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Mock-integrability and stable solitary vortices

Author

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  • Koike, Yukito
  • Nakamula, Atsushi
  • Nishie, Akihiro
  • Obuse, Kiori
  • Sawado, Nobuyuki
  • Suda, Yamato
  • Toda, Kouichi

Abstract

Localized soliton-like solutions to a (2+1)-dimensional hydro-dynamical evolution equation are studied numerically. The equation is the so-called Williams–Yamagata–Flierl equation, which governs geostrophic fluid in a certain parameter range. Although the equation does not have an integrable structure in the ordinary sense, we find there exist shape-keeping solutions with a very long life in a special background flow and an initial condition. The stability of the localization at the fusion process of two soliton-like objects is also investigated. As for the indicator of the long-term stability of localization, we propose a concept of configurational entropy, which has been introduced in analysis for non-topological solitons in field theories.

Suggested Citation

  • Koike, Yukito & Nakamula, Atsushi & Nishie, Akihiro & Obuse, Kiori & Sawado, Nobuyuki & Suda, Yamato & Toda, Kouichi, 2022. "Mock-integrability and stable solitary vortices," Chaos, Solitons & Fractals, Elsevier, vol. 165(P1).
    • Handle: RePEc:eee:chsofr:v:165:y:2022:i:p1:s0960077922009614
    DOI: 10.1016/j.chaos.2022.112782
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    References listed on IDEAS

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    1. Gao, Xin-Yi & Guo, Yong-Jiang & Shan, Wen-Rui, 2022. "Taking into consideration an extended coupled (2+1)-dimensional Burgers system in oceanography, acoustics and hydrodynamics," Chaos, Solitons & Fractals, Elsevier, vol. 161(C).
    2. Lee, Chaeyoung & Jeong, Darae & Shin, Jaemin & Li, Yibao & Kim, Junseok, 2014. "A fourth-order spatial accurate and practically stable compact scheme for the Cahn–Hilliard equation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 409(C), pages 17-28.
    3. Yi-Tian Gao & Bo Tian, 2001. "Variable-Coefficient Balancing-Act Algorithm Extended To A Variable-Coefficient Mkp Model For The Rotating Fluids," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 12(09), pages 1383-1389.
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