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Breathers and rogue waves on the periodic background for the Gerdjikov-Ivanov equation for the Alfvén waves in an astrophysical plasma

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  • Ding, Cui-Cui
  • Gao, Yi-Tian
  • Li, Liu-Qing

Abstract

Alfvén waves in the magnetized astrophysical plasmas are invoked to explain the heating of the stellar coronae, acceleration of the stellar winds, as well as the origin and formation of the galactic and extragalactic jets. Under investigation in this paper is the Gerdjikov-Ivanov equation which is considered as a plasma-physics model for the Alfvén waves propagating parallel to the ambient magnetic field. Based on the existing N-th order analytic solutions for the Gerdjikov-Ivanov equation with N being a positive integer, we construct two types of the breathers on the periodic background, and the k-th order rogue waves on the periodic background in terms of the determinant expression for the transverse magnetic field perturbation are derived via the Taylor expansion when N=2k+1 with k being a non-negative integer. We show that the breathers and rogue waves are located in the periodic background rather than in the constant background. We obtain four different structures, which are the so-called fundamental, triangular, ring and ring-triangular structures, for the higher-order rogue waves on the periodic background. We graphically demonstrate some solutions for the transverse magnetic field perturbation to analyse the characteristics of the four different structures.

Suggested Citation

  • Ding, Cui-Cui & Gao, Yi-Tian & Li, Liu-Qing, 2019. "Breathers and rogue waves on the periodic background for the Gerdjikov-Ivanov equation for the Alfvén waves in an astrophysical plasma," Chaos, Solitons & Fractals, Elsevier, vol. 120(C), pages 259-265.
    • Handle: RePEc:eee:chsofr:v:120:y:2019:i:c:p:259-265
    DOI: 10.1016/j.chaos.2019.01.007
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    Citations

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    Cited by:

    1. Zhai, Yunyun & Ji, Ting & Geng, Xianguo, 2021. "Coupled derivative nonlinear Schrödinger III equation: Darboux transformation and higher-order rogue waves in a two-mode nonlinear fiber," Applied Mathematics and Computation, Elsevier, vol. 411(C).
    2. Nikolay A. Kudryashov & Sofia F. Lavrova & Daniil R. Nifontov, 2023. "Bifurcations of Phase Portraits, Exact Solutions and Conservation Laws of the Generalized Gerdjikov–Ivanov Model," Mathematics, MDPI, vol. 11(23), pages 1-20, November.
    3. Singh, Sudhir & Sakkaravarthi, K. & Murugesan, K., 2022. "Localized nonlinear waves on spatio-temporally controllable backgrounds for a (3+1)-dimensional Kadomtsev-Petviashvili-Boussinesq model in water waves," Chaos, Solitons & Fractals, Elsevier, vol. 155(C).
    4. El-Tantawy, S.A. & Alharbey, R.A. & Salas, Alvaro H., 2022. "Novel approximate analytical and numerical cylindrical rogue wave and breathers solutions: An application to electronegative plasma," Chaos, Solitons & Fractals, Elsevier, vol. 155(C).
    5. Yang, Dan-Yu & Tian, Bo & Qu, Qi-Xing & Zhang, Chen-Rong & Chen, Su-Su & Wei, Cheng-Cheng, 2021. "Lax pair, conservation laws, Darboux transformation and localized waves of a variable-coefficient coupled Hirota system in an inhomogeneous optical fiber," Chaos, Solitons & Fractals, Elsevier, vol. 150(C).

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