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Search Results: 1 - 10 of 4720 matches for " Takao Suzuki "
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A Particular Solution of a Painlevé System in Terms of the Hypergeometric Function {}_{n+1}F_n
Takao Suzuki
Symmetry, Integrability and Geometry : Methods and Applications , 2010,
Abstract: In a recent work, we proposed the coupled Painlevé VI system with A_{2n+1}^{(1)}-symmetry, which is a higher order generalization of the sixth Painlevé equation (P_{VI}). In this article, we present its particular solution expressed in terms of the hypergeometric function {}_{n+1}F_n. We also discuss a degeneration structure of the Painlevé system derived from the confluence of {}_{n+1}F_n.
Affine Weyl group symmetry of the Garnier system
Takao Suzuki
Mathematics , 2003,
Abstract: We show that the Garnier system in n-variables has affine Weyl group symmetry of type $B^{(1)}_{n+3}$. We also formulate the $\tau$ functions for the Garnier system (or the Schlesinger system of rank 2) on the root lattice $Q(C_{n+3})$ and show that they satisfy Toda equations, Hirota-Miwa equations and bilinear differential equations.
A Particular Solution of a Painlevé System in Terms of the Hypergeometric Function ${}_{n+1}F_n$
Takao Suzuki
Mathematics , 2010, DOI: 10.3842/SIGMA.2010.078
Abstract: In a recent work, we proposed the coupled Painlev\'e VI system with $A^{(1)}_{2n+1}$-symmetry, which is a higher order generalization of the sixth Painlev\'e equation ($P_{\rm VI}$). In this article, we present its particular solution expressed in terms of the hypergeometric function ${}_{n+1}F_n$. We also discuss a degeneration structure of the Painlev\'e system derived from the confluence of ${}_{n+1}F_n$.
Six-dimensional Painleve systems and their particular solutions in terms of hypergeometric functions
Takao Suzuki
Mathematics , 2012,
Abstract: In this article, we propose a class of six-dimensional Painleve systems given as the monodromy preserving deformations of the Fuchsian systems. They are expressed as polynomial Hamiltonian systems of sixth order. We also discuss their particular solutions in terms of the hypergeometric functions defined by fourth order rigid systems.
A class of higher order Painleve systems arising from integrable hierarchies of type A
Takao Suzuki
Mathematics , 2010,
Abstract: A relationship between Painleve systems and infinite-dimensional integrable hierarchies is studied. We derive a class of higher order Painleve systems from Drinfeld-Sokolov (DS) hierarchies of type A by similarity reductions. This result allows us to understand some properties of Painleve systems, Hamiltonian structures, Lax pairs and affine Weyl group symmetries.
A q-analogue of the Drinfeld-Sokolov hierarchy of type A and q-Painleve system
Takao Suzuki
Mathematics , 2011,
Abstract: In this article, we propose a q-analogue of the Drinfeld-Sokolov hierarchy of type A. We also discuss its relationship with the q-Painleve VI equation and the q-hypergeometric function.
Classical solutions of the degenerate Garnier system and their coalescence structures
Takao Suzuki
Mathematics , 2004,
Abstract: We study the degenerate Garnier system which generalizes the fifth Painlev\'{e} equation. We present two classes of particular solutions, classical transcendental and algebraic ones. Their coalescence structure is also investigated.
Coupled Painleve VI system with E_6^{(1)} symmetry
Kenta Fuji,Takao Suzuki
Mathematics , 2007,
Abstract: We present an new system of ordinary differential equations with affine Weyl group symmetry of type E_6^{(1)}. This system is expressed as a Hamiltonian system of sixth order with a coupled Painleve VI Hamiltonian.
Higher order Painleve system of type D^{(1)}_{2n+2} arising from integrable hierarchy
Kenta Fuji,Takao Suzuki
Mathematics , 2007,
Abstract: A higher order Painleve system of type D^{(1)}_{2n+2} was introduced by Y. Sasano. It is an extension of the sixth Painleve equation for the affine Weyl group symmetry. It is also expressed as a Hamiltonian system of order 2n with a coupled Painleve VI Hamiltonian. In this paper, we discuss a derivation of this system from a Drinfeld-Sokolov hierarchy.
Drinfeld-Sokolov hierarchies of type A and fourth order Painleve systems
Kenta Fuji,Takao Suzuki
Mathematics , 2009,
Abstract: We study the Drinfeld-Sokolov hierarchies of type A_n^{(1)} associated with the regular conjugacy classes of W(A_n). A class of fourth order Painleve systems is derived from them by similarity reductions.
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