Blow up in finite time and dynamics of blow up solutions for the 𝐿²–critical generalized KdV equation

Abstract

In this paper, we describe the dynamics of blow up solutions for the critical generalized KdV equation such that the initial data is close to the soliton in L 2 L^2 and has decay in L 2 L^2 at the right. In particular, we prove that blow up occurs in finite time, and we obtain an upper bound on the blow up rate.