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Linearization and Special Asymptotic Behaviour of the Second Painlevé Equation

✍ Scribed by Tariq Mahmood Khan

Publisher
Elsevier Science
Year
1998
Tongue
English
Weight
204 KB
Volume
145
Category
Article
ISSN
0022-0396

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✦ Synopsis

Linearization of the initial value problem associated with the special second Painleve equation is discussed using a different isomonodromic spectral problem than the one used in [1]. Further properties of the monodromy data [2, 3] are detected and these properties are used to reduce the problem to a linear singular integral equation via a Riemann Hilbert boundary value problem on an imaginary line. A special asymptotic increasing solution of the Painleve equation is constructed for x Ä & from the above integral equation. Moreover, failure to extract asymptotics for x Ä + is also mentioned.

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