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Unique Continuation for Schrödinger Evolutions, with Applications to Profiles of Concentration and Traveling Waves

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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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Authors and Affiliations

  1. Dpto. de Matemáticas, UPV/EHU, Apto. 644, 48080, Bilbao, Spain

    L. Escauriaza & L. Vega

  2. Department of Mathematics, University of Chicago, Chicago, IL, 60637, USA

    C. E. Kenig

  3. Department of Mathematics, University of California, Santa Barbara, CA, 93106, USA

    G. Ponce

Authors
  1. L. Escauriaza
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  2. C. E. Kenig
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  3. G. Ponce
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  4. L. Vega
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Corresponding author

Correspondence to G. Ponce.

Additional information

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

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