[La hiérarchie de Kadomtsev-Petviashvili symplectique et la solution ratio\-nnelle de Painlevé VI]
Nous établissons des connexions entre une certaine classe d’ équations de Painlevé VI
paramétrée par une dimension conforme
Equivalence is established between a special class of Painlevé VI equations parametrized
by a conformal dimension
Keywords: KP hierarchy, Grassmanian, Frobenius manifold, isomonodromic deformation, painlevé VI
Mots-clés : hiérarchie de Kadomtsev-Petviashvili, formulation Grassmanienne, variétes de Frobenius, déformation isomonodromique, painlevé VI
Aratyn, Henrik 1 ; van de LEUR, Johan
@article{AIF_2005__55_6_1871_0, author = {Aratyn, Henrik and van de LEUR, Johan}, title = {The symplectic {Kadomtsev-Petviashvili} hierarchy and rational solutions of {Painlev\'e} {VI}}, journal = {Annales de l'Institut Fourier}, pages = {1871--1903}, publisher = {Association des Annales de l{\textquoteright}institut Fourier}, volume = {55}, number = {6}, year = {2005}, doi = {10.5802/aif.2145}, zbl = {1093.14015}, mrnumber = {2187939}, language = {en}, url = {https://aif.centre-mersenne.org/articles/10.5802/aif.2145/} }
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 SP - 1871 EP - 1903 VL - 55 IS - 6 PB - Association des Annales de l’institut Fourier UR - https://aif.centre-mersenne.org/articles/10.5802/aif.2145/ DO - 10.5802/aif.2145 LA - en ID - AIF_2005__55_6_1871_0 ER -
%0 Journal Article %A Aratyn, Henrik %A van de LEUR, Johan %T The symplectic Kadomtsev-Petviashvili hierarchy and rational solutions of Painlevé VI %J Annales de l'Institut Fourier %D 2005 %P 1871-1903 %V 55 %N 6 %I Association des Annales de l’institut Fourier %U https://aif.centre-mersenne.org/articles/10.5802/aif.2145/ %R 10.5802/aif.2145 %G en %F AIF_2005__55_6_1871_0
Aratyn, Henrik; van de LEUR, Johan. The symplectic Kadomtsev-Petviashvili hierarchy and rational solutions of Painlevé VI. Annales de l'Institut Fourier, Tome 55 (2005) no. 6, pp. 1871-1903. doi : 10.5802/aif.2145. https://aif.centre-mersenne.org/articles/10.5802/aif.2145/
[1] WDVV equations, Darboux-Egoroff metric and the dressing method (2002) (contribution to the UNESP2002 workshop on Integrable Theories, Solitons and Duality, http://jhep.sissa.it or [arXiv:math-ph/0210038) | MR | Zbl
[2] Integrable structures behind WDVV equations (Teor. Math. Phys.), Volume 134 (2003), pp. 14-26 | Zbl
[3] Solutions of the WDVV Equations and Integrable Hierarchies of KP Type, Commun. Math. Phys., Volume 239 (2003), pp. 155-182 | DOI | MR | Zbl
[4] Multi-component matrix KP hierarchies as symmetry-enhanced scalar KP hierarchies and their Darboux-Bäcklund solutions, in Bäcklund and Darboux transformations., The geometry of solitons (Halifax, NS, 1999) (CRM Proc. Lecture Notes), Volume 29 (2001), pp. 109-120 | Zbl
[5] Transformation groups for soliton equations. 6. KP hierarchies of orthogonal and symplectic type, J. Phys. Soc., Japan, Volume 50 (1981), pp. 3813-3818 | DOI | MR | Zbl
[6] Integrable systems and classification of 2-dimensional topological field theories, Integrable Systems, proceedings of Luminy 1991 conference dedicated to the memory of J.-L. Verdier, eds. O. Babelon, P. Cartier, Y. Kosmann-Schwarzbach (1993), pp. 313-359 | Zbl
[7] Geometry on 2D topological field theories, Integrable Systems and Quantum Groups (Montecatini Terme, 1993) (Lecture Notes in Math.), Volume 1620 (1996), pp. 120-348 | Zbl
