Abstract
In this paper, one-dimensional (1D) nonlinear Schrodinger equations $$ iu_{t}-u_{xx}+mu+\nu|u|^{4}u=0, $$ with Dirichlet boundary conditions are considered. It is proved that for all real parameters m, the above equation admits small-amplitude quasi-periodic solutions corresponding to b-dimensional invariant tori of an associated infinite-dimensional dynamical system. The proof is based on infinite-dimensional KAM theory, partial normal form, and scaling skills.
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