On the collapse of trial solutions for a damped-driven non-linear   Schr\"odinger equation
  We consider the focusing 2D non-linear Schr\"odinger equation, perturbed by a damping term, and driven by multiplicative noise. We show that a physically motivated trial solution does not collapse for any admissible initial condition although the exponent of the non-linearity is critical. Our method is based on the construction of a global solution to a singular stochastic Hamiltonian system used to connect trial solution and Schr\"odinger equation. 
Sigurd Assing, Astrid Hilbert
math-ph math.MP