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A direct Bäcklund transformation for a (3+1)-dimensional Kadomtsev–Petviashvili–Boussinesq-like equation

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Abstract

In this paper, a Kadomtsev–Petviashvili–Boussinesq-like equation in (3+1)-dimensions is firstly introduced by using the combination of the Hirota bilinear Kadomtsev–Petviashvili equation and Boussinesq equation in terms of function f. And then a direct bilinear Bäcklund transformation of this new model is constructed, which consists of seven bilinear equations and ten arbitrary parameters. Based on this constructed bilinear Bäcklund transformation, some classes of exponential and rational traveling wave solutions with arbitrary wave numbers are presented.

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Acknowledgements

This work is supported by the National Natural Science Foundation of China (Nos. 11101029, 11271362 and 11375030), the Fundamental Research Funds for the Central Universities (No. 610806), Beijing City Board of Education Science and Technology Key Project (No. KZ201511232034), Beijing Nova program (No. Z1311090 00413029) and Beijing Finance Funds of Natural Science Program for Excellent Talents (No. 2014000026833ZK19). All the authors deeply appreciate all the anonymous reviewers for their helpful and constructive suggestions, which can help us improve this paper further.

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Authors and Affiliations

  1. Department of Applied Mathematics, University of Science and Technology Beijing, Beijing, 100083, China

    Jian-Ping Yu

  2. Department of Mathematics, Beijing University of Chemical Technology, Beijing, 100029, China

    Yong-Li Sun

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  1. Jian-Ping Yu
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  2. Yong-Li Sun
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Correspondence to Yong-Li Sun.

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Yu, JP., Sun, YL. A direct Bäcklund transformation for a (3+1)-dimensional Kadomtsev–Petviashvili–Boussinesq-like equation. Nonlinear Dyn 90, 2263–2268 (2017). https://doi.org/10.1007/s11071-017-3799-0

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  • DOI: https://doi.org/10.1007/s11071-017-3799-0

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