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Macropterons, micropterons and similarity reductions for the regularized Ostrovsky-Grimshaw model for fluids and plasmas with symbolic computation

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Summary

The Ostrovsky model is widely used to describe mechanical and physical problems such as internal or surface waves in the oceans and magnetic sounds in plasmas. This model has recently been Grimshaw-regularized for certain continuity in the mass field, while computerized symbolic computation becomes a branch of artificial intelligence. In this paper, some similarity reductions are found for the regularized Ostrovsky-Grimshaw model with symbolic computation, to a coupled set of nonlinear ordinary differential equations. The micropterons and macropterons are analytically presented and discussed, and have been found to contain certain solitonic cores plus a number of sinusoidal ``wings''. Examples are the micropterons and macropterons for fluid velocities in the wave propagation direction and transverse direction, respectively.

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Authors and Affiliations

  1. Ministry-of-Education Key Laboratory of Fluid Mechanics and National Laboratory for Computational Fluid Dynamics, Beijing University of Aeronautics and Astronautics, Beijing, 100083, China

    Yi-Tian Gao & Chun-Yi Zhang

  2. State Key Laboratory of Software Development Environment, Beijing University of Aeronautics and Astronautics, Beijing, 100083, China

    Yi-Tian Gao & Bo Tian

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

    Bo Tian

  4. Meteorology Center of Air Force Command Post, Changchun, 130052, China

    Chun-Yi Zhang

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  1. Yi-Tian Gao
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  2. Bo Tian
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  3. Chun-Yi Zhang
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Gao, YT., Tian, B. & Zhang, CY. Macropterons, micropterons and similarity reductions for the regularized Ostrovsky-Grimshaw model for fluids and plasmas with symbolic computation. Acta Mechanica 182, 17–29 (2006). https://doi.org/10.1007/s00707-005-0287-2

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