On the construction of almost periodic solutions for a nonlinear Schrödinger equation

@article{Pschel2002OnTC,
  title={On the construction of almost periodic solutions for a nonlinear Schr{\"o}dinger equation},
  author={J. P{\"o}schel},
  journal={Ergodic Theory and Dynamical Systems},
  year={2002},
  volume={22},
  pages={1537 - 1549}
}
  • J. Pöschel
  • Published 2002
  • Mathematics
  • Ergodic Theory and Dynamical Systems
We describe the construction of almost-periodic solutions for a particular Schrödinger equation on a finite x- interval, depending on some potential V. The construction proceeds by iterating a KAM theorem about the existence of quasi-periodic solutions for some partial differential equations. As a result, we find for ‘almost all’ potentials V uncountably many almost-periodic solutions accumulating at the zero solution. 
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