Communications in Mathematical Physics

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

Multichannel nonlinear scattering for nonintegrable equations

  • A. Soffer
  • M. I. Weinstein


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 ±.


Neural Network Statistical Physic Linear Combination Complex System Asymptotic Behavior 
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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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