Some variants of the focusing NLS equations
Dumas, Éric1
1 Université Grenoble Alpes France
Journées équations aux dérivées partielles (2018), Talk no. 1, 15 p.

The focusing cubic NLS is a canonical model for the propagation of laser beams. In dimensions 2 and 3, it is known that a large class of initial data leads to finite time blow-up. Now, physical experiments suggest that this blow-up does not always occur. This might be explained by the fact that some physical phenomena neglected by the standard NLS model become relevant at large intensities of the beam. We derive from Maxwell’s equations some known variants of NLS and propose some new ones, providing rigorous error estimates for all the models considered. These notes result from the work [9], in collaboration with D. Lannes and J. Szeftel.

Published online:
DOI: 10.5802/jedp.661
Dumas, Éric 1

1 Université Grenoble Alpes France 
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Dumas, Éric. Some variants of the focusing NLS equations. Journées équations aux dérivées partielles (2018), Talk no. 1, 15 p. doi : 10.5802/jedp.661. http://www.numdam.org/articles/10.5802/jedp.661/

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