Parametrization of solutions of the Lewis metric by a Painlevé transcendent III

Gariel, J.; Marcilhacy, G.; Santos, N. O.

doi:10.1063/1.2206689

Cited by 2 publications

(2 citation statements)

References 9 publications

(5 reference statements)

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“…We remark that this equation also arises in extended quantum systems [4][5][6], in relativity [17] and in coefficients in the three-term recurrence relation for orthogonal polynomials with respect to the weight w(θ) = e t cos θ on the unit circle, see [48, equation (3.13)]. The orthogonal polynomials for this weight on the unit circle are related to unitary random matrices [41].…”

Section: Complex Sine-gordon Equationmentioning

confidence: 99%

Classical solutions of the degenerate fifth Painlevé equation

Clarkson

2023

J. Phys. A: Math. Theor.

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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. Here the classiﬁcation and description of the classical solutions of the degenerate ﬁfth Painlevé equation are done directly, than through 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.

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Section: Complex Sine-gordon Equationmentioning

confidence: 99%

Classical solutions of the degenerate fifth Painlevé equation

Clarkson

2023

J. Phys. A: Math. Theor.

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“…which also arises in extended quantum systems [37,38,39], in relativity [74] and reflection coefficients for orthogonal polynomials on the unit circle [140, equation (3.13)]. Equation (2.5) can be shown to possess the Painlevé property, though is not in the list of 50 equations given in [81,Chapter 14].…”

Section: Definition 22mentioning

confidence: 99%