Theoretical and Mathematical Physics

, Volume 128, Issue 1, pp 906–926 | Cite as

Hypergeometric Solutions of Soliton Equations

  • A. Yu. Orlov
  • D. M. Scherbin


We consider multivariable hypergeometric functions related to Schur functions and show that these hypergeometric functions are tau functions of the KP hierarchy and are simultaneously the ratios of Toda lattice tau functions evaluated at certain values of higher Toda lattice times. The variables of the hypergeometric functions are related to the higher times of those hierarchies via a Miwa change of variables. The discrete Toda lattice variable shifts the parameters of the hypergeometric functions. We construct the determinant representation and the integral representation of a special type for the KP tau functions. We write a system of linear differential and difference equations on these tau functions, which play the role of string equations.


Soliton Lattice Variable Difference Equation Integral Representation Lattice Time 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Plenum Publishing Corporation 2001

Authors and Affiliations

  • A. Yu. Orlov
    • 1
    • 2
  • D. M. Scherbin
    • 3
  1. 1.Department of Mathematics, Faculty of ScienceKyoto UniversityKyotoJapan
  2. 2.Nonlinear Wave Processes LaboratoryOceanology InstituteMoscowRussia
  3. 3.Centre de recherches mathématiquesUniversité de MontréalMontréalCanada

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