1,721,043 research outputs found
A Normal Form for the Schrödinger equation with analytic non--linearities
No full textWe discuss a class of normal forms of the completely resonant non-linear Schrodinger equation on a torus. We prove that for generic choices of the initial data one has an integrable normal form. We stress the geometric and combinatorial constructions arising from this study
A KAM algorithm for the resonant non-linear Schrödinger equation
Full text linkWe prove, by applying a KAM algorithm, existence of large families of
stable and unstable quasi periodic solutions for the NLS in any number of independent
frequencies. The main tools are the existence of a non-degenerate integrable normal
form proved in previous papers by the authors and a suitable generalization of the quasi-Toplitz functions
A KAM algorithm for the resonant non-linear Schrödinger equation
No full textWe prove, by applying a KAM algorithm, existence of large families of
stable and unstable quasi periodic solutions for the NLS in any number of independent
frequencies. The main tools are the existence of a non-degenerate integrable normal
form proved in previous papers by the authors and a suitable generalization of the quasi-T oplitz functions
A Normal Form for the Schrödinger Equation with Analytic Non-linearities
No full textWe discuss a class of normal forms of the completely resonant non-linear Schrodinger equation on a torus. We stress the geometric and combinatorial constructions arising from this study
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