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Unveiling single soliton solutions for the (3+1)-dimensional negative order KdV–CBS equation in a long wave propagation

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Abstract

In this study, we explore a captivating (3+1)-dimensional negative-order Korteweg–de Vries Calogero–Bogoyavlenskii–Schiff equation, which combines elements of the Korteweg–de Vries equation and the Calogero–Bogoyavlenskii–Schiff equation. Our research investigates how this model characterises long-wave interactions and its relevance in mathematics, physics, and engineering. We employ unified and singular manifold methods to obtain precise travelling wave solutions expressed in various functional forms. By using Maple and Mathematica software to extract valid solutions, including kink-like soliton, singular periodic wave solution, anti-kink solutions, and singular solitons. These methodologies have shown impressive efficiency in solving complex nonlinear equations, offering precise solutions, and streamlining mathematical processes through transformations. This leads to quicker and more accurate outcomes in diverse scientific and engineering applications. Our findings underscore the model’s superiority over existing methods and its importance in comprehending applied mathematical processes, as demonstrated through 3-D and 2-D graphical representations.

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The corresponding author can provide the data supporting the findings of this study upon a reasonable request.

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Authors and Affiliations

  1. Department of Mathematics, University of the Punjab, Lahore, Pakistan

    Isma Ghulam Murtaza, Nauman Raza & Saima Arshed

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  1. Isma Ghulam Murtaza
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  2. Nauman Raza
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  3. Saima Arshed
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Correspondence to Isma Ghulam Murtaza.

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Ghulam Murtaza, I., Raza, N. & Arshed, S. Unveiling single soliton solutions for the (3+1)-dimensional negative order KdV–CBS equation in a long wave propagation. Opt Quant Electron 56, 614 (2024). https://doi.org/10.1007/s11082-024-06276-z

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