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Journal article
Vortex collapse for the L-2-critical nonlinear Schrodinger equation
Journal of mathematical physics, v 52(8), pp 083503-083503-40
01 Aug 2011
Abstract
The focusing cubic nonlinear Schrodinger equation in two dimensions admits vortex solitons, standing wave solutions with spatial structure, Q((m))(r,theta) = e(im theta) R-(m)(r). In the case of spin m = 1, we prove there exists a class of data that collapse with the vortex soliton profile at the log-log rate. This extends the work of Merle and Raphael (the case m = 0) and suggests that the L-2 mass that may be concentrated at a point during generic collapse may be unbounded. Difficulties with m = 2, or when the spin symmetry is broken, are also discussed. (C) 2011 American Institute of Physics. [doi:10.1063/1.3608054]
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Details
- Title
- Vortex collapse for the L-2-critical nonlinear Schrodinger equation
- Creators
- G. Simpson - Univ Toronto, Toronto, ON M5S 2E4, CanadaI. Zwiers - Univ British Columbia, Vancouver, BC V6T 1Z2, Canada
- Publication Details
- Journal of mathematical physics, v 52(8), pp 083503-083503-40
- Publisher
- American Institute of Physics
- Number of pages
- 40
- Resource Type
- Journal article
- Language
- English
- Academic Unit
- Mathematics
- Web of Science ID
- WOS:000294485200026
- Scopus ID
- 2-s2.0-80052333295
- Other Identifier
- 991019296795804721
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- Collaboration types
- Domestic collaboration
- Web of Science research areas
- Physics, Mathematical