On the collapse of trial solutions for a damped-driven non-linear Schr\"odinger equation
Mathematical Physics
2017-03-03 v3 math.MP
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.
Keywords
Cite
@article{arxiv.1405.0151,
title = {On the collapse of trial solutions for a damped-driven non-linear Schr\"odinger equation},
author = {Sigurd Assing and Astrid Hilbert},
journal= {arXiv preprint arXiv:1405.0151},
year = {2017}
}
Comments
24 pages, corrected some typos, added Prop.2.4 to sharpen the comparison argument, added discussion of conditions