Asymptotic Theory of Particle Trapping in Coherent Nonlinear Alfven   Waves
  A fully nonlinear, time-asymptotic theory of resonant particle trapping in large-amplitude quasi-parallel Alfven waves is presented. The effect of trapped particles on the nonlinear dynamics of quasi-stationary Alfvenic discontinuities and coherent Alfven waves is highly non-trivial and forces to a significant departure of the theory from the conventional DNLS and KNLS equation models. The virial theorem is used to determine the time-asymptotic distribution function. 
M.V. Medvedev, P.H. Diamond, M.N. Rosenbluth, V.I. Shevchenko (UCSD)