Transverse collapse of Alfven wave-trains with small dispersion

While in the presence of dispersion the circular polarization of a weakly nonlinear Alfven wave-train is preserved, and the envelope dynamics governed by the usual scalar nonlinear Schrodinger equation, this is no longer the case in the small dispersion limit. It is shown that the wave amplitude then obeys a vector Schrodinger equation with an anisotropic diffraction term. The transverse collapse developing in three space dimensions then leads to the formation of thin layers of intense gradients instead of the foci characteristic of the dispersive case. The transition between the two regimes when the dispersion is decreased, is also analyzed. (C) 1998 American Institute of Physics.