Bäcklund transformations for discrete Painlevé equations: Discrete PII–PV
نویسندگان
چکیده
منابع مشابه
Bäcklund Transformations for Fourth Painlevé Hierarchies Pilar
Bäcklund transformations (BTs) for ordinary differential equations (ODEs), and in particular for hierarchies of ODEs, are a topic of great current interest. Here we give an improved method of constructing BTs for hierarchies of ODEs. This approach is then applied to fourth Painlevé (PIV ) hierarchies recently found by the same authors [Publ. Res. Inst. Math. Sci. (Kyoto) 37 327–347 (2001)]. We ...
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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...
متن کاملBäcklund transformations for discrete Painlevé equations: Discrete PII–PV
Transformation properties of discrete Painlevé equations are investigated by using an algorithmic method. This method yields explicit transformations which relates the solutions of discrete Painlevé equations, discrete PII–PV, with different values of parameters. The particular solutions which are expressible in terms of the discrete analogue of the classical special functions of discrete Painl...
متن کاملThe Discrete Painlevé I Hierarchy
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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ژورنال
عنوان ژورنال: Chaos, Solitons & Fractals
سال: 2006
ISSN: 0960-0779
DOI: 10.1016/j.chaos.2005.04.029