Abstract:
Asymptotic formulae representing for large time the solution of the Cauchy problem are obtained for the generalized Korteweg–de Vries equation with non-linear term to an integer power greater than three. The error terms are estimated. The method is based on the perturbation theory with respect to a parameter characterizing the smallness of the initial data.
Citation:
P. I. Naumkin, I. A. Shishmarev, “Asymptotic behaviour as t→∞ of the solutions of the generalized Korteweg–de Vries equation”, Sb. Math., 187:5 (1996), 693–733
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\by P.~I.~Naumkin, I.~A.~Shishmarev
\paper Asymptotic behaviour as $t\to \infty$ of the~solutions of the~generalized Korteweg--de~Vries equation
\jour Sb. Math.
\yr 1996
\vol 187
\issue 5
\pages 693--733
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Linking options:
https://www.mathnet.ru/eng/sm129
https://doi.org/10.1070/SM1996v187n05ABEH000129
https://www.mathnet.ru/eng/sm/v187/i5/p71
This publication is cited in the following 4 articles:
Hayashi N. Naumkin P., “On the Modified Korteweg-de Vries Equation”, Math. Phys. Anal. Geom., 4:3 (2001), 197–227
Hayashi, N, “Large time behavior of solutions for the modified Korteweg-de Vries equation”, International Mathematics Research Notices, 1999, no. 8, 395
Hayashi N., Naumkin P., “On the modified Korteweg de Vries equation”, International Seminar Day on Diffraction, Proceedings, 1999, 146–156
Hayashi, N, “Large time asymptotics of solutions to the generalized Korteweg-de Vries equation”, Journal of Functional Analysis, 159:1 (1998), 110
Citation in format AMSBIB
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