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On the non-existence of local Birkhoff coordinates for the focusing NLS equation
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🧮 math.AP
keywords
equationlocalbirkhoffcoordinatesfocusingpotentialsadmitconstruction
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We prove that there exist potentials so that near them the focusing non-linear Schr\"odinger equation does not admit local Birkhoff coordinates. The proof is based on the construction of a local normal form of the linearization of the equation at such potentials.
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