The Korteweg-de Vries equation at regularity

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• 作者：Tristan Buckmaster^a ; ^{tristan.buckmaster@gmail.com" class="auth_mail" title="E-mail the corresponding author} ; Herbert Koch^b ; ^{koch@math.uni-bonn.de" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Korteweg&ndash ; de Vries equation ; Stability of solitons ; Miura map
• 刊名：Annales de l'Institut Henri Poincare (C) Non Linear Analysis
• 出版年：2015
• 出版时间：September-October 2015
• 年：2015
• 卷：32
• 期：5
• 页码：1071-1098
• 全文大小：476 K

文摘

In this paper we will prove the existence of weak solutions to the Korteweg–de Vries initial value problem on the real line with H⁻¹$H^{-1}$ initial data; moreover, we will study the problem of orbital and asymptotic H^s$H^s$ stability of solitons for integers s≥−1$s\ge -1$; finally, we will also prove new a priori H⁻¹$H^{-1}$ bound for solutions to the Korteweg–de Vries equation. The paper will utilise the Miura transformation to link the Korteweg–de Vries equation to the modified Korteweg–de Vries equation.