Codimension One Threshold Manifold for the Critical gKdV Equation

被引：24

作者：

Martel, Yvan ^{[1
]}

Merle, Frank ^{[2
,3
]}

Nakanishi, Kenji ^{[4
]}

Raphael, Pierre ^{[5
]}

机构：

[1] Ecole Polytech, CMLS, CNRS, UMR7640, F-91128 Palaiseau, France

[2] Univ Cergy Pontoise, F-95302 Cergy Pontoise, France

[3] Inst Hautes Etud Sci, CNRS, AGM, UMR8088, F-95302 Cergy Pontoise, France

[4] Kyoto Univ, Dept Math, Kyoto 6068502, Japan

[5] Univ Nice Sophia Antipolis, Lab JA Dieudonne, CNRS, UMR7351, F-06108 Nice 02, France

来源：

COMMUNICATIONS IN MATHEMATICAL PHYSICS | 2016年 / 342卷 / 03期

关键词：

BLOW-UP SOLUTIONS; GLOBAL WELL-POSEDNESS; NONLINEAR SCHRODINGER; STABLE MANIFOLDS; SCATTERING; INSTABILITY; STABILITY; DYNAMICS; TIME;

D O I：

10.1007/s00220-015-2509-3

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

We construct the "threshold manifold" near the soliton for the mass critical gKdV equation, completing results obtained in Martel et al. (Acta Math 212:59-140, 2014, J Math Eur Soc 2015). In a neighborhood of the soliton, this C (1) manifold of codimension one separates solutions blowing up in finite time and solutions in the "exit regime". On the manifold, solutions are global in time and converge locally to a soliton. In particular, the soliton behavior is strongly unstable by blowup.

引用

页码：1075 / 1106

页数：32

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