On positive type initial profiles for the KdV equation

Grudsky, Sergei; Rybkin, Alexei

doi:10.1090/S0002-9939-2014-11943-5

On positive type initial profiles for the KdV equation
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by Sergei Grudsky and Alexei Rybkin PDF

Proc. Amer. Math. Soc. 142 (2014), 2079-2086 Request permission

Abstract:

We show that the KdV flow evolves any real locally integrable initial profile $q$ of the form $q=r^{\prime }+r^{2}$, where $r\in L_{\operatorname {loc}}^{2}$, $r|_{\mathbb {R}_{+}}=0$ into a meromorphic function with no real poles.

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