Numerical study of blow-up in the Davey-Stewartson system

Christian Klein; Benson Muite; Kristelle Roidot

doi:10.3934/dcdsb.2013.18.1361

Numerical study of blow-up in the Davey-Stewartson system

Christian Klein, Benson Muite, Kristelle Roidot

King Abdullah University of Science and Technology

Research output: Contribution to journal › Article › peer-review

17 Scopus citations

Abstract

Nonlinear dispersive partial differential equations such as the nonlinear Schrödinger equations can have solutions that blow up. We numerically study the long time behavior and potential blow-up of solutions to the focusing Davey-Stewartson II equation by analyzing perturbations of the lump and the Ozawa solutions. It is shown in this way that both are unstable to blow-up and dispersion, and that blow-up in the Ozawa solution is generic.

Original language	English (US)
Pages (from-to)	1361-1387
Number of pages	27
Journal	Discrete and Continuous Dynamical Systems - Series B
Volume	18
Issue number	5
DOIs	https://doi.org/10.3934/dcdsb.2013.18.1361
State	Published - Apr 4 2013

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KAUST Repository Item: Exported on 2020-10-01

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abstract = "Nonlinear dispersive partial differential equations such as the nonlinear Schr{\"o}dinger equations can have solutions that blow up. We numerically study the long time behavior and potential blow-up of solutions to the focusing Davey-Stewartson II equation by analyzing perturbations of the lump and the Ozawa solutions. It is shown in this way that both are unstable to blow-up and dispersion, and that blow-up in the Ozawa solution is generic.",

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AU - Roidot, Kristelle

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N2 - Nonlinear dispersive partial differential equations such as the nonlinear Schrödinger equations can have solutions that blow up. We numerically study the long time behavior and potential blow-up of solutions to the focusing Davey-Stewartson II equation by analyzing perturbations of the lump and the Ozawa solutions. It is shown in this way that both are unstable to blow-up and dispersion, and that blow-up in the Ozawa solution is generic.

AB - Nonlinear dispersive partial differential equations such as the nonlinear Schrödinger equations can have solutions that blow up. We numerically study the long time behavior and potential blow-up of solutions to the focusing Davey-Stewartson II equation by analyzing perturbations of the lump and the Ozawa solutions. It is shown in this way that both are unstable to blow-up and dispersion, and that blow-up in the Ozawa solution is generic.

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JO - Discrete and Continuous Dynamical Systems - Series B

JF - Discrete and Continuous Dynamical Systems - Series B

IS - 5

ER -

Numerical study of blow-up in the Davey-Stewartson system

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