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In this work we continue the description of soliton-like solutions of someslowly varying, subcritical gKdV equations.  In this opportunity we describe, almost completely, the allowed behaviors:either the soliton is refracted, or it is reflected by the potential, dependingon its initial energy. This last result describes a new type of soliton-likesolution for gKdV equations, also present in the NLS case.  Moreover, we prove that the solution is not pure at infinity, unlike thestandard gKdV soliton.

Dynamics of soliton-like solutions for slowly varying, generalized gKdV equations: refraction vs. reflection