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Gram-type, breather and hybrid solutions for the (3+1)-dimensional potential Yu-Toda-Sasa-Fukuyama equation in a two-layer liquid

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Abstract

Two-layer fluid models are used for investigating certain nonlinear phenomena in fluid mechanics, medical science and thermodynamics. This paper investigates the (3+1)-dimensional potential Yu-Toda-Sasa-Fukuyama equation in a two-layer liquid. Gram-type solutions are derived via the Kadomtsev-Petviashvili hierarchy reduction. Based on the Gram-type solutions, three-breather solutions and three kinds of hybrid the solutions that behave as the interactions among the V-shaped soliton, kink soliton and breather are derived. Three-breather solutions describe that a breather splits into two breathers or two breathers fuse into a breather. For the three kinds of the hybrid solutions, asymptotic analyses indicate that: (1) the V-shaped soliton is constructed via the interaction between two kink solitons; (2) the V-shaped soliton reduces to a kink soliton at certain conditions; (3) certain interaction results in a decrease (or increase) in the constant background of the V-shaped soliton and kink soliton. Based on the asymptotic analysis for a set of the hybrid solutions, we find the hybrid solutions which describe that a breather splits into two breathers while the breathers are connected to the V-shaped soliton. Furthermore, we show the hybrid solutions which describe that three breathers fuse into the V-shaped soliton.

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Acknowledgements

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

    Yu Zhao, Bo Tian, He-Yuan Tian, Dan-Yu Yang & Yuan Shen

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Zhao, Y., Tian, B., Tian, HY. et al. Gram-type, breather and hybrid solutions for the (3+1)-dimensional potential Yu-Toda-Sasa-Fukuyama equation in a two-layer liquid. Nonlinear Dyn 111, 16353–16365 (2023). https://doi.org/10.1007/s11071-023-08579-4

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