BLOW-UP PHENOMENA AND TRAVELLING WAVE SOLUTIONS TO THE PERIODIC INTEGRABLE DISPERSIVE HUNTER-SAXTON EQUATION

被引：9
作者：
Li, Min [1 ]
Yin, Zhaoyang [1 ,2 ]
机构：
[1] Sun Yat Sen Univ, Dept Math, Guangzhou 510275, Guangdong, Peoples R China
[2] Macau Univ Sci & Technol, Fac Informat Technol, Macau, Peoples R China
来源：
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS | 2017年 / 37卷 / 12期
关键词：
An integrable dispersive Hunter-Saxton equation; the Kato method; Blow-up; travelling wave solutions; the sinh-Gordon equation; CAMASSA-HOLM EQUATION; SHALLOW-WATER EQUATION; EXTREME STOKES WAVES; WELL-POSEDNESS; PARTICLE TRAJECTORIES; GORDON EQUATIONS; OSTROVSKY EQUATION; WEAK SOLUTIONS; SINE-GORDON; SHORT-PULSE;
D O I：
10.3934/dcds.2017280
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper, we mainly study the Cauchy problem of an integrable dispersive Hunter-Saxton equation in periodic domain. Firstly, we establish local well-posedness of the Cauchy problem of the equation in H-s(S),s > 3/2, by applying the Kato method. Secondly, by using some conservative quantities, we give a precise blow-up criterion and a blow-up result of strong solutions to the equation. Finally, based on a sign-preserve property, we transform the original equation into the sinh-Gordon equation. By using the travelling wave solutions of the sinh-Gordon equation and a period stretch between these two equations, we get the travelling wave solutions of the original equation.
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页码：6471 / 6485
页数：15
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