Exponential averaging under rapid quasiperiodic forcing

Reference:

Matthies, K., 2008. Exponential averaging under rapid quasiperiodic forcing. Advances in Differential Equations, 13 (5-6), pp. 427-456.

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Official URL:

http://projecteuclid.org/euclid.ade/1355867341

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.

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