Stable manifolds for an orbitally unstable NLS
Wilhelm Schlag
TL;DR
This paper constructs a local Lipschitz graph around a soliton in the cubic focusing NLS in three dimensions, demonstrating global existence, asymptotic stability, and scattering of solutions near the soliton.
Contribution
It introduces a new method to analyze the stability and scattering of solitons in 3D cubic focusing NLS by constructing a Lipschitz graph around the soliton.
Findings
Global solutions exist near the soliton.
Asymptotic stability of the soliton is established.
Solutions scatter to linear solutions at infinity.
Abstract
We construct a local Lipschitz graph around a soliton of the cubic focusing NLS in three dimensions on which global solutions exist, and asymptotic stability as well as scattering holds.
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Taxonomy
TopicsAdvanced Mathematical Physics Problems · Nonlinear Waves and Solitons · Nonlinear Photonic Systems