Orbital stability of periodic standing waves of the coupled Klein-Gordon-Zakharov equations

被引:1
作者
Li, Qiuying [1 ]
Zheng, Xiaoxiao [2 ]
Wang, Zhenguo [3 ]
机构
[1] Huanghuai Univ, Sch Math & Stat, Zhumadian 463000, Peoples R China
[2] Qufu Normal Univ, Sch Math Sci, Qufu 273155, Peoples R China
[3] Taiyuan Univ, Dept Math, Taiyuan 030032, Peoples R China
来源
AIMS MATHEMATICS | 2023年 / 8卷 / 04期
基金
中国国家自然科学基金;
关键词
coupled Klein-Gordon-Zakharov equations; periodic standing waves; orbital stability; Floquet theory; Hamiltonian system; SOLITARY WAVES; INSTABILITY;
D O I
10.3934/math.2023430
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
This paper investigates the orbital stability of periodic standing waves for the following coupled Klein-Gordon-Zakharov equations {u(tt) - u(xx) + u + alpha uv +beta|u|(2)u = 0, v(tt) - v(xx) = (|u|(2))(xx), where alpha > 0 and beta are two real numbers and alpha > beta. Under some suitable conditions, we show the existence of a smooth curve positive standing wave solutions of dnoidal type with a fixed fundamental period L for the above equations. Further, we obtain the stability of the dnoidal waves for the coupled Klein-Gordon-Zakharov equations by applying the abstract stability theory and combining the detailed spectral analysis given by using Lame ' equation and Floquet theory. When period L -> infinity, dnoidal type will turn into sech-type in the sense of limit. In such case, we can obtain stability of sech-type standing waves. In particular, beta = 0 is advisable, we still can show the the stability of the dnoidal type and sech-type standing waves for the classical Klein-Gordon-Zakharov equations.
引用
收藏
页码:8560 / 8579
页数:20
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