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Teoreticheskaya i Matematicheskaya Fizika, 2005, Volume 142, Number 2, Pages 197–217
DOI: https://doi.org/10.4213/tmf1776 (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
Full-text PDF (352 kB) Citations (8)
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DOI: https://doi.org/10.4213/tmf1776
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.
English version:
Theoretical and Mathematical Physics, 2005, Volume 142, Issue 2, Pages 166–182
DOI: https://doi.org/10.1007/s11232-005-0002-4
Bibliographic databases:
Language: Russian
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
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  • https://www.mathnet.ru/eng/tmf1776
  • https://doi.org/10.4213/tmf1776
  • https://www.mathnet.ru/eng/tmf/v142/i2/p197
    • This publication is cited in the following 8 articles:
    1. 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
    2. 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
    3. 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
    4. 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
    5. 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
    6. 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
    7. 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
    8. Kodama, Y, “Integrable quasiclassical deformations of cubic curves”, Journal of Mathematical Physics, 46:11 (2005), 113502  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus
    Citing articles in Google Scholar: Russian citations, English citations
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    		Теоретическая и математическая физика Theoretical and Mathematical Physics
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