Instability of the soliton for the focusing, mass-critical generalized KdV equation

In this paper we prove instability of the soliton for the focusing, mass-critical generalized KdV equation. We prove that the solution to the generalized KdV equation for any initial data with mass smaller than the mass of the soliton and close to the soliton in $L^2$ norm must eventually move away from the soliton.