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Painlevé test of the McKean and Carleman models

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Abstract

The Painlevé test of the system of nonlinear partial differential first-order equations u1+uk=k1v2+k2u2+k3uv, v1−vx=−k1v2−k2u2−k3uv is performed. The system includes the Carleman and McKean models which are caricatures of the Boltzmann equation. For k 1=k 2=0 the system describes the interaction of two waves u and v. The results of the Painlevé test are discussed in connection with whether or not the system is integrable. We also study in detail the constraint on ϕ (whose vanishing defines a noncharacteristic hypersurface S) which arises at the resonance.

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Authors and Affiliations

  1. Department of Physics, Rand Afrikaans University, PO Box 524, 2000, Johannesburg, South Africa

    W. -H. Steeb & N. Euler

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  1. W. -H. Steeb
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  2. N. Euler
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Steeb, W.H., Euler, N. Painlevé test of the McKean and Carleman models. Lett Math Phys 14, 99–104 (1987). https://doi.org/10.1007/BF00420299

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  • DOI: https://doi.org/10.1007/BF00420299

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