2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/87489A 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.5 pages, 2 eps figures. Relater papers are at http://sdphpd.ucsd.edu/~medvedev/papers.htmlPlasma PhysicsAstrophysicsPattern Formation and SolitonsSpace Physicstext