On the variational structure of breather solutions I: Sine-Gordon equation

被引:22
作者
Alejo, Miguel A. [1 ]
Munoz, Claudio [2 ,3 ]
Palacios, Jose M. [3 ]
机构
[1] Univ Fed Santa Catarina, Dept Matemat, Florianopolis, SC, Brazil
[2] CNRS, Paris, France
[3] Univ Chile, Dept Ingn Matemat DIM, Santiago, Chile
关键词
Sine-Gordon equation; Breather; Stability; ORBITAL STABILITY; SOLITONS; NLS;
D O I
10.1016/j.jmaa.2017.04.056
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
In this paper we describe stability properties of the Sine-Gordon breather solution. These properties are first described by suitable variational elliptic equations, which also implies that the stability problem reduces in some sense to (i) the study of the spectrum of explicit linear systems, and (ii) the understanding of how bad directions (if any) can be controlled using low regularity conservation laws. Then we discuss spectral properties of a fourth-order linear matrix system. Using numerical methods, we confirm that all spectral assumptions leading to the H-2 x H-1 stability of SG breathers are numerically satisfied, even in the ultra-relativistic, singular regime. (C) 2017 Elsevier Inc. All rights reserved.
引用
收藏
页码:1111 / 1138
页数:28
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