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Asymptotic behaviour of solutions of the Korteweg-de Vries equation

✍ Scribed by G. Scharf; W.F. Wreszinski

Publisher
Elsevier Science
Year
1985
Tongue
English
Weight
966 KB
Volume
162
Category
Article
ISSN
0003-4916

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✦ Synopsis

A rigorous proof that any solution of the Kortewegde Vries equation with smooth initial data decaying sufliciently fast at infinity tends as t --$ kcci to a pure N-soliton solution at a spatially uniform rate of 1 II-'E is provided. It is also proved that the solitonless solutions have a spatially uniform decay rate of ItI 2,'3, i.e., faster than the solutions of the corresponding linear equation. Some possible implications for scattering theory are discussed. $I 1985 Academx Press, Inc.

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