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On the collapse of trial solutions for a damped-driven nonlinear Schrödinger equation
Univ Warwick, UK.
Linnaeus University, Faculty of Technology, Department of Mathematics.
2018 (English)In: Nonlinearity, ISSN 0951-7715, E-ISSN 1361-6544, Vol. 31, no 11, p. 4955-4978Article in journal (Refereed) Published
Abstract [en]

We consider the focusing 2D nonlinear Schrodinger 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 Schrodinger equation.

Place, publisher, year, edition, pages
Institute of Physics Publishing (IOPP), 2018. Vol. 31, no 11, p. 4955-4978
Keywords [en]
Schrödinger equation, singular Hamiltonian system, stochastic differential equations
National Category
Mathematics
Research subject
Natural Science, Mathematics
Identifiers
URN: urn:nbn:se:lnu:diva-78607DOI: 10.1088/1361-6544/aad64aISI: 000446784000003Scopus ID: 2-s2.0-85055341017OAI: oai:DiVA.org:lnu-78607DiVA, id: diva2:1260287
Available from: 2018-11-01 Created: 2018-11-01 Last updated: 2019-08-29Bibliographically approved

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Hilbert, Astrid

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