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Krook-Wu model and integrability. (English) Zbl 0899.76310

Summary: Performing the Painlevé PDE test due to J. Weiss, M. Tabor and G. Carnevale [J. Math. Phys. 24, 522-526 (1983; Zbl 0514.35083)] on the Krook-Wu model of the nonlinear Boltzmann equation, it is shown that the equation possesses conditional PP. On solving the constraint equation we have arrived at two exact solutions of the said equation, one of which has turned out to be the generalized form of the Krook-Wu solution and the second solution appears to be quite new.

MSC:

76P05 Rarefied gas flows, Boltzmann equation in fluid mechanics

Citations:

Zbl 0514.35083
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References:

[1] Weiss, J.; Tabor, M.; Carnevale, G., J. Math. Phys., 24, 522 (1983)
[2] Krook, M.; Wu, T. T., Phys. Rev. Lett., 36, 1107 (1976)
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[4] McLeod, J. B.; Olver, P. J., SIAM J. Math. Anal., 14, 488 (1983)
[5] Weiss, J., J. Math. Phys., 24, 1405 (1983)
[6] Weiss, J., J. Math. Phys., 25, 13 (1984)
[7] Steeb, W. H.; Euler, N., Nonlinear Evolution Equations and Painlevé Test (1988), World Scientific: World Scientific Singapore · Zbl 0723.34001
[8] Jimbo, M.; Kruskal, M. D.; Miwa, T., Phys. Lett. A, 92, 59 (1982)
[9] Vijaykumar, K., (Ph.D. thesis (1989), IIT Delhi)
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