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The Similarity Solution for the Korteweg-de Vries Equation and the Related Painlevé Transcendent

R. R. Rosales
Proceedings of the Royal Society of London. Series A, Mathematical and Physical Sciences
Vol. 361, No. 1706 (Jun. 1, 1978), pp. 265-275
Published by: Royal Society
Stable URL: http://www.jstor.org/stable/79575
Page Count: 11
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The Similarity Solution for the Korteweg-de Vries Equation and the Related Painlevé Transcendent
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Abstract

The second Painlevé transcendent is treated in conjunction with the similarity solutions of the Korteweg-de Vries equation and the modified Korteweg-de Vries equation. Asymptotic expansions and numerical solutions are presented; the main result is the existence of a critical value for the amplitude parameter above which the relevant solutions become singular.

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