ON A NEW TWO-COMPONENT b-FAMILY PEAKON SYSTEM WITH CUBIC NONLINEARITY

被引：6
|
作者：
Yan, Kai [1 ,2 ]
Qiao, Zhijun [3 ]
Zhang, Yufeng [4 ]
机构：
[1] Huazhong Univ Sci & Technol, Sch Math & Stat, Wuhan 430074, Hubei, Peoples R China
[2] Huazhong Univ Sci & Technol, Hubei Key Lab Engn Modeling & Sci Comp, Wuhan 430074, Hubei, Peoples R China
[3] Univ Texas Rio Grande Valley, Sch Math & Stat Sci, 1201 W Univ,Dr, Edinburg, TX 78539 USA
[4] China Univ Min & Technol, Coll Sci, Xuzhou 221116, Jiangsu, Peoples R China
来源：
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS | 2018年 / 38卷 / 11期
基金：
中国国家自然科学基金;
关键词：
Two-component b-family system; cubic nonlinearity; peakons; well-posedness; blow-up; global existence; asymptotic behaviors; Camassa-Holm equation; Degasperis-Procesi equation; Novikov equation; SHALLOW-WATER EQUATION; GLOBAL WEAK SOLUTIONS; CAMASSA-HOLM; CAUCHY-PROBLEM; INTEGRABLE EQUATION; WELL-POSEDNESS; WAVE-BREAKING; EXISTENCE; HIERARCHY;
D O I：
10.3934/dcds.2018239
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper, we propose a two-component b-family system with cubic nonlinearity and peaked solitons (peakons) solutions, which includes the celebrated Camassa-Holm equation, Degasperis-Procesi equation, Novikov equation and its two-component extension as special cases. Firstly, we study single peakon and multi-peakon solutions to the system. Then the local well-posedness for the Cauchy problem of the system is discussed. Furthermore, we derive the precise blow-up scenario and global existence for strong solutions to the two-component b-family system with cubic nonlinearity. Finally, we investigate the asymptotic behaviors of strong solutions at in finity within its lifespan provided the initial data decay exponentially and algebraically.
引用
收藏
页码：5415 / 5442
页数：28
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