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CMFD, 2003, Volume 2, Pages 5–44 (Mi cmfd19)  

This article is cited in 3 scientific papers (total in 3 papers)

Hugoniót–Maslov Chains for Singular Vortical Solutions to Quasilinear Hyperbolic Systems and Typhoon Trajectory

S. Yu. Dobrokhotova, E. S. Semenova, B. Tirozzib

a A. Ishlinsky Institite for Problems in Mechanics, Russian Academy of Sciences
b University of Rome "La Sapienza"

Abstract: According to Maslov, many 2D quasilinear systems of PDE possess only three algebras of singular solutions with properties of structural self-similarity and stability. They are the algebras of shock waves, narrow solitons, and square-root point singularities (solitary vortices). Their propagation is described by infinite chains of ODE (the Hugoniót–Maslov chains). We consider the Hugoniót–Maslov chain for the square-root point singularities of the shallow water equations. We discuss different related mathematical questions (in particular, unexpected integrability effects) as well as their possible application to the problem of typhoon dynamics.

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English version:
Journal of Mathematical Sciences, 2004, 124:5, 5209–5249

Bibliographic databases:

UDC: 517.95

Citation: S. Yu. Dobrokhotov, E. S. Semenov, B. Tirozzi, “Hugoniót–Maslov Chains for Singular Vortical Solutions to Quasilinear Hyperbolic Systems and Typhoon Trajectory”, Proceedings of the International Conference on Differential and Functional-Differential Equations — Satellite of International Congress of Mathematicians ICM-2002 (Moscow, MAI, 11–17 August, 2002). Part 2, CMFD, 2, MAI, M., 2003, 5–44; Journal of Mathematical Sciences, 124:5 (2004), 5209–5249

Citation in format AMSBIB
\Bibitem{DobSemTir03}
\by S.~Yu.~Dobrokhotov, E.~S.~Semenov, B.~Tirozzi
\paper Hugoni\'ot--Maslov Chains for Singular Vortical Solutions to Quasilinear Hyperbolic Systems and Typhoon Trajectory
\inbook Proceedings of the International Conference on Differential and Functional-Differential Equations --- Satellite of International Congress of Mathematicians ICM-2002 (Moscow, MAI, 11--17 August, 2002). Part~2
\serial CMFD
\yr 2003
\vol 2
\pages 5--44
\publ MAI
\publaddr M.
\mathnet{http://mi.mathnet.ru/cmfd19}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2129133}
\zmath{https://zbmath.org/?q=an:1069.37049}
\transl
\jour Journal of Mathematical Sciences
\yr 2004
\vol 124
\issue 5
\pages 5209--5249
\crossref{https://doi.org/10.1023/B:JOTH.0000047350.22539.ef}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. S. Yu. Dobrokhotov, E. S. Semenov, B. Tirozzi, “Hugoniot–Maslov Chains for the System of Shallow-Water Equations Taking into Account Energy Exchange”, Math. Notes, 78:5 (2005), 740–743  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    2. Dobrokhotov S.Yu., Tirozzi B., Shafarevich A.I., “Cauchy-Riemann conditions and point singularities of solutions to linearized shallow-water equations”, Russian Journal of Mathematical Physics, 14:2 (2007), 217–223  crossref  mathscinet  zmath  adsnasa  isi
    3. Reutskiy S., Tirozzi B., “Forecast of the trajectory of the center of typhoons and the Maslov decomposition”, Russian Journal of Mathematical Physics, 14:2 (2007), 232–237  crossref  mathscinet  zmath  adsnasa  isi
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