Abstract
When the Vlasov–Maxwell system is written in Hamilton form using nonlocal Poisson bracket, the use of Hamiltonian formal approach for the real kinetic equations still is under discussion. The unique attempt was to approximate the Poisson bracket in Vlasov–Maxwell system by a finite-dimensional one. In this case, there exists a similarity between Vlasov–Maxwell system and the Liouville equation. Hence, the study of the approximate integration methods for analytically integrable and nonintegrable Liouville equations is a cornerstone for development of wavelet solutions for the Vlasov–Maxwell system. This chapter proposes an effective technique of approximate integration for the Cauchy problem of the generalized Liouville equation based on the orthogonal decomposition over Hermite polynomials and Hermite functions. The respective mean convergence theorems are proved.
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