Rarefaction waves of the Korteweg-de Vries equation via nonlinear steepest descent

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• 作者：Kyrylo Andreiev^a ; ^{kijjeue@gmail.com" class="auth_mail" title="E-mail the corresponding author} ; Iryna Egorova^a ; ^{iraegorova@gmail.com" class="auth_mail" title="E-mail the corresponding author} ; Till Luc Lange^b ; Gerald Teschl^b ; ^c ; ^{Gerald.Teschl@univie.ac.at" class="auth_mail" title="E-mail the corresponding author} ;
• 关键词：primary ; 37K40 ; 35Q53 ; secondary ; 37K45 ; 35Q15
• 刊名：Journal of Differential Equations
• 出版年：2016
• 出版时间：15 November 2016
• 年：2016
• 卷：261
• 期：10
• 页码：5371-5410
• 全文大小：690 K

文摘

We apply the method of nonlinear steepest descent to compute the long-time asymptotics of the Korteweg–de Vries equation with steplike initial data leading to a rarefaction wave. In addition to the leading asymptotic we also compute the next term in the asymptotic expansion of the rarefaction wave, which was not known before.