Blow-up phenomena for an integrable two-component Camassa-Holm system with cubic nonlinearity and peakon solutions

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• 作者：Kai Yan^a ; ^{yankai419@163.com" class="auth_mail" title="E-mail the corresponding author} ; Zhijun Qiao^b ; ^{qiao@utpa.edu" class="auth_mail" title="E-mail the corresponding author} ; Yufeng Zhang^c ; ^{zhangmath@126.com" class="auth_mail" title="E-mail the corresponding author}
• 关键词：35G25 ; 35L05
• 刊名：Journal of Differential Equations
• 出版年：2015
• 出版时间：5 December 2015
• 年：2015
• 卷：259
• 期：11
• 页码：6644-6671
• 全文大小：387 K

文摘

This paper is devoted to an integrable two-component Camassa–Holm system with cubic nonlinearity, which includes the cubic Camassa–Holm equation (also called the Fokas–Olver–Rosenau–Qiao equation) as a special case. The one peaked solitons (peakons) and two peakon solutions are described in an explicit formula. Then, the local well-posedness for the Cauchy problem of the system is studied. Moreover, we target at the precise blow-up scenario for strong solutions to the system, and establish a new blow-up result with respect to the initial data.