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

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