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H 1 Interactions of solitary waves for the nonlinear Schrödinger equations

Auteurs : Martel, Yvan (Auteur de la Conférence)
CIRM (Editeur )

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    Résumé : 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.

    Codes MSC :
    35Q51 - Soliton-like equations
    35Q55 - NLS-like equations (nonlinear Schrödinger)
    76B25 - Solitary waves
    35C08 - Soliton solutions of PDE

      Informations sur la Vidéo

      Langue : Anglais
      Date de publication : 22/06/17
      Date de captation : 13/06/17
      Collection : Research talks ; Partial Differential Equations
      Format : MP4
      Durée : 00:36:36
      Domaine : PDE
      Audience : Chercheurs ; Doctorants , Post - Doctorants
      Download : https://videos.cirm-math.fr/2017-06-13_Martel.mp4

    Informations sur la rencontre

    Nom de la rencontre : French-American conference on nonlinear dispersive PDEs / Conférence franco-américaine sur les EDP dispersives non linéaires
    Organisateurs de la rencontre : Carles, Rémi ; Holmer, Justin ; Roudenko, Svetlana
    Dates : 12/06/17 - 16/06/17
    Année de la rencontre : 2017
    URL Congrès : http://conferences.cirm-math.fr/1510.html

    Citation Data

    DOI : 10.24350/CIRM.V.19183003
    Cite this video as: Martel, Yvan (2017). Interactions of solitary waves for the nonlinear Schrödinger equations. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.19183003
    URI : http://dx.doi.org/10.24350/CIRM.V.19183003


    Voir aussi

    Bibliographie

    1. Martel, Y., & Raphael, P. (2015). Strongly interacting blow up bubbles for the mass critical NLS. - https://arxiv.org/abs/1512.00900

    2. Nguyen, T.-V. (2016). Existence of multi-solitary waves with logarithmic relative distances for the NLS equation. - https://arxiv.org/abs/1611.08869

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