  We consider the problem of the soliton propagation, in a slowly varying
medium, for a generalized Korteweg - de Vries equations (gKdV). We study the
effects of inhomogeneities on the dynamics of a standard soliton. We prove that
slowly varying media induce on the soliton solution large dispersive effects at
large time. Moreover, unlike gKdV equations, we prove that there is no
pure-soliton solution in this regime.
