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TMF, 2003, Volume 134, Number 1, Pages 18–31 (Mi tmf137)  

This article is cited in 7 scientific papers (total in 7 papers)

Integrable Structure Behind the WDVV Equations

Kh. Aratina, Zh. van de Lerb

a University of Illinois at Chicago
b Mathematical Research Institute

Abstract: An integrable structure behind the Witten–Dijkgraaf–Verlinde–Verlinde (WDVV) equations is identified with the reduction of the Riemann–Hilbert problem for the homogeneous loop group $\widehat{GL}(N,\mathbb C)$. The reduction requires the dressing matrices to be fixed points of an order-two loop group automorphism resulting in a subhierarchy of the $\widehat{gl}(N,\mathbb C)$ hierarchy containing only odd-symmetry flows. The model has Virasoro symmetry; imposing Virasoro constraints ensures the homogeneity property of the Darboux–Egoroff structure. Dressing matrices of the reduced model provide solutions of the WDVV equations.

Keywords: WDVV equations, dressing, Darboux–Egoroff metrics, Kadomtsev–Petviashvili hierarchies, tau functions, Riemann–Hilbert factorization

DOI: https://doi.org/10.4213/tmf137

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English version:
Theoretical and Mathematical Physics, 2003, 134:1, 14–46

Bibliographic databases:


Citation: Kh. Aratin, Zh. van de Ler, “Integrable Structure Behind the WDVV Equations”, TMF, 134:1 (2003), 18–31; Theoret. and Math. Phys., 134:1 (2003), 14–46

Citation in format AMSBIB
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\paper Integrable Structure Behind the WDVV Equations
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\jour Theoret. and Math. Phys.
\yr 2003
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    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. Aratyn, H, “Darboux-Egoroff metrics, rational Landau-Ginzburg potentials and the Painlevé VI equation”, Journal of Physics A-Mathematical and General, 36:4 (2003), 1013  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus
    2. Aratyn H, van de Leur J, “The symplectic Kadomtsev-Petviashvili hierarchy and rational solutions of Painlevé VI”, Annales de l Institut Fourier, 55:6 (2005), 1871–1903  crossref  mathscinet  zmath  isi  scopus  scopus
    3. Aratyn H., Van de Leur J., “The CKP hierarchy and the WDVV prepotential”, Bilinear Integrable Systems: From Classical To Quatum, Continuous To Discrete, Nato Science Series, Series II: Mathematics, Physics and Chemistry, 201, 2006, 1–11  mathscinet  zmath  isi
    4. Kakei, S, “The sixth Painlevé equation as similarity reduction of (gl)over-cap(3) generalized Drinfel'd-Sokolov hierarchy”, Letters in Mathematical Physics, 79:3 (2007), 221  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus
    5. Aratyn, H, “Solutions of the Painlevé VI Equation from Reduction of Integrable Hierarchy in a Grassmannian Approach”, International Mathematics Research Notices, 2008, rnn080  mathscinet  zmath  isi  elib
    6. Terng Ch.-L., Uhlenbeck K., “Tau Function and Virasoro Action For the N X N KdV Hierarchy”, Commun. Math. Phys., 342:1 (2016), 81–116  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus
    7. Terng Ch.-L., Uhlenbeck K., “Tau Functions and Virasoro Actions For Soliton Hierarchies”, Commun. Math. Phys., 342:1 (2016), 117–150  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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