Abstract
We show that under the Korteweg–de Vries flow an initial profile supported on (−∞, 0) from a very broad function class (without any decay assumption) instantaneously evolves into a meromorphic function with no poles on the real line. Our treatment is based on a suitable modification of the inverse scattering transform and a detailed investigation of the Titchmarsh–Weyl m-function. As a by-product, we improve some related results of others.
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