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Bilinear auto-Bäcklund transformation, breather-wave and periodic-wave solutions for a (3+1)-dimensional Boiti–Leon–Manna–Pempinelli equation

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Abstract

Incompressible fluids are seen in ocean engineering, biomechanics, astrophysics, etc. A (3+1)-dimensional Boiti-Leon-Manna-Pempinelli equation is hereby investigated. With the help of the Hirota method and symbolic computation, we present a bilinear auto-Bäcklund transformation with some analytic solutions. Based on the existing N-soliton solutions, we determine the higher-order breather solutions, where N is a positive integer. Via the Hirota–Riemann method, we derive the periodic-wave solutions. Graphical representations of the second-order breather and periodic waves are investigated. Moreover, we graphically present the second-order breather and periodic waves with the influence of the coefficients in that equation. Our results might be helpful to understand certain nonlinear phenomena in fluid mechanics.

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This paper has no associated data, or the data will not be deposited.

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Acknowledgements

We express our sincere thanks to the Editors and Reviewers for their valuable comments. This work has been supported by the National Natural Science Foundation of China under Grant Nos. 11772017, 11272023 and 11471050, by the Fund of State Key Laboratory of Information Photonics and Optical Communications (Beijing University of Posts and Telecommunications), China (IPOC: 2017ZZ05) and by the Fundamental Research Funds for the Central Universities of China under Grant No. 2011BUPTYB02.

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Authors and Affiliations

  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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  2. Bo Tian
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  4. Tian-Yu Zhou
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Correspondence to Yuan Shen or Bo Tian.

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Shen, Y., Tian, B., Cheng, CD. et al. Bilinear auto-Bäcklund transformation, breather-wave and periodic-wave solutions for a (3+1)-dimensional Boiti–Leon–Manna–Pempinelli equation. Eur. Phys. J. Plus 136, 1159 (2021). https://doi.org/10.1140/epjp/s13360-021-01987-8

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