Dynamic of threshold solutions for energy-critical NLS

2007/10/31 by Thomas Duyckaerts, Duyckaerts, Thomas, Merle, Frank · 4 citations
Mathematics · Engineering · #Advanced Mathematical Physics Problems #Stability and Controllability of Differential Equations

paper · doi:10.48550/arxiv.0710.5915

Abstract

We consider the radial energy-critical non-linear focusing Schrödinger equation in dimension N=3,4,5. An explicit stationnary solution, W, of this equation is known. In a previous work by C. Carlos and F. Merle, the energy E(W) has been shown to be a threshold for the dynamical behavior of solutions of the equation. In the present article, we study the dynamics at the critical level E(u)=E(W) and classify the corresponding solutions. This gives in particular a dynamical characterization of W.

Citations

• Existence of solitary waves in higher dimensions

Cited by

• Dynamics of the Energy-Critical Nonlinear Schrödinger System in \mathbb R⁴
• Finite-mass soliton-type rigidity and four-channel reduction for the three-dimensional nonradial focusing energy-critical nonlinear Schrödinger equation
• Scattering norm estimate near the threshold for the energy-subcritical NLS
• Dynamics of subcritical threshold solutions for the 4d energy-critical NLS

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