    Jamshad Ahmad, Sobia Rani, Taseer Muhammad & Shafqat Ur Rehman

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  2. Sobia Rani
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Contributions

JA: resources, supervision, validation, snd acquisition. SR conceptualization, methodology, writing - original draft, formal analysis, validation, and software. TM: resources, acquisition, conceptualization, visualization, investigation, writing-review, and editing. SUR: conceptualization, formal analysis, writing the original draft, review, software implementation, methodology.

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Correspondence to Jamshad Ahmad.

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Ahmad, J., Rani, S., Muhammad, T. et al. Dispersive soliton solutions to the (4+1)-dimensional Boiti–Leon–Manna–Pempinelli equation via an analytical method. Opt Quant Electron 56, 904 (2024). https://doi.org/10.1007/s11082-024-06489-2

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