Nonlinear Localized Coherent Spectrum of Beam-Beam Interactions

We consider modeling for strong-strong beam-beam interactions beyond preceding linearized/perturbative methods such as soft gaussian approximation or FMM (HFMM) etc. In our approach discrete coherent modes, discovered before, and possible incoherent oscillations appear as a result of multiresolution/multiscale fast convergent decomposition in the bases of high-localized exact nonlinear modes represented by wavelets or wavelet packets functions. The constructed solutions represent the full multiscale spectrum in all internal hidden scales from slow to fast oscillating eigenmodes. Underlying variational method provides algebraical control of the spectrum.