Fluid Models for Kinetic Effects on Coherent Nonlinear Alfven Waves. II.   Numerical Solutions
  The influence of various kinetic effects (e.g. Landau damping, diffusive and collisional dissipation, and finite Larmor radius terms) on the nonlinear evolution of finite amplitude Alfvenic wave trains in a finite-beta environment is systematically investigated using a novel, kinetic nonlinear Schrodinger (KNLS) equation. The dynamics of Alfven waves is sensitive to the sense of polarization as well as the angle of propagation with respect to the ambient magnetic field. Numerical solution for the case with Landau damping reveals the formation of dissipative structures, which are quasi-stationary, S-polarized directional (and rotational) discontinuities which self-organize from parallel propagating, linearly polarized waves. Parallel propagating circularly polarized packets evolve to a few circularly polarized Alfven harmonics on large scales. Stationary arc-polarized rotational discontinuities form from obliquely propagating waves. Collisional dissipation, even if weak, introduces enhanced wave damping when beta is very close to unity. Cyclotron motion effects on resonant particle interactions introduce cyclotron resonance into the nonlinear Alfven wave dynamics. 
M.V. Medvedev, V.I. Shevchenko, P.H. Diamond, V.L. Galinsky (UCSD)