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Documents  Martel, Yvan | enregistrements trouvés : 2

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Research talks;Partial Differential Equations

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.
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 ...

35Q55 ; 76B25 ; 35Q51 ; 35C08

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- 186 p.
ISBN 978-0-19-850277-7

Oxford Lecture Series in Mathematics and its Applications , 0013

Localisation : Ouvrage Rdc (CAZE)

EDP # équation différentielle non linéaire # semigroupe d'opérateurs non linéairs # application des équations différentielles et intégrales

35-02 ; 34G20 ; 35-01 ; 47H20 ; 47N20

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