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Painlevé test of the McKean and Carleman models

✍ Scribed by W. -H. Steeb; N. Euler

Publisher
Springer
Year
1987
Tongue
English
Weight
267 KB
Volume
14
Category
Article
ISSN
0377-9017

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✦ Synopsis

The Painlev6 test of the system of nonlinear partial differential first-order equations U t + U x = kl t~2 + k2 u2 + k3uv , 1) t -1) x = -kll~ 2 -k2 u2 -k3uo is performed. The system includes the Carleman and McKean models which are caricatures of the Boltzmann equation. For k~ = k2 = 0 the system describes the interaction of two waves u and v. The results of the Painlev6 test are discussed in connection with whether or not the system is integrable. We also study in detail the constraint on q~ (whose vanishing defines a noncharacteristic hypersurface S) which arises at the resonance.

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