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Journal article
Local Structure of Singular Profiles for a Derivative Nonlinear Schrodinger Equation
SIAM journal on applied dynamical systems, v 16(1), pp 514-545
01 Jan 2017
Featured in Collection : UN Sustainable Development Goals @ Drexel
Abstract
The derivative nonlinear Schrodinger equation is an L-2-critical nonlinear dispersive model for Alfven waves in a long-wavelength asymptotic regime. Recent numerical studies [X. Liu, G. Simpson, and C. Sulem, Phys. D, 262 (2013), pp. 48-58] on an L-2-supercritical extension of this equation provide evidence of finite time singularities. Near the singular point, the solution is described by a universal profile that solves a nonlinear elliptic eigenvalue problem depending only on the strength of the nonlinearity. In the present work, we describe the deformation of the profile and its parameters near criticality, combining asymptotic analysis and numerical simulations.
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Details
- Title
- Local Structure of Singular Profiles for a Derivative Nonlinear Schrodinger Equation
- Creators
- Yuri Cher - Univ Toronto, Dept Math, Toronto, ON M5S 2E4, CanadaGideon Simpson - Drexel Unixers, Dept Math, Philadelphia, PA 19104 USACatherine Sulem - Univ Toronto, Dept Math, Toronto, ON M5S 2E4, Canada
- Publication Details
- SIAM journal on applied dynamical systems, v 16(1), pp 514-545
- Publisher
- Siam Publications
- Number of pages
- 32
- Grant note
- 1409018 / Direct For Mathematical & Physical Scien; National Science Foundation (NSF); NSF - Directorate for Mathematical & Physical Sciences (MPS) DMS-1409018 / NSF; National Science Foundation (NSF) 46179-13 / NSERC; Natural Sciences and Engineering Research Council of Canada (NSERC) Drexel's University Research Computing Facility
- Resource Type
- Journal article
- Language
- English
- Academic Unit
- Mathematics
- Web of Science ID
- WOS:000398542800019
- Scopus ID
- 2-s2.0-85018716299
- Other Identifier
- 991019169705204721
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- Collaboration types
- Domestic collaboration
- International collaboration
- Web of Science research areas
- Mathematics, Applied
- Physics, Mathematical