Numerical aspects of nonlinear Schrodinger equations in the presence of caustics

Details Numerical aspects of nonlinear Schrodinger equations in the presence of caustics Numerical aspects of nonlinear Schrodinger equations in the presence of caustics

2007-02-26

arxiv.org/abs/math/0702778v1

Math. Models Methods Appl. Sci. 17, 10 (2007) 1531-1553

Mathematics

Numerical Analysis

20 pages. To appear in Math. Mod. Meth. Appl. Sci

Scientific paper

10.1142/S0218202507002376

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.

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