Parallel Computing for the study of the focusing Davey-Stewartson II equation in semiclassical limit*
Institut de Mathématiques de Bourgogne, Université de
Bourgogne, 9 avenue Alain
The asymptotic description of the semiclassical limit of nonlinear Schrödinger equations is a major challenge with so far only scattered results in 1 + 1 dimensions. In this limit, solutions to the NLS equations can have zones of rapid modulated oscillations or blow up. We numerically study in this work the Davey-Stewartson system, a 2 + 1 dimensional nonlinear Schrödinger equation with a nonlocal term, by using parallel computing. This leads to the first results on the semiclassical limit for the Davey-Stewartson equations.
I thank my supervisor C. Klein who interested me in the subject, for helpful discussions and writing corrections. This work benefited from financial support by the Conseil Régional de Bourgogne via a FABER grant allotted to the Pr. Klein, the ANR via the program ANR-09-BLAN-0117-01, and the Marie-Curie IRSES program RIMMP. This work was also granted access to HPC resources of CCRT/IDRIS under the allocation 2011106628 made by GENCI (Grand Equipement National de Calcul Intensif). In this context, I also thank B. Muite who contributed to the GENCI project.
© EDP Sciences, SMAI 2012