University of Cambridge > Talks.cam > Isaac Newton Institute Seminar Series > About plane periodic waves of the nonlinear Schrödinger equations

About plane periodic waves of the nonlinear Schrödinger equations

Add to your list(s) Download to your calendar using vCal

If you have a question about this talk, please contact nobody.

HY2W01 - Modulation theory and dispersive shock waves

In a recent contribution, jointly with Corentin Audiard (Sorbonne), we have obtained a quite extensive theory for the stability analysis of plane periodic waves of general Schrödinger equations. On one hand, we put the one-dimensional theory, or in other words the stability theory for longitudinal perturbations, on a par with the one available for systems of Korteweg type, including results on co-periodic spectral instability, nonlinear co-periodic orbital stability, side-band spectral instability and linearized large-time dynamics in relation with modulation theory, and resolutions of all the involved assumptions in both the small-amplitude and large-period regimes.   On the other hand, we provide extensions of the spectral part of the latter to the multi-dimensional context. Notably, we provide suitable multi-dimensional modulation formal asymptotics, validate those at the spectral level and use them to prove that waves are always spectrally unstable in both the small-amplitude and the large-period regimes. The present talk shall expound some parts of this analysis.

This talk is part of the Isaac Newton Institute Seminar Series series.

Tell a friend about this talk:

This talk is included in these lists:

Note that ex-directory lists are not shown.

 

© 2006-2022 Talks.cam, University of Cambridge. Contact Us | Help and Documentation | Privacy and Publicity