On classical solutions of the KdV equation

Sergei M. Grudsky, Alexei Rybkin

Type: Article

Publication Date: 2020-04-04

Citations: 23

DOI: https://doi.org/10.1112/plms.12326

Abstract

We show that if the initial profile q ( x ) for the Korteweg-de Vries (KdV) equation is essentially semibounded from below and ∫ ∞ x 5 / 2 | q ( x ) | d x < ∞ , (no decay at − ∞ is required) then the KdV has a unique global classical solution given by a determinant formula. This result is best known to date.

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Proceedings of the London Mathematical Society - View
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+	Hankel Operators and Their Applications	2003	Vladimir Peller
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+ PDF Chat	Spatial Analyticity of Solutions to Integrable Systems. I. The KdV Case	2013	Alexei Rybkin
+	The fredholm determinant method for the KdV equations	1984	Christoph Pöppe
+	Inverse scattering on the line	1979	Percy Deift Eugene Trubowitz
+	The Inverse Problem in the Quantum Theory of Scattering	1963	L. D. Faddeyev Bernard D. Seckler
+	ASYMPTOTIC APPROXIMATIONS TO INTEGRALS	1980