简并KdV和NLS模型的紧子波的稳定性

IF 0.9 4区数学 Q3 MATHEMATICS, APPLIED

Quarterly of Applied Mathematics Pub Date : 2021-10-06 DOI:10.1090/qam/1616

S. Hakkaev, A. Ramadan, A. Stefanov

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引用次数: 0

摘要

本文考虑一维空间中的退化半线性Schrödinger方程和Korteweg-de Vries方程。我们构造了两种模型的特殊解，即NLS驻波解和行波解，它们具有紧致的支撑和紧致。我们证明了这些紧子是相应偏微分方程和适当变分问题的唯一钟形解。对于所有的p p值，我们提供了这种波的完整的谱特征。也就是说，我们证明了所有的波在2>p≤8 2>p \leq 8时都是光谱稳定的，而在p>8 p>8时发生单模不稳定。这扩展了Germain, Harrop-Griffiths和Marzuola [Quart]之前的工作。苹果。数学，78 (2020)，pp. 1-32]，他们之前已经建立了一些特定波的轨道稳定性，在p bbb80 p>8范围内。

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On the stability of the compacton waves for the degenerate KdV and NLS models

In this paper, we consider the degenerate semi-linear Schrödinger and Korteweg-de Vries equations in one spatial dimension. We construct special solutions of the two models, namely standing wave solutions of NLS and traveling waves, which turn out to have compact support, compactons. We show that the compactons are unique bell-shaped solutions of the corresponding PDEs and for appropriate variational problems as well. We provide a complete spectral characterization of such waves, for all values of p p . Namely, we show that all waves are spectrally stable for 2 > p ≤ 8 2>p\leq 8 , while a single mode instability occurs for p > 8 p>8 . This extends previous work of Germain, Harrop-Griffiths and Marzuola [Quart. Appl. Math. 78 (2020), pp. 1–32] who have previously established orbital stability for some specific waves, in the range p > 8 p>8 .

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来源期刊

Quarterly of Applied Mathematics 数学-应用数学

CiteScore

1.90

自引率

12.50%

发文量

审稿时长

>12 weeks

期刊介绍： The Quarterly of Applied Mathematics contains original papers in applied mathematics which have a close connection with applications. An author index appears in the last issue of each volume. This journal, published quarterly by Brown University with articles electronically published individually before appearing in an issue, is distributed by the American Mathematical Society (AMS). In order to take advantage of some features offered for this journal, users will occasionally be linked to pages on the AMS website.