Quasi-analytical method for solving nonlinear differential equations for turbulent self-confined magneto-plasmas (Q1082194)

In this paper the authors present a quasi-analytical method for solving systems of nonlinear differential equations of the Navier-Stokes type including strong turbulence with particular reference to self-confined systems. The analytical manipulation is achieved by using the computer code REDUCE and the numerical solution of the dispersion relations and fit programmes are made with FORTRAN. The equations are first transformed to (\(\vec k,\omega)\)-Fourier space. A dispersion relation is established from which the growth rates of instabilities are calculated. As an application of the method the Burgers' equation is solved with the initial conditions (i) \(F(x)=\delta (x)\), (ii) \(F(x)=U \sin kx\). The method avoids difficulties with steep gradients.