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• W3101823488 abstract "The aim of this paper is to develop on the asymptotics of some one-dimensional nonlinear Schrödinger 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 proved rigorously. Furthermore, the scattering operator is numerically studied. Finally, experiments on the cusp caustic are displayed, and similarities with the focus point are discussed. Several shortcomings of spectral time-splitting schemes are investigated." @default.
• W3101823488 created "2020-11-23" @default.
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• W3101823488 date "2007-10-01" @default.
• W3101823488 modified "2023-10-17" @default.
• W3101823488 title "NUMERICAL ASPECTS OF NONLINEAR SCHRÖDINGER EQUATIONS IN THE PRESENCE OF CAUSTICS" @default.
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• W3101823488 doi "https://doi.org/10.1142/s0218202507002376" @default.
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