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Colliding Solitons for the Nonlinear Schrödinger Equation

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Abstract

We study the collision of two fast solitons for the nonlinear Schrödinger equation in the presence of a slowly varying external potential. For a high initial relative speed ||v|| of the solitons, we show that, up to times of order ||v|| after the collision, the solitons preserve their shape (in L 2-norm), and the dynamics of the centers of mass of the solitons is approximately determined by the external potential, plus error terms due to radiation damping and the extended nature of the solitons. We remark on how to obtain longer time scales under stronger assumptions on the initial condition and the external potential.

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Authors and Affiliations

  1. Department of Mathematics, University of Toronto, Toronto, M5S 2E4, Ontario, Canada

    W. K. Abou Salem & I. M. Sigal

  2. Institute for Theoretical Physics, ETH Zürich, Zürich, CH, 8093, Switzerland

    J. Fröhlich

  3. Institut des Hautes Études Scientifique, F-91440, Bures-sur-Yvette, France

    J. Fröhlich

Authors
  1. W. K. Abou Salem
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  2. J. Fröhlich
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  3. I. M. Sigal
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Correspondence to W. K. Abou Salem.

Additional information

Communicated by P. Constantin

Supported in part by NSERC grant NA 7901.

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Abou Salem, W.K., Fröhlich, J. & Sigal, I.M. Colliding Solitons for the Nonlinear Schrödinger Equation. Commun. Math. Phys. 291, 151–176 (2009). https://doi.org/10.1007/s00220-009-0871-8

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  • DOI: https://doi.org/10.1007/s00220-009-0871-8

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