Classical Solutions of the Degenerate Fifth Painlevé Equation
arXiv:2301.01727 · doi:10.1088/1751-8121/acbef1
Abstract
In this paper classical solutions of the degenerate fifth Painlevé equation are classified, which include hierarchies of algebraic solutions and solutions expressible in terms of Bessel functions. Solutions of the degenerate fifth Painlevé equation are known to expressible in terms of the third Painlevé equation. Two applications of these classical solutions are discussed, deriving exact solutions of the complex sine-Gordon equation and of the coefficients in the three-term recurrence relation associated with generalised Charlier polynomials.
arXiv comment19 pages
References in corpus (11)
- Entanglement and alpha entropies for a massive Dirac field in two dimensions
- Entanglement and alpha entropies for a massive scalar field in two dimensions
- Random Unitary Matrices, Permutations and Painleve
- On the Umemura Polynomials for the Painlevé III equation
- Unitary Matrix Models and Painlevé III
- Orthogonal polynomials on a bi-lattice
- Analytic results on the geometric entropy for free fields
- Recurrence coefficients of generalized Charlier polynomials and the fifth Painlevé equation
- On a q-difference Painlevé III equation: II. Rational solutions
- On Airy Solutions of the Second Painlevé Equation
- Variations for Some Painlevé Equations
Cited by in corpus (4)
- Rational Solutions of the Fifth Painlevé Equation. Generalised Laguerre Polynomials
- A Constructive Proof for the Umemura Polynomials of the Third Painlevé Equation
- Discrete equations from Bäcklund transformations of the fifth Painlevé equation
- Asymptotic properties of special function solutions of Painlevé III equation for fixed parameters