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Collision properties of overtaking magnetosonic solitary waves in the ionospheric multi-ion plasmas

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Abstract

We study the magnetosonic waves (MWs) propagating in magnetized plasmas comprising light warm ions, cold heavy ions and hot electrons at the Earth’s ionosphere. The dispersion relation is given and the effects of different physical parameters on the frequency of fast and slow MSWs are shown. We derive a KdV equation for the MSWs in multi-ion plasma and study the two-soliton and three-soliton overtaking collision of KdV MSWs by Hirota’s bilinear method. We show the trajectories and amplitude of solitons in this process, and the phase shift after collision. It is found that when solitons merge, it will form a new soliton whose amplitude first decreases then increases. The effects of physical parameters on the phase shift of multi-soliton collision are presented. It is worth noting that the solitons’ interaction can result in the redistribution of momentum and energy in the plasmas.

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No datasets were generated or analysed during the current study.

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Funding

This work was supported by National Natural Science Foundation of China (Grant No. 12064023), Natural Science Foundation of Gansu Province (Grant No. 20JR5RA209).

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Authors and Affiliations

  1. School of Electronic Engineering, Lanzhou City University, Lanzhou, China

    Dong-Ning Gao

  2. College of Physics and Electronic Engineering, Northwest Normal University, Lanzhou, China

    Heng Zhang

  3. Department of Physics, Gansu Minzu Normal University, Hezuo, China

    Zhong-Zheng Li

Authors
  1. Dong-Ning Gao
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  2. Heng Zhang
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  3. Zhong-Zheng Li
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Contributions

Dong-Ning Gao wrote the main manuscript text, Heng Zhang sought data and prepared figures 1-7 and Zhong-Zheng Li prepared figures 8-13. All authors reviewed the manuscript.

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Correspondence to Dong-Ning Gao.

