French-American conference on nonlinear dispersive PDEs / Conférence franco-américaine sur les EDP dispersives non linéaires

Collection French-American conference on nonlinear dispersive PDEs / Conférence franco-américaine sur les EDP dispersives non linéaires

Organizer(s) Carles, Rémi ; Holmer, Justin ; Roudenko, Svetlana

Date(s) 12/06/2017 - 16/06/2017

linked URL http://conferences.cirm-math.fr/1510.html

00:00:00 / 00:00:00

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Soliton resolution for derivative NLS equation

By Catherine Sulem

We consider the Derivative Nonlinear Schrödinger equation for general initial conditions in weighted Sobolev spaces that can support bright solitons (but exclude spectral singularities). We prove global wellposedness and give a full description of the long-time behavior of the solutions in the form of a finite sum of localized solitons and a dispersive component. Our analysis provides explicit formulae for the multi-soliton component as well as the correction dispersive term. We use the inverse scattering approach and the nonlinear steepest descent method of Deift and Zhou (1993) revisited by the $\bar{\partial}$-analysis of Dieng-McLaughlin (2008) and complemented by the recent work of Borghese-Jenkins-McLaughlin (2016) on soliton resolution for the focusing nonlinear Schrödinger equation. This is a joint work with R. Jenkins, J. Liu and P. Perry.

Information about the video

Date of recording 13/06/2017
Date of publication 22/06/2017
Institution CIRM
Licence CC BY NC ND
Language English
Audience Researchers
Director(s) Guillaume Hennenfent
Format MP4

Citation data

DOI 10.24350/CIRM.V.19182903
Cite this video Sulem, Catherine (13/06/2017). Soliton resolution for derivative NLS equation. CIRM. Audiovisual resource. DOI: 10.24350/CIRM.V.19182903
URL https://dx.doi.org/10.24350/CIRM.V.19182903

Domain(s)

Analysis of PDEs

Bibliography

Jenkins, R., Liu, J., Perry, P., & Sulem, C. (2017). Global Well-posedness and soliton resolution for the Derivative Nonlinear Schrödinger equation. <arXiv:1706.06252> - https://arxiv.org/abs/1706.06252

MSC codes

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