Abstract.
We consider the energy-critical non-linear focusing Schrödinger equation in dimension N = 3, 4, 5. An explicit stationary solution, W, of this equation is known. In [KeM], 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.
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This work was partially supported by the French ANR Grant ONDNONLIN.
Received: March 2007, Accepted: October 2007
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Duyckaerts, T., Merle, F. Dynamic of Threshold Solutions for Energy-Critical NlS. GAFA Geom. funct. anal. 18, 1787–1840 (2009). https://doi.org/10.1007/s00039-009-0707-x
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DOI: https://doi.org/10.1007/s00039-009-0707-x