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Viewing the Solar System via a variable-coefficient nonlinear dispersive-wave system

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Abstract

Oceans crossing the Solar System attract people’s attention: the Earth, Enceladus, and Titan. On a variable-coefficient nonlinear dispersive-wave system for the shallow oceanic environment, our symbolic computation yields two non-auto-Bäcklund transformations and auto-Bäcklund transformations with some solitons, with regard to the wave elevation and surface velocity of the water wave, which depend on the variable coefficients. This paper could be of some use for the future oceanic studies in the Solar System.

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Notes

  1. 1.Examples are the investigations on the interaction of linear modulated waves and unsteady dispersive hydrodynamic states with the applications to the shallow water waves [17], water-wave scattering by multiple thin vertical barriers [16], water-wave scattering by three thin vertical barriers [18], internal tides over a shallow ridge with a high-resolution downscaling regional ocean model [19], shallow overturning circulation in the Indian Ocean [20] and propagation of long-crested water waves [21].

  2. Two branches appear because of the choices based on the “±” signs.

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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 Fundamental Research Funds for the Central Universities of China under Grant No. 2019XD-A11.

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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

    Xin-Yi Gao, Yong-Jiang Guo & Wen-Rui Shan

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  1. Xin-Yi Gao
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Gao, XY., Guo, YJ. & Shan, WR. Viewing the Solar System via a variable-coefficient nonlinear dispersive-wave system. Acta Mech 231, 4415–4420 (2020). https://doi.org/10.1007/s00707-020-02747-y

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