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N-soliton, Mth-order breather, Hth-order lump, and hybrid solutions of an extended (3+1)-dimensional Kadomtsev-Petviashvili equation

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Abstract

Investigated in this paper is an extended (3+1)-dimensional Kadomtsev-Petviashvili equation. We determine the N-soliton solutions of that equation via an existing bilinear form, and then construct the Mth-order breather and Hth-order lump solutions from the N-soliton solutions using the complex conjugated transformations and long-wave limit method, where N, M, and H are the positive integers. In addition, we develop the hybrid solutions composed of the first-order breather and one soliton, the first-order lump and one soliton, as well as the first-order lump and first-order breather. Through those solutions, we demonstrate the (1) one breather or lump, (2) interaction between the two breathers or lumps, (3) interaction between the one breather and one soliton, (4) interaction between the one lump and one soliton, and (5) interaction between the one lump and one breather. We observe that the amplitude, shape, and velocity of the one breather or lump remain unchanged during the propagation. We also find that the amplitudes, shapes, and velocities of the solitons, breathers, and lumps remain unchanged after the interactions, suggesting that those interactions are elastic.

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Acknowledgements

We express our sincere thanks to the Editors and Reviewers for their valuable comments.

Funding

This work has been supported by the BUPT Excellent Ph.D. Students Foundation under Grant No. CX2022156.

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  1. State Key Laboratory of Information Photonics and Optical Communications, and School of Science, Beijing University of Posts and Telecommunications, Beijing, 100876, China

    Yuan Shen, Bo Tian, Chong-Dong Cheng & Tian-Yu Zhou

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  1. Yuan Shen
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Shen, Y., Tian, B., Cheng, CD. et al. N-soliton, Mth-order breather, Hth-order lump, and hybrid solutions of an extended (3+1)-dimensional Kadomtsev-Petviashvili equation. Nonlinear Dyn 111, 10407–10424 (2023). https://doi.org/10.1007/s11071-023-08369-y

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