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Integrability, multi-solitons, breathers, lumps and wave interactions for generalized extended Kadomtsev–Petviashvili equation

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Abstract

In this paper, we take into consideration a general form of the extended Kadomtsev–Petviashvili equation, which has several applications in applied sciences and engineering. The Painlevé analysis via WTC–Kruskal algorithm is first used to validate the integrability of this nonlinear model. Thereafter, we determine the multi-solitons, breather solutions, lump waves, rouge waves, lump with solitary waves interaction, and breather with solitons interaction by using various ansatz’s functions based on bilinear formalism and symbolic computation. The solitary wave ansatz method is used to extract the bight solitons, dark solitons, singular solitons, and the periodic function solutions. In addition, the Ma-breather, Kuznetsov–Ma breather, and their associated rogue wave solutions are also discussed. In order to demonstrate several physical structures, the figures relating to these solutions are illustrated by selecting appropriate parametric values in 2D, 3D, and contour plots with the assistance of the symbolic package Mathematica 13.1. The dynamics of nonlinear wave models are addressed by these solutions.

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Acknowledgements

The authors would like to thank the EXCEL Scholars Program and the Department of Mathematics at Lafayette College for their support of this project.

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  1. Department of Mathematics, Lafayette College, Easton, PA, USA

    Lanre Akinyemi

  2. Department of Computer Science, Lafayette College, Easton, PA, USA

    Eliso Morazara

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  1. Lanre Akinyemi
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Akinyemi, L., Morazara, E. Integrability, multi-solitons, breathers, lumps and wave interactions for generalized extended Kadomtsev–Petviashvili equation. Nonlinear Dyn 111, 4683–4707 (2023). https://doi.org/10.1007/s11071-022-08087-x

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