DG-MP-PDE Seminar: Vianney Combet (UBC)

We consider the problem of existence and uniqueness of multi-soliton solutions for the L²-supercritical generalized Korteweg-de Vries equation. We recall that a multi-soliton is a solution which behaves as a sum of N solitons in large time. After a survey of existing results in the subcritical and critical cases, and also in the 1-soliton case, we will state the theorem of existence and uniqueness of an N-parameter family of N-solitons in the supercritical case. Finally, we will sketch a proof of the classification part of this theorem.