Stable manifolds for all monic supercritical NLS in one dimension

Abstract

We show that all supercritical monic focusing NLS in one space dimension exhibit asymptotic stability of perturbed standing waves provided the perturbations are chosen on a small hypersuface in a suitable space.

81 pages

References in corpus (5)

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• Global Strichartz estimates for nontrapping perturbations of the Laplacian
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Cited by in corpus (8)

• Stable directions for small nonlinear Dirac standing waves
• On the asymptotic stability of bound states in 2D cubic Schroedinger equation
• A Centre-Stable Manifold for the Focussing Cubic NLS in $R^{1+3}$
• A Critical Centre-Stable Manifold for the Cubic Focusing Schroedinger Equation in Three Dimensions
• Spectral Theory and Nonlinear PDE: a Survey
• Dispersive estimates for Schroedinger operators: A survey
• A Critical Centre-Stable Manifold for Schroedinger's Equation in R^3
• Non-dispersive vanishing and blow up at infinity for the energy critical nonlinear Schrödinger equation in R^3