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A boundary value problem associated with the second Painleve transcendent and the Korteweg-de Vries equation. (English) Zbl 0426.34019
MSC:
34B99Boundary value problems for ODE
References:
[1]P. C. T. de Boer & G. S. S. Ludford, Spherical electric probe in a continuum gas. Plasma Phys. 17, 29-43 (1975). · doi:10.1088/0032-1028/17/1/004
[2]E. L. Ince, Ordinary Differential Equations. New York: Dover 1944.
[3]E. Hille, Ordinary Differential Equations in the Complex Domain. New York: Wiley 1976.
[4]M. J. Ablowitz & H. Segur, Exact linearization of a Painlevé transcendent. Phys. Rev. Letters 38, 1103-1106 (1977). · doi:10.1103/PhysRevLett.38.1103
[5]G. N. Watson, A Treatise on the Theory of Bessel Functions. (2nd ed., Cambridge, 1944).
[6]R. Rosales, The similarity solution for the Korteweg-de Vries equation and the related Painlevé transcendent. Preprint.
[7]P. Boutroux, Recherches sur les transcendents de M. Painlevé et l’étude asymptotique des équations différentielles du second ordre. Ann. École Norm. Supér. (3) 30, 255-375 (1913);
[8]P. Boutroux, Recherches sur les transcendents de M. Painlevé et l’étude asymptotique des équations différentielles du second ordre. Ann. École Norm. Supér. (3) 31, 99-159 (1914).
[9]R. M. Miura, The Korteweg-de Vries equation: a survey of results. SIAM Rev. 18, 412-459 (1976). · Zbl 0333.35021 · doi:10.1137/1018076
[10]E. C. Titchmarsh, Eigenfunctions Expansions (Part I, Oxford, 1962).