Center Manifold for Nonintegrable Nonlinear Schrödinger Equations on the Line

摘要: In this paper we study the following nonlinear Schrodinger equation on line, where f is real-valued, and it satisfies suitable conditions regularity, growth as a function of u decay x→±∞. The generic potential, V, real-valued chosen so that spectrum consists one simple negative eigenvalue absolutely-continuous filling [0, ∞). solutions to have, in general, localized dispersive component. bound states, bifurcate from zero solution at energy H, define an invariant center manifold orbits time-periodic solutions. We prove all small approach particular periodic orbit t→±∞. are different for Our result implies also states asymptotically stable, sense each with initial data near state asymptotic t→±∞ nearby are,