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On the collapse of trial solutions for a damped-driven nonlinear Schrödinger equation
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Assing, Sigurd and Hilbert, Astrid (2018) On the collapse of trial solutions for a damped-driven nonlinear Schrödinger equation. Nonlinearity, 31 (11). 4955. doi:10.1088/1361-6544/aad64a ISSN 0951-7715.
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Official URL: https://doi.org/10.1088/1361-6544/aad64a
Abstract
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.
Item Type: | Journal Article | ||||||||
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Subjects: | Q Science > QC Physics | ||||||||
Divisions: | Faculty of Science, Engineering and Medicine > Science > Statistics | ||||||||
Library of Congress Subject Headings (LCSH): | Schrödinger equation, Hamiltonian systems | ||||||||
Journal or Publication Title: | Nonlinearity | ||||||||
Publisher: | Institute of Physics Publishing Ltd. | ||||||||
ISSN: | 0951-7715 | ||||||||
Official Date: | November 2018 | ||||||||
Dates: |
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Volume: | 31 | ||||||||
Number: | 11 | ||||||||
Article Number: | 4955 | ||||||||
DOI: | 10.1088/1361-6544/aad64a | ||||||||
Institution: | University of Warwick | ||||||||
Status: | Peer Reviewed | ||||||||
Publication Status: | Published | ||||||||
Access rights to Published version: | Restricted or Subscription Access | ||||||||
Date of first compliant deposit: | 2 November 2018 | ||||||||
Date of first compliant Open Access: | 2 November 2018 | ||||||||
Open Access Version: |
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