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Soliton solutions and interactions of the Zakharov-Kuznetsov equation in the electron-positron-ion plasmas

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Abstract.

Analytically investigated in this paper is the Zakharov-Kuznetsov equation which describes the propagation of the electrostatic excitations in the electron-positron-ion plasmas. By means of the Hirota method and symbolic computation, the bilinear form for the Zakharov-Kuznetsov equation is derived, and then the N-soliton solution is constructed. Parametric analysis is carried out in order to illustrate that the soliton amplitude and width are affected by the phase velocity, ion-to-electron density ratio, rotation frequency and cyclotron frequency. Propagation characteristics and interaction behaviors of the solitons are also discussed through the graphical analysis. The effects of the nonlinearity A, dispersion B and disturbed wave velocity C on the amplitude and velocity of the solitons are derived. First, the amplitude is proportional to the nonlinearity A and inversely proportional to dispersion B. Second, the velocity increases as the dispersion B increases. Third, the velocity increases as the disturbed wave velocity C (4B > C) increases; the velocity decreases as the disturbed wave velocity C (4B < C) increases.

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Authors and Affiliations

  1. School of Science, P.O. Box 122, Beijing University of Posts and Telecommunications, Beijing, 100876, China

    Qi-Xing Qu, Bo Tian, Wen-Jun Liu, Kun Sun, Pan Wang, Yan Jiang & Bo Qin

  2. State Key Laboratory of Software Development Environment, Beijing University of Aeronautics and Astronautics, Beijing, 100191, China

    Bo Tian

  3. Key Laboratory of Information Photonics and Optical Communications (BUPT), Ministry of Education, P.O. Box 128, Beijing University of Posts and Telecommunications, Beijing, 100876, China

    Bo Tian

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  1. Qi-Xing Qu
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  2. Bo Tian
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  6. Yan Jiang
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  7. Bo Qin
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Correspondence to Bo Tian.

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Qu, QX., Tian, B., Liu, WJ. et al. Soliton solutions and interactions of the Zakharov-Kuznetsov equation in the electron-positron-ion plasmas. Eur. Phys. J. D 61, 709–715 (2011). https://doi.org/10.1140/epjd/e2010-10342-5

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  • DOI: https://doi.org/10.1140/epjd/e2010-10342-5

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