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Communications in Mathematical Physics

, Volume 133, Issue 1, pp 119–146 | Cite as

Multichannel nonlinear scattering for nonintegrable equations

  • A. Soffer
  • M. I. Weinstein
Article

Abstract

We consider a class of nonlinear Schrödinger equations (conservative and dispersive systems) with localized and dispersive solutions. We obtain a class of initial conditions, for which the asymptotic behavior (t→±∞) of solutions is given by a linear combination of nonlinear bound state (time periodic and spatially localized solution) of the equation and a purely dispersive part (decaying to zero with time at the free dispersion rate). We also obtain a result ofasymptotic stability type: given data near a nonlinear bound state of the system, there is a nonlinear bound state of nearby energy and phase, such that the difference between the solution (adjusted by a phase) and the latter disperses to zero. It turns out that in general, the time-period (and energy) of the localized part is different fort→+∞ from that fort→−∞. Moreover the solution acquires an extra constant asymptotic phasee iy ±.

Keywords

Neural Network Statistical Physic Linear Combination Complex System Asymptotic Behavior 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag 1990

Authors and Affiliations

  • A. Soffer
    • 1
  • M. I. Weinstein
    • 2
  1. 1.Department of MathematicsPrinceton UniversityPrincetonUSA
  2. 2.Department of MathematicsUniversity of MichiganAnn ArborUSA

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