A wave equation with a Dirac distribution.
Complete blow up and global behaviour of solutions of
Multi solitary waves for nonlinear Schrödinger equations
Note on coupled linear systems related to two soliton collision for the quartic gKdV equation.
Existence de solutions explosives dans l’espace d’énergie pour l’équation de Korteweg–de Vries généralisée critique
On the collision of two solitons for the generalized KdV equation in the nonintegrable case
Blow up and near soliton dynamics for the critical gKdV equation
These notes present the main results of [, , ] concerning the mass critical (gKdV) equation for initial data in close to the soliton. These works revisit the blow up phenomenon close to the family of solitons in several directions: definition of the stable blow up and classification of all possible behaviors in a suitable functional setting, description of the minimal mass blow up in , construction of various exotic blow up rates in , including grow up in infinite time.
Blow up for the critical gKdV equation. II: Minimal mass dynamics
We consider the mass critical (gKdV) equation for initial data in . We first prove the existence and uniqueness in the energy space of a minimal mass blow up solution and give a sharp description of the corresponding blow up soliton-like bubble. We then show that this solution is the universal attractor of all solutions near the ground state which have a defocusing behavior. This allows us to sharpen the description of near soliton dynamics obtained in [29].
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