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Journal article
NUMERICAL SIMULATIONS OF THE ENERGY-SUPERCRITICAL NONLINEAR SCHRODINGER EQUATION
Journal of hyperbolic differential equations, v 7(2)
01 Jun 2010
Abstract
We present numerical simulations of the defocusing nonlinear Schrodinger (NLS) equation with an energy supercritical nonlinearity. These computations were motivated by recent works of Kenig-Merle and Kilip-Visan who considered some energy supercritical wave equations and proved that if the solution is a priori bounded in the critical Sobolev space (i.e. the space whose homogeneous norm is invariant under the scaling leaving the equation invariant), then it exists for all time and scatters. In this paper, we numerically investigate the boundedness of the H-2-critical Sobolev norm for solutions of the NLS equation in dimension five with quintic nonlinearity. We find that for a class of initial conditions, this norm remains bounded, the solution exists for long time, and scatters.
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Details
- Title
- NUMERICAL SIMULATIONS OF THE ENERGY-SUPERCRITICAL NONLINEAR SCHRODINGER EQUATION
- Creators
- J. Colliander - University of TorontoG. Simpson - University of TorontoC. Sulem - University of Toronto
- Publication Details
- Journal of hyperbolic differential equations, v 7(2)
- Publisher
- World Scientific
- Number of pages
- 18
- Resource Type
- Journal article
- Language
- English
- Academic Unit
- Mathematics
- Web of Science ID
- WOS:000283688300004
- Scopus ID
- 2-s2.0-77954197655
- Other Identifier
- 991019296540804721
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- Web of Science research areas
- Mathematics, Applied
- Physics, Mathematical