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arXiv · 1405.0151

On the collapse of trial solutions for a damped-driven non-linear Schr\"odinger equation

Sigurd Assing·Astrid Hilbert
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Abstract

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.

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Sigurd Assing, Astrid Hilbert. 2014-05-01. On the collapse of trial solutions for a damped-driven non-linear Schr\"odinger equation. https://arxiv.org/abs/1405.0151

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