Communications in Mathematical Physics

, Volume 250, Issue 3, pp 613–642

Solitary Wave Dynamics in an External Potential

  • J. Fröhlich
  • S. Gustafson
  • B.L.G. Jonsson
  • I.M. Sigal
Article

DOI: 10.1007/s00220-004-1128-1

Cite this article as:
Fröhlich, J., Gustafson, S., Jonsson, B. et al. Commun. Math. Phys. (2004) 250: 613. doi:10.1007/s00220-004-1128-1

Abstract

We study the behavior of solitary-wave solutions of some generalized nonlinear Schrödinger equations with an external potential. The equations have the feature that in the absence of the external potential, they have solutions describing inertial motions of stable solitary waves. We consider solutions of the equations with a non-vanishing external potential corresponding to initial conditions close to one of these solitary wave solutions and show that, over a large interval of time, they describe a solitary wave whose center of mass motion is a solution of Newton’s equations of motion for a point particle in the given external potential, up to small corrections corresponding to radiation damping.

Copyright information

© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  • J. Fröhlich
    • 1
  • S. Gustafson
    • 2
  • B.L.G. Jonsson
    • 3
    • 4
    • 5
  • I.M. Sigal
    • 4
    • 6
  1. 1.Institute für Theoretische PhysikETH HönggerbergZürichSwitzerland
  2. 2.Department of MathematicsUniversity of British ColumbiaVancouverCanada
  3. 3.The Fields Institute for Research in Mathematical SciencesTorontoCanada
  4. 4.Department of MathematicsUniversity of TorontoTorontoCanada
  5. 5.The AlfvénlaboratoryRoyal Institute of TechnologyStockholmSweden
  6. 6.Department of MathematicsUniversity of Notre DameNotre DameUSA