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Bilinear Bäcklund, Lax pairs, breather waves, lump waves and soliton interaction of (2+1)-dimensional non-autonomous Kadomtsev–Petviashvili equation

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Abstract

This article describes the characteristic of integrability via Painlevé analysis of the Kadomtsev–Petviashvili (KP) equation under the influence of an external force along with a damping. Introducing the Hirota’s approach multi-soliton solution of the said equation is acquired in excited systems. Utilizing the obtained solutions, the interaction of solitary wave is observed with special care. It has been observed that interactive autonomous solitons appear to remain in their original shape after collision. However, the non-autonomous soliton changes its shape and directions after collision. The background from which the solitons rise also significantly changes due to the action of external forces. The lump-type wave and some complicated mixed soliton are derived from the bilinear form of the said equation with the appropriate choice of polynomial functions. In addition, the lump solution is obtained by the long wave limit method which is appeared physically the same as the previous one. On the basis of the obtained mixed soliton, the interaction of the strip soliton and lump wave is graphically described. During the investigation of the interaction, fusion-type situation appears. Finally, from the analytical results of the relevant motions, it is also confirmed that the velocity, maximum altitude, and interacting natures of the wave quantities are all influenced by the damping and forcing terms. The interacting natures of the wave quantities are entirely investigated also from numerical understanding.

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Acknowledgements

In addition to the authors’ gratitude for the reviewers’ comments and suggestions, we also want to appreciate the help of the reviewers in improving the quality of the paper. Mr. Subrata Roy (JRF) sincerely appreciates the Fellowship granted by University Grants Commission (UGC) [No. 1106/2018].

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Authors and Affiliations

  1. Department of Mathematics, Cooch Behar Panchanan Barma University, Cooch Behar, West Bengal, 736101, India

    Subrata Roy & Rishi Raj Kairi

  2. Department of Mathematics, Mathabhanga College, Cooch Behar, West Bengal, 736164, India

    Santanu Raut

  3. Department of Mathematics, Siksha Bhavana, Visva-Bharati, Santiniketan, 731235, India

    Prasanta Chatterjee

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  1. Subrata Roy
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SR contributed to writing—original draft preparation and writing—review and editing. SR contributed to software, visualization, and methodology. RRK contributed to conceptualization. PC contributed to investigation.

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Correspondence to Santanu Raut.

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Roy, S., Raut, S., Kairi, R.R. et al. Bilinear Bäcklund, Lax pairs, breather waves, lump waves and soliton interaction of (2+1)-dimensional non-autonomous Kadomtsev–Petviashvili equation. Nonlinear Dyn 111, 5721–5741 (2023). https://doi.org/10.1007/s11071-022-08126-7

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