STABILITY OF ISOTROPIC SELF-SIMILAR DYNAMICS FOR SCALAR-WAVE COLLAPSE

The scalar model for collapse of Langmuir waves in plasmas is studied numerically in two and three dimensions, for both radially symmetric and anisotropic initial conditions. Using a dynamic rescaling method, singular solutions are shown to become isotropic and self-similar near collapse. In two dimensions, the self-similar profile is not universal. In the limit where the mass of the wave tends to its minimal value for collapse, the solution approaches a subsonic regime different from the generic singularity of the nonlinear Schrodinger equation.