Almost periodic invariant tori for the NLS on the circle

Abstract In this paper we study the existence and linear stability of almost periodic solutions for a NLS equation on circle with external parameters. Starting from seminal result Bourgain in [15] quintic NLS, propose novel approach allowing to prove unified framework persistence finite infinite dimensional invariant tori, which are support desired solutions. The is given through rather abstract “counter-term theorem” la Herman, directly original elliptic variables without passing action-angle ones. Our allows us find “many more” respect existing literature consider also non-translation PDEs.