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

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:259

Article

Yan, Kai¹  Qiao, Zhijun²  Zhang, Yufeng³ 

[1] Huazhong Univ Sci & Technol, Sch Math & Stat, Wuhan 430074, Hubei, Peoples R China

[2] Univ Texas Pan Amer, Dept Math, Edinburg, TX 78541 USA

[3] China Univ Min & Technol, Coll Sci, Xuzhou 221116, Jiangsu, Peoples R China

关键词: Two-component Camassa-Holm system;    Cubic nonlinearity;    Fokas-Olver-Rosenau-Qiao equation;    Peakons;    Well-posedness;    Blow-up;   

DOI  :  10.1016/j.jde.2015.08.004

来源: Elsevier

【 摘 要 】

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. (C) 2015 Elsevier Inc. All rights reserved.

【 授权许可】

Free