A numericalapproach to Blow-up issues for Davey-Stewartson II systems

Christian Klein; Jean-Claude Saut

doi:10.3934/cpaa.2015.14.1443

Article Contents

2015, Volume 14, Issue 4: 1443-1467. Doi: 10.3934/cpaa.2015.14.1443

This issue Previous Article Global and almost global existence of small solutions to a dissipative wave equation in 3D with nearly null nonlinear terms Next Article On the pointwise decay estimate for the wave equation with compactly supported forcing term

A numerical approach to Blow-up issues for Davey-Stewartson II systems

Christian Klein^1, and
Jean-Claude Saut^2,

1.
Institut de Mathématiques de Bourgogne, Université de Bourgogne, 9 avenue Alain Savary, 21078 Dijon Cedex
2.
Laboratoire de Mathématiques, UMR 8628, Université Paris-Sud et CNRS, 91405 Orsay

Received: May 31, 2014

Revised: June 30, 2014

Published: June 2015

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Abstract

We provide a numerical study of various issues pertaining to the dynamics of the Davey-Stewartson II systems. In particular we investigate whether or not the properties (blow-up, radiation,...) displayed by the focusing and defocusing Davey-Stewartson II integrable systems persist in the non integrable cases.

Keywords:

Davey-Stewartson equations,
blow-up,
long time behavior numerical approaches.

Mathematics Subject Classification: Primary: 35Q55, 35B44; Secondary: 35B65, 65M20.

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