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A new (n+1)-dimensional generalized Kadomtsev–Petviashvili equation: integrability characteristics and localized solutions

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Abstract

Searching for higher-dimensional integrable models is one of the most significant and challenging issues in nonlinear mathematical physics. This paper aims to extend the classic lower-dimensional integrable models to arbitrary spatial dimension. We investigate the celebrated Kadomtsev–Petviashvili (KP) equation and propose its (n+1)-dimensional integrable extension. Based on the singularity manifold analysis and binary Bell polynomial method, it is found that the (n+1)-dimensional generalized KP equation has N-soliton solutions, and it also possesses the Painlevé property, Lax pair, Bäcklund transformation as well as infinite conservation laws, and thus the (n+1)-dimensional generalized KP equation is proven to be completely integrable. Moreover, various types of localized solutions can be constructed starting from the N-soliton solutions. The abundant interactions including overtaking solitons, head-on solitons, one-order lump, two-order lump, breather, breather-soliton mixed solutions are analyzed by some graphs.

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Acknowledgements

The authors would like to sincerely and deeply thank the editor and the anonymous referees for their helpful comments and concrete constructive suggestions, which led to an improved version of this paper.

Funding

This work is supported by the National Natural Science Foundation of China (No. 11871328).

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Authors and Affiliations

  1. Department of Information Management, School of Management, Shanghai University, Shanghai, 200444, China

    Gui-Qiong Xu

  2. Department of Mathematics, Saint Xavier University, Chicago, IL, 60655, USA

    Abdul-Majid Wazwaz

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  1. Gui-Qiong Xu
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Xu, GQ., Wazwaz, AM. A new (n+1)-dimensional generalized Kadomtsev–Petviashvili equation: integrability characteristics and localized solutions. Nonlinear Dyn 111, 9495–9507 (2023). https://doi.org/10.1007/s11071-023-08343-8

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