Abstract
We prove unique continuation properties for solutions of the evolution Schrödinger 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 Schrödinger equations.
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Communicated by P. Constantin
The first and fourth authors are supported by MEC grant, MTM2004-03029.
The second and third authors by NSF grants DMS-0456583 and DMS-0456833 respectively.
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Escauriaza, L., Kenig, C.E., Ponce, G. et al. Unique Continuation for Schrödinger Evolutions, with Applications to Profiles of Concentration and Traveling Waves. Commun. Math. Phys. 305, 487–512 (2011). https://doi.org/10.1007/s00220-011-1256-3
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DOI: https://doi.org/10.1007/s00220-011-1256-3