### Abstract

Original language | English |
---|---|

Pages (from-to) | 427-456 |

Number of pages | 30 |

Journal | Advances in Differential Equations |

Volume | 13 |

Issue number | 5-6 |

Publication status | Published - 2008 |

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*Advances in Differential Equations*,

*13*(5-6), 427-456.

**Exponential averaging under rapid quasiperiodic forcing.** / Matthies, Karsten.

Research output: Contribution to journal › Article

*Advances in Differential Equations*, vol. 13, no. 5-6, pp. 427-456.

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TY - JOUR

T1 - Exponential averaging under rapid quasiperiodic forcing

AU - Matthies, Karsten

PY - 2008

Y1 - 2008

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=84894055260&partnerID=8YFLogxK

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

M3 - Article

VL - 13

SP - 427

EP - 456

JO - Advances in Differential Equations

JF - Advances in Differential Equations

SN - 1079-9389

IS - 5-6

ER -