A KAM algorithm for the resonant non--linear Schr\"odinger equation
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algorithmequationnon--linearodingerresonantschrcompletelyderived
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In this note we use the normal forms of the completely resonant non--linear Schr\"odinger equation on a torus (NLS) derived in previous work in order to produce, under a KAM algorithm, large families of stable and unstable quasi periodic solutions for the NLS in any number of independent frequencies.
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