Numerical aspects of nonlinear Schrodinger equations in the presence of causticsReport as inadecuate




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1 ICP - Institut CNRS-PAULI 2 I3M - Institut de Mathématiques et de Modélisation de Montpellier 3 IAC - Istituto per le Applicazioni del Calcolo -Mauro Picone-

Abstract : The aim of this text is to develop on the asymptotics of some 1-D nonlinear Schrodinger equations from both the theoretical and the numerical perspectives, when a caustic is formed. We review rigorous results in the field and give some heuristics in cases where justification is still needed. The scattering operator theory is recalled. Numerical experiments are carried out on the focus point singularity for which several results have been proven rigorously. Furthermore, the scattering operator is numerically studied. Finally, experiments on the cusp caustic are displayed, and similarities with the focus point are discussed.

Keywords : Nonlinear Schrodinger equation time-splitting scheme Fourier scheme WKB expansion caustics





Author: Rémi Carles - Laurent Gosse -

Source: https://hal.archives-ouvertes.fr/



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