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Long-time Asymptotics for the NLS equation via dbar methods
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We present a new method for obtaining sharp asymptotics of solutions of the defocussing nonlinear Schr\"odinger (NLS) equation, based on dbar methods and under essentially minimal regularity assumptions on initial data.
Forward citations
Cited by 3 Pith papers
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Large-time asymptotics for the defocusing Manakov system on a nonzero background
The defocusing Manakov system on a nonzero background has long-time soliton-region asymptotics given by a modulated N-soliton plus an explicit t^{-1/2} radiation correction.
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Soliton resolution for the coupled complex short pulse equation
For the coupled complex short pulse equation, long-time solutions split into self-symmetric solitons or composite breathers plus t^{-1/2} radiation, with O(t^{-1} ln t) errors, while the opposite sector decays as O(t^{-1}).
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Asymptotic stability of solutions to the good Boussinesq equation in dispersive wave region
Long-time asymptotics of the good Boussinesq equation are obtained via Dbar-steepest descent for reflection coefficients in H^{3,4}, yielding an optimal O(t^{-3/4}) error and asymptotic stability in the dispersive region.
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