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- W2128677788 abstract "We consider the applications of a numerical-analytical approach based on multiscale variational wavelet tech- nique to the systems with collective type behaviour de- scribed by some forms of Vlasov-Poisson/Maxwell equa- tions. We calculate the exact fast convergent represen- tations for solutions in high-localized wavelet-like bases functions, which correspond to underlying hidden (coher- ent) nonlinear eigenmodes. This helps to control stabil- ity/unstability scenario of evolution in parameter space on pure algebraical level. i=1 wjis(x − xji), (2) where s(x − xji) is a shape function of distributing par- ticles on the grids in configuration space, are replaced by powerful technique from local nonlinear harmonic analy- sis, based on underlying symmetries of functional space such as affine or more general. The solution has the mul- tiscale/multiresolution decomposition via nonlinear high- localized eigenmodes, which corresponds to the full mul- tiresolution expansion in all underlying time/phase space scales. Starting from Vlasov-Poisson equations in part 2, we consider the approach based on multiscale variational- wavelet formulation in part 3. We give the explicit repre- sentation for all dynamical variables in the base of com- pactly supported wavelets or nonlinear eigenmodes. Our solutions are parametrized by solutions of a number of re- duced algebraical problems one from which is nonlinear with the same degree of nonlinearity as initial problem and the others are the linear problems which correspond to the particular method of calculations inside concrete wavelet scheme. Because our approach started from variational for- mulation we can control evolution of instability on the pure algebraical level of reduced algebraical system of equa- tions. This helps to control stability/unstability scenario of evolution in parameter space on pure algebraical level. In all these models numerical modeling demonstrates the appearance of coherent high-localized structures and as a result the stable patterns formation or unstable chaotic be- haviour." @default.
- W2128677788 created "2016-06-24" @default.
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- W2128677788 date "2002-06-16" @default.
- W2128677788 modified "2023-09-27" @default.
- W2128677788 title "MULTISCALE DECOMPOSITION FOR VLASOV-POISSON EQUATIONS" @default.
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