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831
HEUN EQUATION AND PAINLEVÉ EQUATION
, 2005
"... Abstract. We relate two parameter solutions of the sixth Painlevé equation and finitegap solutions of the Heun equation by considering monodromy on a certain class of Fuchsian differential equations. In the appendix, we present formulae on differentials of elliptic modular functions, and obtain the ..."
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Cited by 2 (1 self)
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Abstract. We relate two parameter solutions of the sixth Painlevé equation and finitegap solutions of the Heun equation by considering monodromy on a certain class of Fuchsian differential equations. In the appendix, we present formulae on differentials of elliptic modular functions, and obtain
Folding transformations of the Painlevé equations
, 2005
"... New symmetries of the Painlevé differential equations, called folding transformations, are determined. These transformations are not birational but algebraic transformations of degree 2, 3, or 4. These are associated with quotients of the spaces of initial conditions of each Painlevé equation. We ma ..."
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Cited by 34 (3 self)
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New symmetries of the Painlevé differential equations, called folding transformations, are determined. These transformations are not birational but algebraic transformations of degree 2, 3, or 4. These are associated with quotients of the spaces of initial conditions of each Painlevé equation. We
Dynamics of the sixth Painleve equation
 Proceedings of Conference Internationale Theories Asymptotiques et Equations de Painleve, Seminaires et Congres, Soc
"... Abstract. The sixth Painlevé equation is hiding extremely rich geometric structures behind its outward appearance. This article tries to give as a total picture as possible of its dynamical natures, based on the RiemannHilbert approach recently developed by the authors, using various techniques f ..."
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Cited by 1 (0 self)
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Abstract. The sixth Painlevé equation is hiding extremely rich geometric structures behind its outward appearance. This article tries to give as a total picture as possible of its dynamical natures, based on the RiemannHilbert approach recently developed by the authors, using various techniques
On the Linearization of the Painlevé Equations
, 2007
"... We extend similarity reductions of the coupled (2+1)dimensional threewave resonant interaction system, to its Lax pair. Thus we obtain new 3×3 matrix Fuchs–Garnier pairs for the third and fifth Painlevé equations, together with the previously known Fuchs– Garnier pair for the fourth and sixth Pain ..."
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We extend similarity reductions of the coupled (2+1)dimensional threewave resonant interaction system, to its Lax pair. Thus we obtain new 3×3 matrix Fuchs–Garnier pairs for the third and fifth Painlevé equations, together with the previously known Fuchs– Garnier pair for the fourth and sixth
NONLINEAR QUASICLASSICS AND THE PAINLEVÉ EQUATIONS
, 2008
"... A centuryold history of calculation of asymptotics for solutions to Painlevé equations (usually denoted Pj, j=1,2,...,6) as their variable x tends to infinity was started by pioneer works by Painlevé, Gambier and Boutroux [1]. In 19801981 papers by Jimbo, Miwa and Flashka, Newell [2] initiated the ..."
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A centuryold history of calculation of asymptotics for solutions to Painlevé equations (usually denoted Pj, j=1,2,...,6) as their variable x tends to infinity was started by pioneer works by Painlevé, Gambier and Boutroux [1]. In 19801981 papers by Jimbo, Miwa and Flashka, Newell [2] initiated the
QUIVERS AND DIFFERENCE PAINLEVÉ EQUATIONS
, 2007
"... We will describe natural Lax pairs for the difference Painlevé equations with affine Weyl symmetry groups of types E6, E7 and E8, showing that they do indeed arise as symmetries of certain Fuchsian systems of differential equations. ..."
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We will describe natural Lax pairs for the difference Painlevé equations with affine Weyl symmetry groups of types E6, E7 and E8, showing that they do indeed arise as symmetries of certain Fuchsian systems of differential equations.
Hypergeometric solutions to the qPainlevé equations
 Internat. Math. Res. Notices
"... Hypergeometric solutions to seven qPainlevé equations in Sakai’s classification are constructed. Geometry of plane curves is used to reduce the qPainlevé equations to the threeterm recurrence relations for qhypergeometric functions. 1 ..."
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Cited by 38 (5 self)
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Hypergeometric solutions to seven qPainlevé equations in Sakai’s classification are constructed. Geometry of plane curves is used to reduce the qPainlevé equations to the threeterm recurrence relations for qhypergeometric functions. 1
SYMMETRIES IN THE THIRD PAINLEVÉ EQUATION
, 704
"... Abstract. The third Painlevé equation PIII is known to have symmetry of the affine Weyl group of type C (1) 2 with respect to the Bäcklund transformations. We introduce a new representation of this system. 0. Statement of main results It is wellknown by K. Okamoto that the third Painlevé equation h ..."
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Abstract. The third Painlevé equation PIII is known to have symmetry of the affine Weyl group of type C (1) 2 with respect to the Bäcklund transformations. We introduce a new representation of this system. 0. Statement of main results It is wellknown by K. Okamoto that the third Painlevé equation
Lax forms of the qPainlevé equations
, 810
"... All qPainlevé equations which are obtained from the qanalog of the sixth Painlevé equation are expressed in a Lax formalism. They are characterized by the data of the associated linear qdifference equations. The degeneration pattern from the qPainlevé equation of type A2 is also presented. ..."
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Cited by 4 (0 self)
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All qPainlevé equations which are obtained from the qanalog of the sixth Painlevé equation are expressed in a Lax formalism. They are characterized by the data of the associated linear qdifference equations. The degeneration pattern from the qPainlevé equation of type A2 is also presented.
New expressions for discrete Painlevé equations
 Funkcial. Ekvac
"... It is known that discrete Painlevé equations have symmetries of the affine Weyl groups. In this paper we propose a new representation of discrete Painlevé equations in which the symmetries become clearly visible. We know how to obtain discrete Painlevé equations from certain rational surfaces in con ..."
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Cited by 6 (0 self)
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It is known that discrete Painlevé equations have symmetries of the affine Weyl groups. In this paper we propose a new representation of discrete Painlevé equations in which the symmetries become clearly visible. We know how to obtain discrete Painlevé equations from certain rational surfaces
Results 1  10
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831