Painlevé transcendents
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11: Peter A. Clarkson
12: Mark J. Ablowitz
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►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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13: 32.2 Differential Equations
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§32.2(i) Introduction
►The six Painlevé equations – are as follows: … ►The solutions of – are called the Painlevé transcendents. The six equations are sometimes referred to as the Painlevé transcendents, but in this chapter this term will be used only for their solutions. …14: 32.4 Isomonodromy Problems
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►Suppose
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15: Bibliography I
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The method of isomonodromic deformations and relation formulas for the second Painlevé transcendent.
Izv. Akad. Nauk SSSR Ser. Mat. 51 (4), pp. 878–892, 912 (Russian).
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Quasi-linear Stokes phenomenon for the second Painlevé transcendent.
Nonlinearity 16 (1), pp. 363–386.
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Connection formulae for the fourth Painlevé transcendent; Clarkson-McLeod solution.
J. Phys. A 31 (17), pp. 4073–4113.
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16: 32.3 Graphics
§32.3 Graphics
… ►17: 32.7 Bäcklund Transformations
§32.7 Bäcklund Transformations
… ►With the exception of , a Bäcklund transformation relates a Painlevé transcendent of one type either to another of the same type but with different values of the parameters, or to another type. … ►18: 32.6 Hamiltonian Structure
§32.6 Hamiltonian Structure
… ►19: 32.11 Asymptotic Approximations for Real Variables
§32.11 Asymptotic Approximations for Real Variables
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Replica field theories, Painlevé transcendents, and exact correlation functions.
Phys. Rev. Lett. 89 (25), pp. (250201–1)–(250201–4).
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Connection formulae for the first Painlevé transcendent in the complex domain.
Lett. Math. Phys. 27 (4), pp. 243–252.
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Elliptic asymptotics of the first and second Painlevé transcendents.
Uspekhi Mat. Nauk 49 (1(295)), pp. 77–140 (Russian).
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