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Appendix

Appendix

$$\begin{aligned} a={}&3+3k^{2}+6\mu _{e}+3k^{2}\mu _{e}+6s\chi \mu _{e}+3sk^{2}\chi \mu _{e} \\ &{}+3 \mu _{e}^{2}+6s\chi \mu _{e}^{2}+3s^{2}\chi ^{2}\mu _{e}^{2}+6s^{2} \chi \mu _{h} \\ &{}+3k^{2}s^{2}\chi \mu _{h} +6s^{2}\chi \mu _{e}\mu _{h}+6s^{3}\chi ^{2}\mu _{e}\mu _{h} \\ &{}+3s^{4} \chi ^{2}\mu _{h}^{2}. \end{aligned}$$
(A.1)
$$\begin{aligned} b={}&3k^{2}\mu _{e}+3k^{2}\beta \mu _{e}+3k^{4}\beta \mu _{e}+5k^{2} \beta \theta \mu _{e} \\ &{}+5k^{4}\beta \theta \mu _{e}+3s k^{2}\chi \mu _{e}+5s k^{2}\chi \beta \theta \mu _{e} \\ &{}+5sk^{4} \beta \theta \chi \mu _{e} +3k^{2} \mu _{e}^{2} +3k^{2}\beta \mu _{e}^{2}+5k^{2} \beta \theta \mu _{e}^{2} \\ &{}+3s k^{2} \beta \chi \mu _{e}^{2}+10s k^{2}\beta \theta \chi \mu _{e}^{2}+3s^{2} \chi ^{2}\mu _{e}^{2} \\ &{}+5k^{2}s^{2}\beta \theta \chi ^{2}\mu _{e}^{2}+3k^{2}s^{2} \chi \mu _{h}+5k^{2}s^{2}\beta \theta \chi \mu _{h} \\ &{}+5k^{4}s^{2}\beta \theta \chi \mu _{h}+6s^{2} \chi \mu _{e}\mu _{h} +6k^{2}s^{2} \beta \chi \mu _{e}\mu _{h} \\ &{}+3k^{4}s^{2}\beta \chi \mu _{e}\mu _{h} +10 k^{2}s^{2}\beta \theta \chi \mu _{e}\mu _{h}+6s^{3}\chi ^{2}\mu _{e} \mu _{h} \\ &{}+10k^{2}s^{3}\beta \theta \chi ^{2} \mu _{e}\mu _{h}+6s^{2} \chi \mu _{e}^{2}\mu _{h} +3k^{2}s^{2}\chi \mu _{e}^{2}\mu _{h} \\ &{}+3k^{2}s^{2} \beta \chi \mu _{e}^{2}\mu _{h}+3k^{2}s^{3}\beta \chi ^{2}\mu _{e}^{2} \mu _{h}+3s^{2}\mu _{h}^{2} \\ &{}+3s^{2}k^{2}\mu _{h}^{2}+6 s^{3}\chi \mu _{h}^{2}+3 s^{4}\chi ^{2}\mu _{h}^{2}+5k^{2}s^{4}\beta \theta \chi ^{2}\mu _{h}^{2} \\ &{}+ 6s^{2}\mu _{e}\mu _{h}^{2}+3k^{2}s^{2}\mu _{e} \mu _{h}^{2}+6s^{3} \chi \mu _{e} \mu _{h}^{2} \\ &{}+3k^{2}s^{3}\chi \mu _{e} \mu _{h}^{2}+3k^{2}s^{4} \beta \chi ^{2} \mu _{e}\mu _{h}^{2}+3s^{2}\mu _{e}^{2}\mu _{h}^{2}. \end{aligned}$$
(A.2)
$$\begin{aligned} c={}&3k^{4}s^{2}\beta \chi \mu _{e} \mu _{h}+5k^{4}s^{2}\beta ^{2} \theta \chi \mu _{e} \mu _{h} +5k^{6}s^{2}\beta ^{2}\theta \chi \mu _{e} \mu _{h} \\ &{}+3k^{2}s^{2}\chi \mu _{e}^{2}\mu _{h}+3k^{2}s^{2}\beta \chi \mu _{e}^{2}\mu _{h}+5k^{2}s^{2}\beta \theta \chi \mu _{e}^{2}\mu _{h} \\ &{}+5k^{4}s^{2}\beta \theta \chi \mu _{e}^{2}\mu _{h}+5k^{4}s^{2}\beta ^{2} \theta \chi \mu _{e}^{2}\mu _{h} \\ &{}+3k^{2}s^{3}\beta \chi ^{2} \mu _{e}^{2} \mu _{h}+5k^{4}s^{3}\beta ^{2}\theta \chi ^{2} \mu _{e}^{2}\mu _{h} \\ &{}+3k^{2}s^{2} \mu _{e}\mu _{h}^{2}+3k^{2}s^{2}\beta \mu _{e}\mu _{h}^{2} +3k^{4}s^{2}\beta \mu _{e}\mu _{h}^{2} \\ &{}+5k^{2}s^{2}\beta \theta \mu _{e} \mu _{h}^{2}+5k^{4}s^{2}\beta \theta \mu _{e}\mu _{h}^{2}+3k^{2}s^{3} \chi \mu _{e}\mu _{h}^{2} \\ &{}+6k^{2}s^{3}\beta \chi \mu _{e}\mu _{h}^{2}+5k^{2}s^{3} \beta \theta \chi \mu _{e}\mu _{h}^{2} \\ &{}+5k^{4}s^{3}\beta \theta \chi \mu _{e}\mu _{h}^{2}+3k^{2}s^{4}\beta \chi ^{2} \mu _{e}\mu _{h}^{2} \\ &{}+5k^{4}s^{2} \beta \theta \chi ^{2} \mu _{e}\mu _{h}^{2}+3k^{2}s^{2}\mu _{e}^{2} \mu _{h}^{2}+3k^{2}s^{2}\beta \mu _{e}^{2}\mu _{h}^{2} \\ &{}+5k^{2}s^{2} \beta \theta \mu _{e}^{2}\mu _{h}^{2}+3k^{2}s^{3}\beta \chi \mu _{e}^{2} \mu _{h}^{2}. \end{aligned}$$
(A.3)

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Gao, DN., Zhang, H. & Li, ZZ. Collision properties of overtaking magnetosonic solitary waves in the ionospheric multi-ion plasmas. Astrophys Space Sci 369, 20 (2024). https://doi.org/10.1007/s10509-024-04278-7

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