Blow-up phenomena and peakons for the b-family of FORQ/MCH equations

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:266

Article

Yang, Shaojie¹  Qiao, Zhijun²  Xu, Tianzhou¹ 

[1] Beijing Inst Technol, Sch Math & Stat, Beijing 100081, Peoples R China

[2] Univ Texas Rio Grande Valley, Sch Math & Stat Sci, Edinburg, TX 78539 USA

关键词: b-family of FORQ/MCH equations;    Local well-posedness;    Blow-up;    Peakons;   

DOI  :  10.1016/j.jde.2018.11.018

来源: Elsevier

【 摘 要 】

This paper is devoted to studying the modified b-family of equations with cubic nonlinearity, called the b-family of FORQ/MCH equations, which includes the cubic Camassa-Holm equation (also called Fokas-Olver-Rosenau-Qiao equation) as a special case. We first study the local well-posedness for the Cauchy problem of the equation, and then make good use of fine structure of the equation, we derive the precise blow-up scenario and a new blow-up result with respect to initial data. Finally, peakon solutions are derived. (C) 2018 Elsevier Inc. All rights reserved.

【 授权许可】

Free