RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB
General information
Latest issue
Archive
Impact factor
Subscription
Guidelines for authors
License agreement
Submit a manuscript

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



TMF:
Year:
Volume:
Issue:
Page:
Find






Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register


TMF, 2005, Volume 142, Number 2, Pages 197–217 (Mi tmf1776)  

This article is cited in 8 scientific papers (total in 8 papers)

Whitham hierarchy in growth problems

A. V. Zabrodinab

a Institute for Theoretical and Experimental Physics (Russian Federation State Scientific Center)
b Institute of biochemical physics of the Russian Academy of Sciences

Abstract: We discuss the recently established equivalence between the Laplacian growth in the limit of zero surface tension and the universal Whitham hierarchy known in soliton theory. This equivalence allows distinguishing a class of exact solutions of the Laplacian growth problem in the multiply connected case. These solutions correspond to finite-dimensional reductions of the Whitham hierarchy representable as equations of hydrodynamic type, which are solvable by the generalized hodograph method.

Keywords: Saffman–Taylor problem, Laplacian growth, Whitham equations, Schwarz function

DOI: https://doi.org/10.4213/tmf1776

Full text: PDF file (352 kB)
References: PDF file   HTML file

English version:
Theoretical and Mathematical Physics, 2005, 142:2, 166–182

Bibliographic databases:


Citation: A. V. Zabrodin, “Whitham hierarchy in growth problems”, TMF, 142:2 (2005), 197–217; Theoret. and Math. Phys., 142:2 (2005), 166–182

Citation in format AMSBIB
\Bibitem{Zab05}
\by A.~V.~Zabrodin
\paper Whitham hierarchy in growth problems
\jour TMF
\yr 2005
\vol 142
\issue 2
\pages 197--217
\mathnet{http://mi.mathnet.ru/tmf1776}
\crossref{https://doi.org/10.4213/tmf1776}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2141773}
\zmath{https://zbmath.org/?q=an:1178.37062}
\adsnasa{http://adsabs.harvard.edu/cgi-bin/bib_query?2005TMP...142..166Z}
\elib{http://elibrary.ru/item.asp?id=9135943}
\transl
\jour Theoret. and Math. Phys.
\yr 2005
\vol 142
\issue 2
\pages 166--182
\crossref{https://doi.org/10.1007/s11232-005-0002-4}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000227756500002}
\elib{http://elibrary.ru/item.asp?id=13493300}


Linking options:
  • http://mi.mathnet.ru/eng/tmf1776
  • https://doi.org/10.4213/tmf1776
  • http://mi.mathnet.ru/eng/tmf/v142/i2/p197

    SHARE: VKontakte.ru FaceBook Twitter Mail.ru Livejournal Memori.ru


    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. Kodama, Y, “Integrable quasiclassical deformations of cubic curves”, Journal of Mathematical Physics, 46:11 (2005), 113502  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus
    2. Martinez-Alonso L, “Genus-zero Whitham hierarchies in conformal-map dynamics”, Physics Letters B, 641:6 (2006), 466–473  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus  scopus
    3. Alonso LM, Medina E, Manas M, “String equations in Whitham hierarchies: tau-functions and Virasoro constraints”, Journal of Mathematical Physics, 47:8 (2006), 083512  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus
    4. Manas M, Medina E, Alonso LM, “On the Whitham hierarchy: dressing scheme, string equations and additional symmetries”, Journal of Physics A-Mathematical and General, 39:10 (2006), 2349–2381  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus
    5. Gustafsson B, Putinar M, “Selected topics on quadrature domains”, Physica D-Nonlinear Phenomena, 235:1–2 (2007), 90–100  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus  scopus
    6. Alonso LM, Medina E, “Semiclassical expansions in the Toda hierarchy and the Hermitian matrix model”, Journal of Physics A-Mathematical and Theoretical, 40:47 (2007), 14223–14241  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus
    7. Mineev-Weinstein, M, “Random matrices in 2D, Laplacian growth and operator theory”, Journal of Physics A-Mathematical and Theoretical, 41:26 (2008), 263001  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus
    8. Teo L.-P., “Conformal Mappings and Dispersionless Toda Hierarchy II: General String Equations”, Comm Math Phys, 297:2 (2010), 447–474  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus  scopus
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
    Number of views:
    This page:290
    Full text:97
    References:30
    First page:1

     
    Contact us:
     Terms of Use  Registration  Logotypes © Steklov Mathematical Institute RAS, 2019