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Paper Title: Perturbative Solution of the Fokker-Planck Equation for a Multidimensional Nonlinear Dissipative Dynamical System
Primary Author: Y. Alexahin
Institution: JINR, Dubna 141980 Russia
Secondary Authors and Institutions:
Working Groups IR (background, magnets) & Optics
An algorithm is presented which permits to find stationary solution of the Fokker-Planck equation for a multidimensional nonlinear dissipative dynamical system subject to random excitations. The system is assumed to be sufficiently far from resonances so that the normal form variables for the deterministic motion can be found. Then the logarithm of the distribution function is sought for in the form of power series in the nonlinear resonance strengthes, the expansion coefficients being polynomials in the action variables. The described method permits to study non-Gaussian tails in distribution function due to nonlinearities in both deterministic and random forces.