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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
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Full Text: DOI
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. · Zbl 0063.02971
[3] E. Hille, Ordinary Differential Equations in the Complex Domain. New York: Wiley 1976. · Zbl 0343.34007
[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). · Zbl 0063.08184
[6] R. Rosales, The similarity solution for the Korteweg-de Vries equation and the related Painlevé transcendent. Preprint. · Zbl 0384.65041
[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); · Zbl 44.0382.02
[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). · Zbl 45.0478.02
[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). · Zbl 0099.05201