Painlevé property
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1: 32.16 Physical Applications
§32.16 Physical Applications
…2: Mark J. Ablowitz
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►Their similarity solutions lead to special ODEs which have the Painlevé property; i.
…ODEs with the Painlevé property contain the well-known Painlevé equations which are special second order scalar equations; their solutions are often called Painlevé transcendents.
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3: 32.2 Differential Equations
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►An equation is said to have the Painlevé property if all its solutions are free from movable branch points; the solutions may have movable poles or movable isolated essential singularities (§1.10(iii)), however.
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►There are fifty equations with the Painlevé property.
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4: Bibliography G
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Do integrable mappings have the Painlevé property?.
Phys. Rev. Lett. 67 (14), pp. 1825–1828.
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5: Bibliography B
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Integrable Hamiltonian systems and the Painlevé property.
Phys. Rev. A (3) 25 (3), pp. 1257–1264.
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6: Bibliography F
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The transformation properties of the sixth Painlevé equation and one-parameter families of solutions.
Lett. Nuovo Cimento (2) 30 (17), pp. 539–544.
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7: Bibliography S
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The relation between asymptotic properties of the second Painlevé equation in different directions towards infinity.
Differ. Uravn. 23 (5), pp. 834–842 (Russian).
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8: Bibliography C
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Stability properties of disk polynomials.
Numer. Algorithms.
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Properties of generalized Freud polynomials.
J. Approx. Theory 225, pp. 148–175.
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The second Painlevé equation, its hierarchy and associated special polynomials.
Nonlinearity 16 (3), pp. R1–R26.
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The fourth Painlevé equation and associated special polynomials.
J. Math. Phys. 44 (11), pp. 5350–5374.
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Chazy’s second-degree Painlevé equations.
J. Phys. A 39 (39), pp. 11955–11971.
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9: 32.11 Asymptotic Approximations for Real Variables
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§32.11(i) First Painlevé Equation
… ►§32.11(ii) Second Painlevé Equation
… ►§32.11(iii) Modified Second Painlevé Equation
… ►§32.11(iv) Third Painlevé Equation
… ►§32.11(v) Fourth Painlevé Equation
…10: Bibliography H
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Some properties and applications of the repeated integrals of the error function.
Proc. Manchester Lit. Philos. Soc. 80, pp. 85–102.
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A boundary value problem associated with the second Painlevé transcendent and the Korteweg-de Vries equation.
Arch. Rational Mech. Anal. 73 (1), pp. 31–51.
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Poncelet Polygons and the Painlevé Equations.
In Geometry and Analysis (Bombay, 1992), Ramanan (Ed.),
pp. 151–185.
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On a Painlevé-type boundary-value problem.
Quart. J. Mech. Appl. Math. 37 (4), pp. 525–538.
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Analytical structure and properties of Coulomb wave functions for real and complex energies.
Ann. Physics 155 (2), pp. 461–493.
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