Abstract

This article is devoted to the nonlinear Schrödinger equation [InlineMediaObject not available: see fulltext.] when the parameter ε approaches zero. All possible asymptotic behaviors of bounded solutions can be described by means of envelopes, or alternatively by adiabatic profiles. We prove that for every envelope, there exists a family of solutions reaching that asymptotic behavior, in the case of bounded intervals. We use a combination of the Nehari finite dimensional reduction together with degree theory. Our main contribution is to compute the degree of each cluster, which is a key piece of information in order to glue them.