奇摄动下正弦-戈登扭结的渐近稳定性

IF 2.3 1区 数学 Q1 MATHEMATICS
Jonas Luhrmann, Wilhelm Schlag
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引用次数: 0

摘要

我们建立了在加权Sobolev范数中足够小的奇扰动下正弦-戈登扭结的渐近稳定性。我们的方法是微扰的,不依赖于正弦-戈登模型的完全可积性。我们证明的关键要素是正弦-戈登扭结周围线性化算子的一个特殊的因式分解性质,Klein-Gordon方程中摄动的二次非线性所表现出的一个显著的非共振性质,以及一个变系数二次范式。我们强调对奇摄动的限制不能绕过线性化算子的奇阈值共振的影响。我们的技术已应用于几个著名的不可积模型的孤子稳定性问题,例如,对于ϕ4模型的结的渐近稳定性问题,以及在一维空间中聚焦二次和三次Klein-Gordon方程的孤子的条件渐近稳定性问题。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Asymptotic stability of the sine-Gordon kink under odd perturbations
We establish the asymptotic stability of the sine-Gordon kink under odd perturbations that are sufficiently small in a weighted Sobolev norm. Our approach is perturbative and does not rely on the complete integrability of the sine-Gordon model. Key elements of our proof are a specific factorization property of the linearized operator around the sine-Gordon kink, a remarkable nonresonance property exhibited by the quadratic nonlinearity in the Klein–Gordon equation for the perturbation, and a variable coefficient quadratic normal form. We emphasize that the restriction to odd perturbations does not bypass the effects of the odd threshold resonance of the linearized operator. Our techniques have applications to soliton stability questions for several well-known nonintegrable models, for instance, to the asymptotic stability problem for the kink of the ϕ4 model as well as to the conditional asymptotic stability problem for the solitons of the focusing quadratic and cubic Klein–Gordon equations in one space dimension.
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来源期刊
CiteScore
3.40
自引率
0.00%
发文量
61
审稿时长
6-12 weeks
期刊介绍: Information not localized
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