Blow up and near soliton dynamics for the critical gKdV equation
Yvan Martel, Frank Merle, Pierre Raphaël (2011-2012)
Séminaire Laurent Schwartz — EDP et applications
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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. ...