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Auto-Bäcklund transformations, bilinear forms, multiple-soliton, quasi-soliton and hybrid solutions of a (3+1)-dimensional modified Korteweg-de Vries-Zakharov-Kuznetsov equation in an electron-positron plasma

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Abstract

Electron-positron plasmas appear in the early Universe and many cosmic environments. In this paper, a (3+1)-dimensional modified Korteweg-de Vries-Zakharov-Kuznetsov equation in an electron-positron plasma is studied. Based on the truncated Painlevé expansion, auto-Bäcklund transformations are derived. Via the Hirota method, bilinear forms are derived. Based on the bilinear forms, multiple-soliton solutions are obtained. Via the two- and four-soliton solutions under the complex conjugated transformations, one- and two-quasi-soliton solutions are derived. Via the three-soliton solutions under the complex conjugated transformations, we obtain hybrid solutions composed of a soliton and a quasi-soliton wave. Via the asymptotic analysis, we derive that the interactions between these solitons are elastic.

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Notes

  1. Detailed definitions of \(a, c \text { and }d\) can be found in Refs. [12, 13].

  2. More relevant studies on the nonlinear evolution equations have been presented, e.g., in Refs. [68,69,70,71,72].

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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 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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Zhou, TY., Tian, B., Zhang, CR. et al. Auto-Bäcklund transformations, bilinear forms, multiple-soliton, quasi-soliton and hybrid solutions of a (3+1)-dimensional modified Korteweg-de Vries-Zakharov-Kuznetsov equation in an electron-positron plasma. Eur. Phys. J. Plus 137, 912 (2022). https://doi.org/10.1140/epjp/s13360-022-02950-x

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