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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Interactions of solitary waves for the nonlinear Schrödinger equations

By Yvan Martel

I will present two cases of strong interactions between solitary waves for the nonlinear Schrödinger equations (NLS). In the mass sub- and super-critical cases, a work by Tien Vinh Nguyen proves the existence of multi-solitary waves with logarithmic distance in time, extending a classical result of the integrable case (1D cubic NLS equation). In the mass-critical case, a work by Yvan Martel and Pierre Raphaël gives a new class of blow up multi-solitary waves blowing up in infinite time with logarithmic rate. These special behaviours are due to strong interactions between the waves, in contrast with most previous works on multi-solitary waves of (NLS) where interactions do not affect the general behaviour of each solitary wave.

Information about the video

Citation data

  • DOI 10.24350/CIRM.V.19183003
  • Cite this video Martel, Yvan (13/06/2017). Interactions of solitary waves for the nonlinear Schrödinger equations. CIRM. Audiovisual resource. DOI: 10.24350/CIRM.V.19183003
  • URL https://dx.doi.org/10.24350/CIRM.V.19183003

Domain(s)

Bibliography

  • Martel, Y., & Raphael, P. (2015). Strongly interacting blow up bubbles for the mass critical NLS. <arXiv:1512.00900> - https://arxiv.org/abs/1512.00900
  • Nguyen, T.-V. (2016). Existence of multi-solitary waves with logarithmic relative distances for the NLS equation. <arXiv:1611.08869> - https://arxiv.org/abs/1611.08869

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