Inner Transition Layer in Solutions of the Discrete Painlevé II Equation

IF 1.7 3区物理与天体物理 Q2 PHYSICS, MATHEMATICAL

Russian Journal of Mathematical Physics Pub Date : 2024-10-03 DOI:10.1134/S1061920824030130

V.Yu. Novokshenov

引用次数: 0

Abstract

We study real-valued asymptotic solutions of the discrete Painlevé equation of second type (dPII)

In the case of \(n/\nu = O(1)\), and as \(n\to\infty\), the asymptotics is nonuniform. Near the point \(n= 2\nu\), an inner transition layer occurs, which matches regular asymptotics to the left and to the right of this point. The matching procedure involves classical Painlevé II transcendents. The asymptotics are applied to discrete gap probabilities and random matrix theory.

DOI 10.1134/S1061920824030130

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离散潘列维方程 II 解中的内过渡层

我们研究了第二类离散潘列维方程（dPII）的实值渐近解在 \(n/\nu = O(1)\) 的情况下，当 \(n\to\infty\) 时，渐近是不均匀的。在点\(n= 2\nu\) 附近，会出现一个内部过渡层，它与该点左侧和右侧的规则渐近线相匹配。匹配过程涉及经典的潘列韦 II 超越。渐近线被应用于离散间隙概率和随机矩阵理论。 doi 10.1134/s1061920824030130

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来源期刊

Russian Journal of Mathematical Physics 物理-物理：数学物理

CiteScore

3.10

自引率

14.30%

发文量

审稿时长

>12 weeks

期刊介绍： Russian Journal of Mathematical Physics is a peer-reviewed periodical that deals with the full range of topics subsumed by that discipline, which lies at the foundation of much of contemporary science. Thus, in addition to mathematical physics per se, the journal coverage includes, but is not limited to, functional analysis, linear and nonlinear partial differential equations, algebras, quantization, quantum field theory, modern differential and algebraic geometry and topology, representations of Lie groups, calculus of variations, asymptotic methods, random process theory, dynamical systems, and control theory.