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TMF, 2006, Volume 146, Number 2, Pages 222–250 (Mi tmf2033)  

This article is cited in 17 scientific papers (total in 17 papers)

Hypergeometric Functions as Infinite-Soliton Tau Functions

A. Yu. Orlov

P. P. Shirshov institute of Oceanology of RAS

Abstract: It is known that resonant multisoliton solutions depend on higher times and a set of parameters (integrals of motion). We show that soliton tau functions of the Toda lattice (and of the multicomponent Toda lattice) are tau functions of a dual hierarchy, where the higher times and the parameters (integrals of motion) exchange roles. The multisoliton solutions turn out to be rational solutions of the dual hierarchy, and the infinite-soliton tau functions turn out to be hypergeometric-type tau functions of the dual hierarchy. The variables in the dual hierarchies exchange roles. Soliton momenta are related to the Frobenius coordinates of partitions in the decomposition of rational solutions with respect to Schur functions. As an example, we consider partition functions of matrix models: their perturbation series is, on one hand, a hypergeometric tau function and, on the other hand, can be interpreted as an infinite-soliton solution.

Keywords: solitons, rational solutions, tau function, hypergeometric function, duality

DOI: https://doi.org/10.4213/tmf2033

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English version:
Theoretical and Mathematical Physics, 2006, 146:2, 183–206

Bibliographic databases:

Received: 10.01.2004
Revised: 10.04.2005

Citation: A. Yu. Orlov, “Hypergeometric Functions as Infinite-Soliton Tau Functions”, TMF, 146:2 (2006), 222–250; Theoret. and Math. Phys., 146:2 (2006), 183–206

Citation in format AMSBIB
\by A.~Yu.~Orlov
\paper Hypergeometric Functions as Infinite-Soliton Tau Functions
\jour TMF
\yr 2006
\vol 146
\issue 2
\pages 222--250
\jour Theoret. and Math. Phys.
\yr 2006
\vol 146
\issue 2
\pages 183--206

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    This publication is cited in the following articles:
    1. Alexandrov A. Chapuy G. Eynard B. Harnad J., “Weighted Hurwitz Numbers and Topological Recursion”, Commun. Math. Phys.  crossref  mathscinet  isi
    2. Harnad J., Orlov A.Yu., “Fermionic construction of tau functions and random processes'”, Phys. D, 235:1-2 (2007), 168–206  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus  scopus
    3. Goulden I.P., Jackson D.M., “The KP hierarchy, branched covers, and triangulations”, Adv. Math., 219:3 (2008), 932–951  crossref  mathscinet  zmath  isi  elib  scopus  scopus
    4. Garoufalidis S., Mariño M., “Universality and asymptotics of graph counting problems in non-orientable surfaces”, J. Combin. Theory Ser. A, 117:6 (2010), 715–740  crossref  mathscinet  zmath  isi  elib  scopus  scopus
    5. J. Ambjørn, L. O. Chekhov, “A matrix model for hypergeometric Hurwitz numbers”, Theoret. and Math. Phys., 181:3 (2014), 1486–1498  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib  elib
    6. Mironov A. Morozov A. Sleptsov A. Smirnov A., “On Genus Expansion of Superpolynomials”, Nucl. Phys. B, 889 (2014), 757–777  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus
    7. Alexandrov A. Mironov A. Morozov A. Natanzon S., “On KP-Integrable Hurwitz Functions”, J. High Energy Phys., 2014, no. 11, 080  crossref  mathscinet  zmath  isi  scopus  scopus
    8. Mironov A. Morozov A. Morozov A., “On Colored Homfly Polynomials For Twist Knots”, Mod. Phys. Lett. A, 29:34 (2014), 1450183  crossref  zmath  adsnasa  isi  scopus  scopus
    9. H. Itoyama, A. D. Mironov, A. Yu. Morozov, “Matching branches of a nonperturbative conformal block at its singularity divisor”, Theoret. and Math. Phys., 184:1 (2015), 891–923  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    10. Itoyama H. Mironov A. Morozov A., “Ward Identities and Combinatorics of Rainbow Tensor Models”, J. High Energy Phys., 2017, no. 6, 115  crossref  mathscinet  zmath  isi  scopus  scopus
    11. Mironov A. Morozov A., “On the Complete Perturbative Solution of One-Matrix Models”, Phys. Lett. B, 771 (2017), 503–507  crossref  zmath  isi  scopus  scopus
    12. Alexandrov A. Chapuy G. Eynard B. Harnad J., “Weighted Hurwitz Numbers and Topological Recursion: An Overview”, J. Math. Phys., 59:8 (2018), 081102  crossref  mathscinet  zmath  isi  scopus
    13. Ambjorn J. Chekhov L.O., “Spectral Curves For Hypergeometric Hurwitz Numbers”, J. Geom. Phys., 132 (2018), 382–392  crossref  mathscinet  zmath  isi  scopus
    14. Itoyama H. Mironov A. Morozov A., “Tensorial Generalization of Characters”, J. High Energy Phys., 2019, no. 12, 127  crossref  mathscinet  isi
    15. Mironov A. Morozov A. Natanzon S., “Cut-and-Join Structure and Integrability For Spin Hurwitz Numbers”, Eur. Phys. J. C, 80:2 (2020), 97  crossref  isi
    16. Itoyama H. Mironov A. Morozov A., “Complete Solution to Gaussian Tensor Model and Its Integrable Properties”, Phys. Lett. B, 802 (2020), 135237  crossref  mathscinet  isi
    17. Mironov A. Morozov A., “Hook Variables: Cut-and-Join Operators and Tau-Functions”, Phys. Lett. B, 804 (2020), 135362  crossref  mathscinet  isi
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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