Lattice equations arising from discrete Painlevé systems. I. (A2+A1)(1)and (A1+A1′)(1) cases
نویسندگان
چکیده
منابع مشابه
On Discrete Painlevé Equations Associated with the Lattice Kdv Systems and the Painlevé Vi Equation
1 Abstract A new integrable nonautonomous nonlinear ordinary difference equation is presented which can be considered to be a discrete analogue of the Painlevé V equation. Its derivation is based on the similarity reduction on the two-dimensional lattice of integrable partial difference equations of KdV type. The new equation which is referred to as GDP (generalised discrete Painlevé equation) ...
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The discrete Painlevé I equation (dPI) is an integrable difference equation which has the classical first Painlevé equation (PI) as a continuum limit. dPI is believed to be integrable because it is the discrete isomonodromy condition for an associated (single-valued) linear problem. In this paper, we derive higher-order difference equations as isomonodromy conditions that are associated to the ...
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Discrete Painlevé equations are studied from various points of view as integrable systems [2], [7]. They are discrete equations which are reduced to the Painlevé differential equations in a suitable limiting process, and moreover, which pass the singularity confinement test. Passing this test can be thought of as a difference version of the Painlevé property. The Painlevé differential equations...
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The τ-function theory of Painlevé systems is used to derive recurrences in the rank n of certain random matrix averages over U (n). These recurrences involve auxilary quantities which satisfy discrete Painlevé equations. The random matrix averages include cases which can be interpreted as eigenvalue distributions at the hard edge and in the bulk of matrix ensembles with unitary symmetry. The re...
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In this study, we consider the asymptotic behaviour of the first discrete Painlevé equation in the limit as the independent variable becomes large. Using an asymptotic series expansion, we identify two types of solutions which are pole-free within some sector of the complex plane containing the positive real axis. Using exponential asymptotic techniques, we determine Stokes phenomena effects pr...
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ژورنال
عنوان ژورنال: Journal of Mathematical Physics
سال: 2015
ISSN: 0022-2488,1089-7658
DOI: 10.1063/1.4931481