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Painlevé analysis, bilinear form, Bäcklund transformation, solitons, periodic waves and asymptotic properties for a generalized Calogero–Bogoyavlenskii–Konopelchenko–Schiff system in a fluid or plasma

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Abstract

In this paper, the investigation is conducted on a generalized Calogero–Bogoyavlenskii–Konopelchenko–Schiff system in a fluid or plasma. We conduct the Painlevé analysis and find that it fails to pass the Painlevé test. Bilinear form, Bäcklund transformation and soliton solutions are derived with the help of the Hirota method. By means of the Riemann theta function method, we obtain the one-periodic wave solutions. We derive the amplitude, velocity and direction of propagation for the one soliton, and find that the coefficients in the system affect the velocities of the one/two solitons, but the amplitudes and propagation directions of the one/two solitons keep unchanged. We graphically demonstrate that the interaction between the two solitons is elastic and analyse the effects of the coefficients in the system on the solitons and periodic waves. We analyse the asymptotic properties of the one-periodic wave solutions which reveal the connection between the one-periodic wave solutions and the one-soliton solutions, i.e., the one-periodic wave solutions tend to the one-soliton solutions under the limit process.

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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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  1. State Key Laboratory of Information Photonics and Optical Communications, and School of Science, Beijing University of Posts and Telecommunications, Beijing, 100876, China

    Shao-Hua Liu, Bo Tian & Meng Wang

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  1. Shao-Hua Liu
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  2. Bo Tian
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  3. Meng Wang
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Correspondence to Bo Tian.

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Liu, SH., Tian, B. & Wang, M. Painlevé analysis, bilinear form, Bäcklund transformation, solitons, periodic waves and asymptotic properties for a generalized Calogero–Bogoyavlenskii–Konopelchenko–Schiff system in a fluid or plasma. Eur. Phys. J. Plus 136, 917 (2021). https://doi.org/10.1140/epjp/s13360-021-01828-8

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