Our analysis is based on variational--wavelet approach to rational (in dynamical variables) approximation with possible related constraint equations. It allows to control contribution from each scale of underlying multiscales and represent solutions via multiscale nonlinear eigenmodes expansions. Our approach provides the best convergence properties of the corresponding exact representations and does not use perturbations or/and linearization procedures. Reduced algebraical structure provides the control of stability/unstability scenario of evolution in parameter space on pure algebraical level.
1. Proc. EPAC02, pp.1323,1344,1434,1482,1595, Paris, 2002 or arXiv preprints, physics/0206053,0206052,0206051,0206050,0206049,0206054; nlin.PS/0206024
Antonina N. Fedorova, Michael G. Zeitlin
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