Localized Coherent Structures and Patterns Formation in Collective Models of Beam Motion

We present applications of variational -- wavelet approach to three different models of nonlinear beam motions with underlying collective behaviour: Vlasov-Maxwell-Poisson systems, envelope dynamics, beam-beam model. We have the representation for dynamical variables as a multiresolution (multiscales) expansion via high-localized nonlinear eigenmodes in the base of compactly supported wavelet bases. Numerical modelling demonstrates formation of coherent structures and stable patterns.