Mathematica package applications to physical problems

Abstract:
In recent years a remarkable progress was achieved in the development of the Wolfram Research Mathematica package, especially in the newest Mathematica 5.1 version. As a consequence, rich new possibilities are opened for the solution of physical problems by the use of this package. The present contribution is concentrated on the discussion of the Mathematica package applications to the treatment of particles, waves and vortices in plasma physics. Test particle motion in a given external field can be considered which allow us to calculate and display sets of phase trajectories.

Dispersion relations for waves can be easily obtained even in the presence of many different modes. Green functions for the complicated wave models like the Hasegawa-Mima model and its three-dimensional generalizations can be calculated and plotted. Graphical procedures allow us to perform a good presentation of the calculation results. As for nonlinear waves, perturbation theory algorithms are built and solutions are obtained up to the third order. In this case Laplace and Fourier transforms are used to solve intermediate linear equations. Symmetry considerations essentially facilitate the calculations.