Nonlinear Alfven waves in a finite-beta plasma

The derivative nonlinear Schroedinger equation for parallel nonlinear and weakly dispersive MHD waves is extended to finite beta values as well as to three spatial dimensions, by means of the reductive perturbation method. Kinetic effects are included by means of the hybrid fluid and kinetic guiding-centre model of Grad, H., Proceedings of the Symposium on Electromagnetics and Fluid Dynamics of Gaseous Plasmas, p. 37, Polytechnic Press of the Polytechnic Institute of Brooklyn, N.Y., 1961. The resulting equation contains a nonlinear and non-local term representing the effect of resonant particles. (author)