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 TMF, 2004, Volume 139, Number 1, Pages 62–76 (Mi tmf39)

Calculation of Integrals of the Hugoniot–Maslov Chain for Singular Vortical Solutions of the Shallow-Water Equation

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: We discuss the problems of the Hugoniot–Maslov chain integrability for singular vortical solutions of the shallow-water equations on the $\beta$ plane. We show that the complex variables used to derive the chain automatically give most of the integrals of the complete and the truncated chains. We also study how some of these integrals are related to the Lagrangian invariant (potential vorticity). We discuss how to choose solutions of the chain that can be used to describe the actual trajectories of tropical cyclones.

Keywords: singular vortical solutions, trajectories, shallow water, integrals, chains

DOI: https://doi.org/10.4213/tmf39

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English version:
Theoretical and Mathematical Physics, 2004, 139:1, 500–512

Bibliographic databases:

Citation: 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”, TMF, 139:1 (2004), 62–76; Theoret. and Math. Phys., 139:1 (2004), 500–512

Citation in format AMSBIB
\Bibitem{DobSemTir04}
\by S.~Yu.~Dobrokhotov, E.~S.~Semenov, B.~Tirozzi
\paper Calculation of Integrals of the Hugoniot--Maslov Chain for Singular Vortical Solutions of the Shallow-Water Equation
\jour TMF
\yr 2004
\vol 139
\issue 1
\pages 62--76
\mathnet{http://mi.mathnet.ru/tmf39}
\crossref{https://doi.org/10.4213/tmf39}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2076909}
\zmath{https://zbmath.org/?q=an:1178.37070}
\elib{https://elibrary.ru/item.asp?id=13461484}
\transl
\jour Theoret. and Math. Phys.
\yr 2004
\vol 139
\issue 1
\pages 500--512
\crossref{https://doi.org/10.1023/B:TAMP.0000022742.45549.22}

• http://mi.mathnet.ru/eng/tmf39
• https://doi.org/10.4213/tmf39
• http://mi.mathnet.ru/eng/tmf/v139/i1/p62

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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
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