Alfven-wave propagation described by a nonlinear Landau-damping equation

General similarity solutions of temporal decay of a power spectrum of Alfven waves in a magnetized plasma are classified in terms of Lie group parameters. One class of these solutions can be mapped to a solution of the Abel equation. A second class is transformed to a solitary-wave. solution where the spectrum at. short wavelengths is more rapidly damped than at long wavelengths.