  We present the application of the variational-wavelet approach to the
construction and analysis of solutions of Wigner/von Neumann/Moyal and related
equations corresponding to the nonlinear (polynomial) dynamical problems.
(Naive) deformation quantization, the multiresolution representation (exact
multiscale decompostion) and the variational approach are the key points. We
construct the solutions via the high-localized nonlinear eigenmodes in the base
of the compactly supported wavelets and the wavelet packets. We demonstrate the
appearance of (stable) localized patterns (waveletons) and consider
entanglement and decoherence as possible applications.
