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

2002/10/01 by JÜRGEN PÖSCHEL · 2 citations

paper · doi:10.1017/s0143385702001086

Abstract

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.

Cited by

• On the existence of full dimensional KAM tori for 1D periodic nonlinear Schrödinger equation
• Invariant sets through resonant normal form for infinite dimensional holomorphic vector fields

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