Fedorova A.N., Zeitlin M.G.

NONLINEAR MOTION IN ELECTROMAGNETIC FIELDS VIA MULTISCALE EXPANSIONS

We consider a number of dynamical problems which are described by the systems of ordinary or partial differential equations with polynomial or rational nonlinearities and with or without some constraints. We consider different variational--wavelet approaches for constructing explicit solutions of these problems. We have the solutions as a multiresolution expansion in the base of compactly supported wavelets or wavelet packet bases. In the general case we consider biorthogonal wavelet expansions and corresponding variational approach. Our solutions are parameterized by solutions of reduced algebraical problems. We consider applications of our general constructions to a number of nonlinear beam dynamics and accelerator physics problems. We represent the solutions via exact multiscale nonlinear (eigen)mode expansions. The localization is the best both in initial space and in corresponding Fourier space representation or in phase space. We can compare the contribution to the energy spectrum from each level of resolution or from each scale of underlying scale of spaces. |