This article is cited in 3 papers

Renormalization in the Cauchy problem for the Korteweg–de Vries equation

S. V. Zakharov

Institute of Mathematics and Mechanics, Ural Division, RAS, Yekaterinburg, Russia

Abstract: We consider the Cauchy problem for the Korteweg–de Vries equation with a small parameter at the highest derivative and a large gradient of the initial function. We construct an asymptotic solution of this problem by the renormalization method.

Keywords: Korteweg–de Vries equation, Cauchy problem, asymptotic solution, renormalization.

Received: 29.10.2012

DOI: 10.4213/tmf8437

 English version: Theoretical and Mathematical Physics, 2013, 175:2, 592–595

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