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Painlevé analysis, auto-Bäcklund transformation and analytic solutions of a (2\(+\)1)-dimensional generalized Burgers system with the variable coefficients in a fluid

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Abstract

Burgers-type equations are used to describe certain phenomena in gas dynamics, traffic flow, plasma astrophysics and ocean dynamics. In this paper, a (2\(+\)1)-dimensional generalized Burgers system with the variable coefficients in a fluid is investigated. We obtain the Painlevé-integrable constraints of the system with respect to the variable coefficients. Based on the truncated Painlevé expansions, an auto-Bäcklund transformation is constructed, along with some soliton solutions. Via a truncated Painlevé expansions, certain multiple kink solutions are derived. Via a complex-conjugate transformation, some breather solutions, half-periodic kink solutions and hybrid solutions composed of the breathers and kink waves are seen.

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Acknowledgements

We express our sincerely 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 11805020, 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

    Tian-Yu Zhou, Bo Tian, Yu- Qi Chen & Yuan Shen

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  1. Tian-Yu Zhou
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Zhou, TY., Tian, B., Chen, Y.Q. et al. Painlevé analysis, auto-Bäcklund transformation and analytic solutions of a (2\(+\)1)-dimensional generalized Burgers system with the variable coefficients in a fluid. Nonlinear Dyn 108, 2417–2428 (2022). https://doi.org/10.1007/s11071-022-07211-1

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