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

Christian Klein; Benson Muite; Kristelle Roidot

doi:10.3934/dcdsb.2013.18.1361

Article Contents

2013, Volume 18, Issue 5: 1361-1387. Doi: 10.3934/dcdsb.2013.18.1361

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

1.
Institut de Mathématiques de Bourgogne, Université de Bourgogne, 9 avenue Alain Savary, 21078 Dijon Cedex
2.
Department of Mathematics, University of Michigan, 2074 East Hall, 530 Church Street, MI 48109

Received: December 2011

Revised: February 2013

Published: July 2013

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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.

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Mathematics Subject Classification: Primary: 35Q35, 65M70; Secondary: 65L05, 65M20.

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