  This paper concerns the problem of collision of two solitons for the quartic
generalized Korteweg-de Vries equation. We introduce a new framework to
describe the collision in the special case where one soliton is small with
respect to the other. We prove that the two soliton survive the collision, we
describe the collision phenomenon (computation of the first order of the
resulting shifts on the solitons). Moreover, we prove that in this situation,
there does not exist pure two-soliton solutions.
