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Painlevé transcendents

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1: 32.16 Physical Applications
§32.16 Physical Applications
Statistical Physics
Integrable Continuous Dynamical Systems
Other Applications
For the Ising model see Barouch et al. (1973), Wu et al. (1976), and McCoy et al. (1977). …
2: 32 Painlevé Transcendents
Chapter 32 Painlevé Transcendents
3: 32.13 Reductions of Partial Differential Equations
§32.13 Reductions of Partial Differential Equations
§32.13(i) Korteweg–de Vries and Modified Korteweg–de Vries Equations
§32.13(ii) Sine-Gordon Equation
§32.13(iii) Boussinesq Equation
4: 32.12 Asymptotic Approximations for Complex Variables
§32.12 Asymptotic Approximations for Complex Variables
5: 32.17 Methods of Computation
§32.17 Methods of Computation
6: 32.14 Combinatorics
§32.14 Combinatorics
where the distribution function F ( s ) is defined here by … The distribution function F ( s ) given by (32.14.2) arises in random matrix theory where it gives the limiting distribution for the normalized largest eigenvalue in the Gaussian Unitary Ensemble of n × n Hermitian matrices; see Tracy and Widom (1994). …
7: 32.15 Orthogonal Polynomials
§32.15 Orthogonal Polynomials
8: 32.5 Integral Equations
§32.5 Integral Equations
9: Alexander A. Its
 Matveev), published by Springer in 1994, and Painlevé Transcendents: The Riemann-Hilbert Approach (with A. …
10: 15.17 Mathematical Applications
This topic is treated in §§15.10 and 15.11. …