Quasi-analytical method for solving nonlinear differential equations for turbulent self-confined magneto-plasmas

A quasi-analytical method is presented which permits calculating highly nonlinear behavior of selfconfined plasma configurations. Using the possibilities of the analytic computer code REDUCE, the equations are transformed to ( k,ω)-Fourier space. The use of analytical methods also in back-transformation avoids difficulties with steep gradients. A dispersion relation is established from which growth rates of instabilities can be calculated. The application of the method is demonstrated for Burgers' equation with a specific initial condition for which an analytical solution is known.