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Bilinear form, bilinear auto-Bäcklund transformation, breather and lump solutions for a (3\(+\)1)-dimensional generalised Yu–Toda–Sasa–Fukuyama equation in a two-layer liquid or a lattice

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Abstract

Two-layer fluids are seen in fluid mechanics, thermodynamics and medical sciences. Lattices are seen in solid-state physics. In a two-layer liquid or a lattice, a (\(3+1\))-dimensional generalised Yu–Toda–Sasa–Fukuyama equation is hereby studied with symbolic computation. Via the Hirota method, bilinear form and bilinear auto-Bäcklund transformation under certain coefficient constraints are obtained. Breather solutions are worked out based on the Hirota method and extended homoclinic test approach. Considering that the periods of breather solutions tend to infinity, we derive the lump solutions under a limit procedure. We observe that the amplitudes of the breather and lump remain unchanged during the propagation. Furthermore, we graphically present the breathers and lumps under the influence of different coefficients in the equation.

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Acknowledgements

The authors express their 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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  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, Xin Zhao, Wen-Rui Shan & Yan Jiang

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  1. Yuan Shen
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  2. Bo Tian
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  3. Xin Zhao
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  4. Wen-Rui Shan
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  5. Yan Jiang
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Correspondence to Bo Tian.

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Shen, Y., Tian, B., Zhao, X. et al. Bilinear form, bilinear auto-Bäcklund transformation, breather and lump solutions for a (3\(+\)1)-dimensional generalised Yu–Toda–Sasa–Fukuyama equation in a two-layer liquid or a lattice. Pramana - J Phys 95, 137 (2021). https://doi.org/10.1007/s12043-021-02163-4

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