相关论文: Higher order Painleve system of type D^{(1)}_{2n+2…
The higher order Painleve system of type D^{(1)}_{2n+2} was proposed by Y. Sasano as an extension of the sixth Painleve equation for the affine Weyl group symmetry with the aid of algebraic geometry for Okamoto initial value space. In this…
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…
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.
In 2006, Y. Sasano proposed higher-order Painlev\'e systems, which admit affine Weyl group symmetry of type $D^{(1)}_l$, $l=4, 5, 6, \dots$. In this paper, we study the integrability of a four-dimensional Painlev\'e system, which has…
We find four kinds of six-parameter family of coupled Painlev\'e VI systems in dimension four with affine Weyl group symmetry of types $B_6^{(1)}$, $D_6^{(1)}$ and $D_7^{(2)}$. Each system is the first example which gave higher-order…
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.
A series of systems of nonlinear equations with affine Weyl group symmetry of type $A^{(1)}_l$ is studied. This series gives a generalization of Painlev\'e equations $P_{IV}$ and $P_{V}$ to higher orders.
In this paper, we completely classify the rational solutions of the Sasano system of type $A_5^{(2)}$, which is given by the coupled Painlev\'e III system. This system of differential equations has the affine Weyl group symmetry of type…
Higher order Painleve equations invariant under extended affine Weyl groups $A^{(1)}_n$ are obtained through self-similarity limit of a class of pseudo-differential Lax hierarchies with symmetry inherited from the underlying generalized…
We find a four-parameter family of coupled Painlev\'e VI systems in dimension four with affine Weyl group symmetry of type $A_7^{(2)}$. This is the first example which gave higher-order Painlev\'e equations of type $A_{2l+5}^{(2)}$. We then…
The sixth Painleve equation arises from a Drinfel'd-Sokolov hierarchy associated with the affine Lie algebra of type D_4 by similarity reduction.
We find a four-parameter family of coupled Painlev\'e VI systems in dimension four with affine Weyl group symmetry of type $E_6^{(2)}$. This is the first example which gave higher order Painlev\'e type systems of type $E_{6}^{(2)}$. We…
Scaling symmetry of gl_n-type Drinfel'd-Sokolov hierarchy is investigated. Applying similarity reduction to the hierarchy, one can obtain the Schlesinger equation with (n+1) regular singularities. Especially in the case of n=3, the…
We find a two-parameter family of ordinary differential systems in dimension five with the affine Weyl group symmetry of type $D_3^{(2)}$. We show its symmetry and holomorphy conditions. This is the second example which gave higher order…
In this paper, we study the second member of the second Painlev\'e hierarchy $P_{II}^{(2)}$. We show that the birational transformations take this equation to the polynomial Hamiltonian system in dimension four, and this Hamiltonian system…
We find a three-parameter family of ordinary differential systems in dimension six with affine Weyl group symmetry of type $D_4^{(2)}$. This is the second example which gave higher order Painlev\'e type systems of type $D_{4}^{(2)}$. We…
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…
In the previous work we introduced the higher order $q$-Painlev\'{e} system $q$-$P_{(n+1,n+1)}$ as a generalization of the Jimbo-Sakai's $q$-Painlev\'{e} VI equation. It is derived from a $q$-analogue of the Drinfeld-Sokolov hierarchy of…
We revise a method by Kalnins, Kress and Miller (2010) for constructing a canonical form for symmetry operators of arbitrary order for the Schr\"odinger eigenvalue equation $H\Psi \equiv (\Delta_2 +V)\Psi=E\Psi$ on any 2D Riemannian…
We present a general scheme to derive higher-order members of the Painleve VI (PVI) hierarchy of ODE's as well as their difference analogues. The derivation is based on a discrete structure that sits on the background of the PVI equation…