Introduction to the theory of nonlinear resonances

Computational and Applied Mathematics Colloquium

Meeting Details

For more information about this meeting, contact Kris Jenssen, Hope Shaffer, Yuxi Zheng.

Speaker: Elena Kartashova, Johannes Kepler University, Linz, Austria

Abstract: Nonlinear resonances are ubiquitous in physics. Famous experiments of Tesla show how disastrous resonances can be: he studied experimentally vibrations of an iron column which ran downward into the foundation of the building, and caused sort of a small earthquake in Manhattan, with smashed windows and swayed buildings. Nonlinear resonances appear in hydrodynamics, mechanics, astronomy, etc. etc. - and usually they are studied in the frame of one specific application area. In this talk we present some general methods (i.e. independent of an application area) from the theory of nonlinear resonances, which allow us to 1) find solutions of kinematic resonance conditions; 2) write out explicitly dynamical systems describing resonantly interacting waves; 3) solve these dynamical systems, whether analytically or numerically. We will show how these methods work, taking atmospheric planetary waves as our main example.

Room Reservation Information

Room Number: 106 McAllister

Date: 11/21/2008

Time: 3:35pm - 4:25pm