The inverse scattering transform for weak Wigner-von Neumann type potentials

Abstract

In the context of the Cauchy problem for the Korteweg-de Vries equation we extend the inverse scattering transform to initial data that behave at plus infinity like a sum of Wigner-von Neumann type potentials with small coupling constants. Our arguments are based on the theory of Hankel operators.

arXiv commentTo appear in Nonlinearity

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• Long-Time Asymptotics for the Korteweg-de Vries Equation via Nonlinear Steepest Descent
• On the inverse scattering problem for Jacobi matrices with the spectrum on an interval, a finite system of intervals or a Cantor set of positive length
• Almost Periodicity in Time of Solutions of the KdV Equation
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Cited by in corpus (1)

• Norming constants of embedded bound states and bounded positon solutions of the Korteweg-de Vries equation