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Abstract We consider the derivative nonlinear Schrödinger equation in one spatial dimension, which is known to be completely integrable. We prove that the orbits of $L^2$ bounded and equicontinuous sets of initial data remain bounded and equicontinuous, not only under this flow, but also under the entire hierarchy. This allows us to remove the small-data restriction from prior conservation laws and global well-posedness results.more » « less
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