  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.
