# Abstracts

## XX International Linac Conference

## MOE15 (Poster)

**Presenter: **Antonina Fedorova (IPME RAS)

** email: **anton@math.ipme.ru

**Status: **Complete

**FullText: **
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**Eprint:** physics/0008200
# Multiresolution Representations for Solutions of Vlasov-
Maxwell-Poisson Equations

A. FEDOROVA*, M. ZEITLIN (IPME RAS)

We present applications of methods from nonlinear(local) Fourier analysis
or wavelet analysis to a number of nonlinear accelerator physics problems. This is
continuation of our results which were presented on PAC97/99, EPAC98/00[1]. Our
approach is based on methods provided possibility to work with well-localized in
phase space bases, which gives the most sparse representation for the general type of
operators and good convergence properties[2]. Consideration of Vlasov-Maxwell models
is based on a number of anzatzes, which reduce initial problems to a number of
dynamical systems and on variational-wavelet approach to polynomial/rational[3]
approximations for nonlinear dynamics. This approach allows us to control
contribution to dynamical behaviour from each scale of underlying multiresolution
expansion.

1.Nonlinear Accelerator Problems via Wavelets, parts 1-8, Proc.PAC99,
IEEE, 1614,1617,1620,2900,2903,2906,2909,2912. 2.American Institute of Physics, Conf.
Proc., vol. 468, Nonlinear and Collective Phenomena in Beam Physics, pp. 48-68,
69-93, 1999 3.Variational-Wavelet Approach to RMS Envelope Equations Los Alamos,
physics/0003095

*e-mail: anton@math.ipme.ru, http://www.ipme.ru/zeitlin.html

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