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