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Bifurcations, chaotic behavior, sensitivity analysis and soliton solutions of the extended Kadometsev–Petviashvili equation

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Abstract

The main aim of this study is to conduct an in-depth exploration of a recently introduced extended variant of the Kadomtsev–Petviashvili (KP) equation. To achieve this goal, we employ the Galilean transformation to derive the dynamic framework associated with the governing equation. Subsequently, we apply the principles of planar dynamical system theory to perform a bifurcation analysis. By incorporating a perturbed element into the established dynamic framework, we explore the potential emergence of chaotic behaviors within the extended KP equation. This investigation is supported by the presentation of phase portraits in both two and three dimensions. Additionally, to ascertain the stability of solutions, we conduct a sensitivity analysis on the dynamic framework employing the Runge–Kutta method. Our results affirm that minor variations in initial conditions have minimal impact on solution stability. Furthermore, employing the modified tanh method, we construct multiple instances of solitons and kinks for the proposed model.

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Acknowledgements

This work was partially supported by Science and Technology General Project of Jiangxi Provincial Department of Education (No. GJJ219018) and Science and Technology General Project of Nanchang Normal College of Applied Technology (No. NYSJG21927).

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Authors and Affiliations

  1. Department of Mathematics, Nanchang Normal College of Applied Technology, Nanchang, 330036, Jiangxi, People’s Republic of China

    Chongkun Xu

  2. School of Mathematical Sciences, Jiangsu University, Zhenjiang, 212013, Jiangsu, People’s Republic of China

    Mati ur Rahman

  3. Department of Computer Science and Mathematics, Lebanese American University, Beirut, Lebanon

    Mati ur Rahman

  4. Department of Mathematics, Saveetha School of Engineering, Saveetha Institute of Medical and Technical Sciences, Chennai, 602105, Tamil Nadu, India

    Homan Emadifar

  5. MEU Research Unit, Middle East University, Amman, 11831, Jordan

    Homan Emadifar

  6. Department of Mathematics, Hamedan Branch, Islamic Azad University, Hamedan, Iran

    Homan Emadifar

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  1. Chongkun Xu
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  2. Mati ur Rahman
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Correspondence to Homan Emadifar.

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Xu, C., ur Rahman, M. & Emadifar, H. Bifurcations, chaotic behavior, sensitivity analysis and soliton solutions of the extended Kadometsev–Petviashvili equation. Opt Quant Electron 56, 405 (2024). https://doi.org/10.1007/s11082-023-05958-4

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