Stability of the standing waves for a class of coupled nonlinear Klein-Gordon equations

被引：0
作者：
Jian Zhang
Zai-hui Gan
Bo-ling Guo
机构：
[1] Sichuan Normal University,College of Mathematics and Software Science
[2] Institute of Applied Physics and Computational Mathematics,undefined
来源：
Acta Mathematicae Applicatae Sinica, English Series | 2010年 / 26卷
关键词：
Coupled nonlinear Klein-Gordon equations; Stability; Standing wave; Variational calculus; 35G25; 35L15; 35Q51;
D O I：
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学科分类号：
摘要：
This paper deals with the standing waves for a class of coupled nonlinear Klein-Gordon equations with space dimension N ≥ 3, 0 < p, q < 2 / N−2 and p + q < 4/N. By using the variational calculus and scaling argument, we establish the existence of standing waves with ground state, discuss the behavior of standing waves as a function of the frequency ω and give the sufficient conditions of the stability of the standing waves with the least energy for the equations under study.
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页码：427 / 442
页数：15
相关论文
共 25 条
[1]  
Berestycki H.(1983)Nonlinear scalar field equations I, II Arch. Rat. Mech. Anal. 82 313-375
[2]  
Lions P.L.(2001)Long time behavior for damped generalized coupled nonlinear wave equations. II. Unbounded domain Comm. Nonlinear Sci. Numerical Simulation 6 107-110
[3]  
Fang S.(2005)Instability of standing waves for Klein-Gondon-Zakharov equations with different propagation speeds in three space dimensions J. Math Anal. Appl. 307 219-231
[4]  
Guo B.(2006)Standing waves for a class of coupled nonlinear Klein-Gordon equations Acta Math Sci. 26 559-569
[5]  
Gan Z.(1996)Orbital stability of solitary waves of the long wave-shor wave resonance equations Comm Nonlinear Sci Nuuerical Simulation 1 37-42
[6]  
Zhang J.(2001)Existence of the periodic solution for the weakly damped Schrödinger-Boussinesq equation J. Math Anal. Appl. 262 453-472
[7]  
Gan Z.(2001)The behavior of attractors for damped Schrödinger-Boussinesq equation Comm. Nonlinear Sci. Nuuerical Simulation 6 54-60
[8]  
Zhang J.(1974)Instability and non-existence of global solutions to nonlinear wave equations of the form Trans. Amer. Math Soc. 92 1-21
[9]  
Guo B.(1995) = − Ann. Inst. Henri Poincaré 63 111-117
[10]  
Chen L.(1995) − Ann. Inst. Henri Poincaré 62 69-80
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