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Kink degeneracy and rogue potential solution for the (3+1)-dimensional B-type Kadomtsev–Petviashvili equation

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Abstract

In this paper, we obtained the exact breather-type kink soliton and breather-type periodic soliton solutions for the (3 + 1)-dimensional B-type Kadomtsev–Petviashvili (BKP) equation using the extended homoclinic test technique. Some new nonlinear phenomena, such as kink and periodic degeneracies, are investigated. Using the homoclinic breather limit method, some new rational breather solutions are found as well. Meanwhile, we also obtained the rational potential solution which is found to be just a rogue wave. These results enrich the variety of the dynamics of higher-dimensional nonlinear wave field.

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Acknowledgements

The authors thank the reviewer for valuable suggestions and help.

This work was supported by the Chinese Natural Science Foundation (Grant Nos 11361048, 10971169), Sichuan Educational Science Foundation (Grant No. 15ZB0113) and Southwest University of Science and Technology Foundation (Grant No. 14zx1108).

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Authors and Affiliations

  1. Applied Technology College, Southwest University of Science and Technology, Mianyang, 621010, People’s Republic of China

    ZHENHUI XU

  2. School of Science, Southwest University of Science and Technology, Mianyang, 621010, People’s Republic of China

    HANLIN CHEN

  3. School of Mathematics and Physics, Yunnan University, Kunming, 650091, People’s Republic of China

    ZHENGDE DAI

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  1. ZHENHUI XU
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  2. HANLIN CHEN
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  3. ZHENGDE DAI
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Correspondence to ZHENHUI XU.

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XU, Z., CHEN, H. & DAI, Z. Kink degeneracy and rogue potential solution for the (3+1)-dimensional B-type Kadomtsev–Petviashvili equation. Pramana - J Phys 87, 31 (2016). https://doi.org/10.1007/s12043-016-1232-8

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  • DOI: https://doi.org/10.1007/s12043-016-1232-8

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