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Matematicheskie Zametki, 2002, Volume 71, Issue 6, Pages 902–913
DOI: https://doi.org/10.4213/mzm394 (Mi mzm394) 		 
This article is cited in 4 scientific papers (total in 4 papers)

Hugoniót–Maslov Conditions for Vortex Singular Solutions of the Shallow Water Equations

E. S. Semenov

Russian Research Centre "Kurchatov Institute"
Full-text PDF (224 kB) Citations (4)
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DOI: https://doi.org/10.4213/mzm394
Abstract: For the “phase” of vortex singular solutions of the shallow water equations we justify the Hamilton–Jacobi equation corresponding to the hydrodynamical mode of perturbation propagation. We also obtain the next correction to the Cauchy–Riemann conditions describing how the singular part of the solution affects the smooth background.
Received: 14.01.2002
English version:
Mathematical Notes, 2002, Volume 71, Issue 6, Pages 825–835
DOI: https://doi.org/10.1023/A:1015877013833
Bibliographic databases:
UDC: 517.9
Language: Russian
Citation: E. S. Semenov, “Hugoniót–Maslov Conditions for Vortex Singular Solutions of the Shallow Water Equations”, Mat. Zametki, 71:6 (2002), 902–913; Math. Notes, 71:6 (2002), 825–835
Citation in format AMSBIB
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  • https://doi.org/10.4213/mzm394
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    • This publication is cited in the following 4 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., Tirozzi B., “A Perturbative Theory of the Evolution of the Center of Typhoons”, Zeta Functions, Topology and Quantum Physics, Developments in Mathematics, 14, eds. Aoki T., Kanemitsu S., Nakahara M., Ohno Y., Springer, 2005, 31–50  crossref  mathscinet  zmath  isi  scopus
    3. 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
    4. S. Yu. Dobrokhotov, E. S. Semenov, B. Tirozzi, “Hugoniót–Maslov Chains for Singular Vortical Solutions to Quasilinear Hyperbolic Systems and Typhoon Trajectory”, Journal of Mathematical Sciences, 124:5 (2004), 5209–5249  mathnet  crossref  mathscinet  zmath
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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