Coherent Structures and Pattern Formation in Vlasov-Maxwell-Poisson Systems

We present the applications of methods from nonlinear local harmonic analysis for calculations in nonlinear collective dynamics described by different forms of Vlasov-Maxwell-Poisson equations. Our approach is based on methods provided the 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. The consideration is based on a number of anzatzes, which reduce initial problems to a number of dynamical systems and on variational-wavelet approach to polynomial approximations for nonlinear dynamics. This approach allows us to construct the solutions via nonlinear high-localized eigenmodes expansions in the base of compactly supported wavelet bases and control contribution from each scale of underlying multiscales. Numerical modelling demonstrates formation of coherent structures and stable patterns.