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TMF, 2000, Volume 125, Number 3, Pages 491–518 (Mi tmf681)  

This article is cited in 5 scientific papers (total in 5 papers)

Integrability of truncated Hugoniot–Maslov chains for trajectories of mesoscale vortices on shallow water

S. Yu. Dobrokhotov

A. Ishlinsky Institite for Problems in Mechanics, Russian Academy of Sciences

Abstract: The problem of trajectories of “large” (mesoscale) shallow-water vortices manifests integrability properties. The Maslov hypothesis states that such vortices can be generated using solutions with weak pointlike singularities of the type of the square root of a quadratic form; such square-root singular solutions may describe the propagation of mesoscale vortices in the atmosphere (typhoons and cyclones). Such solutions are necessarily described by infinite systems of ordinary differential equations (chains) in the Taylor coefficients of solutions in the vicinities of singularities. A proper truncation of the “vortex chain” for a shallow-water system is a system of 17 nonlinear equations. This system becomes the Hill equation when the Coriolis force is constant and almost becomes the physical pendulum equations when the Coriolis force depends on the latitude. In a rough approximation, we can then explicitly describe possible trajectories of mesoscale vortices, which are analogous to oscillations of a rotating solid body swinging on an elastic thread.

DOI: https://doi.org/10.4213/tmf681

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English version:
Theoretical and Mathematical Physics, 2000, 125:3, 1724–1741

Bibliographic databases:

Received: 29.05.2000
Revised: 03.07.2000

Citation: S. Yu. Dobrokhotov, “Integrability of truncated Hugoniot–Maslov chains for trajectories of mesoscale vortices on shallow water”, TMF, 125:3 (2000), 491–518; Theoret. and Math. Phys., 125:3 (2000), 1724–1741

Citation in format AMSBIB
\Bibitem{Dob00}
\by S.~Yu.~Dobrokhotov
\paper Integrability of truncated Hugoniot--Maslov chains for trajectories of mesoscale vortices on shallow water
\jour TMF
\yr 2000
\vol 125
\issue 3
\pages 491--518
\mathnet{http://mi.mathnet.ru/tmf681}
\crossref{https://doi.org/10.4213/tmf681}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1839658}
\zmath{https://zbmath.org/?q=an:1008.76009}
\transl
\jour Theoret. and Math. Phys.
\yr 2000
\vol 125
\issue 3
\pages 1724--1741
\crossref{https://doi.org/10.1023/A:1026614414836}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. Dobrokhotov, SY, “Proof of Maslov's conjecture about the structure of weak point singular solutions of the shallow water equations”, Russian Journal of Mathematical Physics, 8:1 (2001), 25  mathscinet  zmath  isi
    2. Dobrokhotov, SY, “On Maslov's conjecture about the structure of weak point singularities of shallow-water equations”, Doklady Mathematics, 64:1 (2001), 127  mathscinet  zmath  isi
    3. E. S. Semenov, “Hugoniót–Maslov Conditions for Vortex Singular Solutions of the Shallow Water Equations”, Math. Notes, 71:6 (2002), 825–835  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    4. Dobrokhotov, SY, “On the Hamiltonian property of the truncated Hugoniot-Maslov chain for trajectories of mesoscale vortices”, Doklady Mathematics, 65:3 (2002), 453  mathscinet  zmath  isi
    5. S. Yu. Dobrokhotov, E. S. Semenov, B. Tirozzi, “Calculation of Integrals of the Hugoniot–Maslov Chain for Singular Vortical Solutions of the Shallow-Water Equation”, Theoret. and Math. Phys., 139:1 (2004), 500–512  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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