Periodic and solitary waves in a Korteweg-de Vries equation with delay

被引：0
|
作者：
Qiao, Qi [1 ]
Yan, Shuling [2 ]
Zhang, Xiang [3 ,4 ]
机构：
[1] Suzhou Univ Sci & Technol, Sch Math Sci, Suzhou 215009, Jiangsu, Peoples R China
[2] Jiangsu Normal Univ, Sch Math & Stat, Xuzhou 221116, Jiangsu, Peoples R China
[3] Shanghai Jiao Tong Univ, Sch Math Sci, MOE LSC, Shanghai 200240, Peoples R China
[4] Shanghai Jiao Tong Univ, CMA Shanghai, Shanghai 200240, Peoples R China
来源：
PROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH SECTION A-MATHEMATICS | 2023年
基金：
国家重点研发计划;
关键词：
Korteweg-de Vries equation with delay; periodic wave; solitary wave; geometric singular perturbation theory; Abelian integral; SINGULAR PERTURBATION-THEORY; TRAVELING-WAVES; EXISTENCE; STABILITY; KDV; DYNAMICS;
D O I：
10.1017/prm.2023.88
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
For a perturbed generalized Korteweg-de Vries equation with a distributed delay, we prove the existence of both periodic and solitary waves by using the geometric singular perturbation theory and the Melnikov method. We further obtain monotonicity and boundedness of the speed of the periodic wave with respect to the total energy of the unperturbed system. Finally, we establish a relation between the wave speed and the wavelength.
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收藏
页数：23
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