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

Published online by Cambridge University Press:  02 October 2002

JÜRGEN PÖSCHEL
JÜRGEN PÖSCHEL
Affiliation:
Mathematisches Institut A, Universität Stuttgart, Pfaffenwaldring 57, D-70569 Stuttgart, Germany (e-mail: poschel@mathematik.uni-stuttgart.de)
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Abstract

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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.

Information

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 22 , Issue 5 , October 2002, pp. 1537 - 1549
Copyright
© 2002 Cambridge University Press