The symplectic Kadomtsev-Petviashvili hierarchy and rational solutions of Painlevé VI

Henrik Aratyn[1]; Johan van de LEUR

  • [1] University of Illinois at Chicago, department of physics, 845 W. Taylor St., Chicago IL 60607-7059 (USA), University of Utrecht, Mathematical Institute, P.O. Box 80010, 3508 TA Utrecht (The Netherlands)

Annales de l’institut Fourier (2005)

  • Volume: 55, Issue: 6, page 1871-1903
  • ISSN: 0373-0956

Abstract

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Equivalence is established between a special class of Painlevé VI equations parametrized by a conformal dimension μ , time dependent Euler top equations, isomonodromic deformations and three-dimensional Frobenius manifolds. The isomonodromic tau function and solutions of the Euler top equations are explicitly constructed in terms of Wronskian solutions of the 2-vector 1-constrained symplectic Kadomtsev-Petviashvili (CKP) hierarchy by means of Grassmannian formulation. These Wronskian solutions give rational solutions to the Painlevé VI equation for μ = 1 , 2 , ...

How to cite

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Aratyn, Henrik, and van de LEUR, Johan. "The symplectic Kadomtsev-Petviashvili hierarchy and rational solutions of Painlevé VI." Annales de l’institut Fourier 55.6 (2005): 1871-1903. <http://eudml.org/doc/116237>.

@article{Aratyn2005,
abstract = {Equivalence is established between a special class of Painlevé VI equations parametrized by a conformal dimension $\mu $, time dependent Euler top equations, isomonodromic deformations and three-dimensional Frobenius manifolds. The isomonodromic tau function and solutions of the Euler top equations are explicitly constructed in terms of Wronskian solutions of the 2-vector 1-constrained symplectic Kadomtsev-Petviashvili (CKP) hierarchy by means of Grassmannian formulation. These Wronskian solutions give rational solutions to the Painlevé VI equation for $\mu =1,2,\{\ldots \} $},
affiliation = {University of Illinois at Chicago, department of physics, 845 W. Taylor St., Chicago IL 60607-7059 (USA), University of Utrecht, Mathematical Institute, P.O. Box 80010, 3508 TA Utrecht (The Netherlands)},
author = {Aratyn, Henrik, van de LEUR, Johan},
journal = {Annales de l’institut Fourier},
keywords = {KP hierarchy; Grassmanian; Frobenius manifold; isomonodromic deformation; painlevé VI; KP (CKP) hierarchy; Bäcklund-Darboux transformation},
language = {eng},
number = {6},
pages = {1871-1903},
publisher = {Association des Annales de l'Institut Fourier},
title = {The symplectic Kadomtsev-Petviashvili hierarchy and rational solutions of Painlevé VI},
url = {http://eudml.org/doc/116237},
volume = {55},
year = {2005},
}

TY - JOUR
AU - Aratyn, Henrik
AU - van de LEUR, Johan
TI - The symplectic Kadomtsev-Petviashvili hierarchy and rational solutions of Painlevé VI
JO - Annales de l’institut Fourier
PY - 2005
PB - Association des Annales de l'Institut Fourier
VL - 55
IS - 6
SP - 1871
EP - 1903
AB - Equivalence is established between a special class of Painlevé VI equations parametrized by a conformal dimension $\mu $, time dependent Euler top equations, isomonodromic deformations and three-dimensional Frobenius manifolds. The isomonodromic tau function and solutions of the Euler top equations are explicitly constructed in terms of Wronskian solutions of the 2-vector 1-constrained symplectic Kadomtsev-Petviashvili (CKP) hierarchy by means of Grassmannian formulation. These Wronskian solutions give rational solutions to the Painlevé VI equation for $\mu =1,2,{\ldots } $
LA - eng
KW - KP hierarchy; Grassmanian; Frobenius manifold; isomonodromic deformation; painlevé VI; KP (CKP) hierarchy; Bäcklund-Darboux transformation
UR - http://eudml.org/doc/116237
ER -

References

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