On the stability analysis of periodic sine-Gordon traveling waves

被引：30

作者：

Jones, Christopher K. R. T. ^{[1
]}

Marangell, Robert ^{[2
]}

Miller, Peter D. ^{[3
]}

Plaza, Ramon G. ^{[4
]}

机构：

[1] Univ N Carolina, Dept Math, Chapel Hill, NC 27599 USA

[2] Univ Sydney, Sch Math & Stat F07, Sydney, NSW 2006, Australia

[3] Univ Michigan, Dept Math, Ann Arbor, MI 48109 USA

[4] Univ Nacl Autonoma Mexico, Dept Matemat & Mecan, IIMAS FENOMEC, Mexico City 01000, DF, Mexico

来源：

PHYSICA D-NONLINEAR PHENOMENA | 2013年 / 251卷

基金：

澳大利亚研究理事会; 美国国家科学基金会;

关键词：

Nonlinear waves; Partial differential equations; Periodic traveling waves; Sine-Gordon equation; Spectral analysis; Stability; DE-VRIES EQUATION; MODEL;

D O I：

10.1016/j.physd.2013.02.003

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We study the spectral stability properties of periodic traveling waves in the sine-Gordon equation, including waves of both subluminal and superluminal propagation velocities as well as waves of both librational and rotational types. We prove that only subluminal rotational waves are spectrally stable and establish exponential instability in the other three cases. Our proof corrects a frequently cited one given by Scott (1969) [12]. (C) 2013 Elsevier B.V. All rights reserved.

引用

页码：63 / 74

页数：12

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