A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2012; you can also visit the original URL.
The file type is
We consider the effect of random inhomogeneities on the focusing singularity of the nonlinear Schrödinger equation in three dimensions, in the high frequency limit. After giving a phase space formulation of the high frequency limit using the Wigner distribution, we derive a nonlinear diffusion equation for the evolution of the wave energy density when random inhomogeneities are present. We show that this equation is linearly stable even in the case of a focusing nonlinearity provided that it isdoi:10.1137/s003613999935559x fatcat:fn3uhf6xpfafzpstewmftx3fgu