# On the collapse of trial solutions for a damped-driven nonlinear Schrödinger equation

@article{Assing2014OnTC,
title={On the collapse of trial solutions for a damped-driven nonlinear Schr{\"o}dinger equation},
author={Sigurd Assing and Astrid Hilbert},
journal={Nonlinearity},
year={2014},
volume={31},
pages={4955 - 4978}
}
• Published 1 May 2014
• Mathematics
• Nonlinearity
We consider the focusing 2D nonlinear Schrödinger 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 nonlinearity 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 Schrödinger equation.

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