### Elena Kartashova

Research Institute for Symbolic Computation, Johannes Kepler Universitaet, Linz

### Nonlinear resonance analysis as a base for novel numerical models

**Wednesday 17th March 14:05-14:55pm,
New Law School Seminar 030 (Building F10). **
Nonlinear Resonance Analysis (NRA) is a natural next step after Fourier analysis developed for linear PDEs. The main subject of NRA is evolutionary nonlinear PDEs, possessing resonant solutions. Importance of NRA is due to its wide application area -- from climate predictability to cancer diagnostic to breaking of the wing of an aircraft.

In my talk I plan to give a brief overview of the methods and results available in NRA, and illustrate it with some examples from fluid mechanics. In particular, it will be shown how
1) to use a general method of q-class decomposition for computing resonant modes for a variety of physically relevant dispersion functions;
2) to construct NR-reduced models for numerical simulations basing on the resonance clustering; theoretical comparision with Galerkin-like models will be made and illustrated by the results of some numerical simulations with nonlinear PDE.
3) to employ NR-reduced models for interpreting of real-life phenomena (in the Earth`s atmosphere) and results of laboratory experiments with water tanks.

A short presentation of the software available in this area will be given.