Finite time collapse of N classical fields described by coupled   nonlinear Schrodinger equations
  We prove the finite-time collapse of a system of N classical fields, which are described by N coupled nonlinear Schrodinger equations. We derive the conditions under which all of the fields experiences this finite-time collapse. Finally, for two-dimensional systems, we derive constraints on the number of particles associated with each field that are necessary to prevent collapse. 
D. C. Roberts and A. C. Newell