KdV equation beyond standard assumptions on initial data

Abstract

We show that the Cauchy problem for the KdV equation can be solved by the inverse scattering transform (IST) for any initial data bounded from below, decaying sufficiently rapidly at plus infinity, but unrestricted otherwise. Thus our approach doesn't require any boundary condition at minus infinity.

To appear in Physica D: nonlinear phenomena

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Cited by in corpus (5)

• Nonautonomous symmetries of the KdV equation and step-like solutions
• Global well-posedness for $H^{-1}(\mathbb{R})$ perturbations of KdV with exotic spatial asymptotics
• KdV on an incoming tide
• The effect of a positive bound state on the KdV solution. A case study
• The conservative Camassa-Holm flow with step-like irregular initial data