Unique Continuation for Schr\"odinger Evolutions, with applications to profiles of concentration and traveling waves
L. Escauriaza, C. E. Kenig, G. Ponce, and L. Vega
TL;DR
This paper establishes unique continuation properties for solutions to the time-dependent Schr"odinger equation and explores implications for blow-up solution profiles and traveling wave structures.
Contribution
It introduces new unique continuation results for Schr"odinger evolutions with time-dependent potentials, impacting understanding of solution concentration and wave profiles.
Findings
Unique continuation properties proven for Schr"odinger solutions with time-dependent potentials.
Results on possible concentration profiles of blow-up solutions.
Analysis of traveling wave solution profiles.
Abstract
We prove unique continuation properties for solutions of the evolution Schr\"odinger equation with time dependent potentials. As an application of our method we also obtain results concerning the possible concentration profiles of blow up solutions and the possible profiles of the traveling waves solutions of semi-linear Schr\"odinger equations.
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