Exponential averaging under rapid quasiperiodic forcing

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Abstract

We derive estimates on the magnitude of the interaction between a wide class of analytic partial differential equations and a high-frequency quasiperiodic oscillator. Assuming high regularity of initial conditions, the equations are transformed to an uncoupled system of an infinite dimensional dynamical system and a linear quasiperiodic flow on a torus; up to coupling terms which are exponentially small in the smallest frequency of the oscillator. The main technique is based on a careful balance of similar results for ordinary differential equations by Sim´o, Galerkin approximations and high regularity of the initial conditions. Similar finite order estimates assuming less regularity are also provided. Examples include reaction-diffusion and nonlinear Schr¨odinger equations.
Original languageEnglish
Pages (from-to)427-456
Number of pages30
JournalAdvances in Differential Equations
Volume13
Issue number5-6
Publication statusPublished - 2008

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