[8] Monodromy of certain Painlevé VI trascendents and reflection groups, Invent. Math., Volume 141 (2000), pp. 55-147 | DOI | MR | Zbl
[9] Frobenius manifolds and Virasoro constraints., Selecta Math. (N.S.), Volume 5 (1999) no. 4, pp. 423-466 | DOI | MR | Zbl
[10] Geometric Bäcklund-Darboux transformations for the KP hierarchy, Publ. Res. Inst. Math. Sci., Volume 37 (2001) no. 4, pp. 479-519 | DOI | MR | Zbl
[11] An analytic description of the vector constrained KP hierarchy, Commun. Math Phys., Volume 193 (1998), pp. 627-641 | DOI | MR | Zbl
[12] Constrained and Rational Reductions of the KP hierarchy, Supersymmetry and Integrable Models (Springer Lecture Notes in Physics), Volume 502 (1998), pp. 167-182 | Zbl
[13] Twistor spaces, Einstein metrics and isomonodromic deformations, J. Diff. Geom., Volume 42 (1995), pp. 30-112 | MR | Zbl
[14] Poncelet polygons and the Painlevé transcendents (Geometry and Analysis) (1996), pp. 151-185 | Zbl
[15] A new family of Einstein metrics, manifolds and geometry (Manifolds and geometry (Pisa, 1993), Sympos. Math., XXXVI) (1996), pp. 190-222 | Zbl
[16] Monodromy preserving deformations of linear ordinary differential equations with rational coefficients I, Physica 2D, Volume 2 (1981), pp. 306-352 | DOI | MR
[17] Monodromy preserving deformations of linear ordinary differential equations with rational coefficients II, Physica 2D, Volume 3 (1981), pp. 407-448 | MR
[18] Monodromy preserving deformations of linear ordinary differential equations with rational coefficients III, Physica 2D, Volume 4 (1981), pp. 26-46 | DOI | MR
[19] Solitons and Infinite Dimensional Lie Algebras, Publ. RIMS, Kyoto Univ., Volume 19 (1983), pp. 943-1001 | DOI | MR | Zbl
[20] The
[21] Twisted
[22] The construction of Frobenius Manifolds from KP tau-Functions, Commun. Math. Phys., Volume 205 (1999), pp. 587-616 | DOI | MR | Zbl
[23] Symmetric functions and Hall polynomials. Second edition., Oxford Mathematical Monographs, Oxford University Press, New York, 1995 | MR | Zbl
[24] Introduction to the theory of isomonodromic deformations of linear ordinary differential equations with rational coefficients, The Painlevé property, one century later (CRM series in mathematical physics) (1999), pp. 35-76 | Zbl
[25] Picard and Chazy solutions to the Painlevé VI equation (Math. Annalen), Volume 321 (2001), pp. 131-169 | Zbl
[26] Prym varieties and soliton equations, Infinite-dimensional Lie algebras and groups (Luminy-Marseille, 1988) (Adv. Ser. Math. Phys.), Volume 7 (1989), pp. 407-448 | Zbl
- Bäcklund transformations for certain rational solutions of Painlevé VI, Journal of Nonlinear Mathematical Physics, Volume 20 (2021) no. Supplement 1, p. 3 | DOI:10.1080/14029251.2013.862430
- Bäcklund transformation of Frobenius Painlevé equations, Modern Physics Letters B, Volume 32 (2018) no. 17, p. 1850181 | DOI:10.1142/s0217984918501816
- BKP and CKP revisited: the odd KP system, Inverse Problems, Volume 25 (2009) no. 4, p. 045001 | DOI:10.1088/0266-5611/25/4/045001
- Solutions of the Painlevé VI Equation from Reduction of Integrable Hierarchy in a Grassmannian Approach, International Mathematics Research Notices, Volume 2008 (2008) | DOI:10.1093/imrn/rnn080
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