An Elliptic Garnier System
نویسندگان
چکیده
منابع مشابه
An Elliptic Garnier System from Interpolation
Considering a certain interpolation problem, we derive a series of elliptic difference isomonodromic systems together with their Lax forms. These systems give a multivariate extension of the elliptic Painlevé equation.
متن کاملEigenvalues of an Elliptic System
We describe the spectrum of a non-self-adjoint elliptic system on a finite interval. Under certain conditions we find that the eigenvalues form a discrete set and converge asymptotically at infinity to one of several straight lines. The eigenfunctions need not generate a basis of the relevant Hilbert space, and the larger eigenvalues are extremely sensitive to small perturbations of the operato...
متن کاملAffine Weyl group symmetry of the Garnier system
In this paper, we show that the Garnier system in n-variables has affine Weyl group symmetry of type B (1) n+3. We also formulate the τ functions for the Garnier system (or the Schlesinger system of rank 2) on the root lattice Q(Cn+3) and show that they satisfy Toda equations, Hirota-Miwa equations and bilinear differential equations.
متن کاملToda equation and special polynomials associated with the Garnier system
We prove that a certain sequence of tau functions of the Garnier system satisfies Toda equation. We construct a class of algebraic solutions of the system by the use of Toda equation; then show that the associated tau functions are expressed in terms of the universal character, which is a generalization of Schur polynomial attached to a pair of partitions. This article is based on the results i...
متن کاملStudies on the Garnier System in Two Variables
We study some Hamiltonian structures of the Garnier system in two variables from the viewpoints of its symmetry and holomorphy properties. We also give a generalization of Okamoto transformation of the sixth Painlevé system.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Communications in Mathematical Physics
سال: 2017
ISSN: 0010-3616,1432-0916
DOI: 10.1007/s00220-017-2934-6