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 is defined here by … ►The distribution function 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 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
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► Matveev), published by Springer in 1994, and Painlevé Transcendents: The Riemann-Hilbert Approach (with A.
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