A continuous analog of the binary Darboux transformation for the KdV equation

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• Alexei Rybkin (University of Alaska Fairbanks)
• Wednesday 19 October 2022, 11:00-11:30
• Seminar Room 1, Newton Institute.

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HY2W04 - Statistical mechanics, integrability and dispersive hydrodynamics

In the KdV context we put forward a continuous version of the binary Darboux transformation (aka the double commutation method). Our approach is based on the Riemann-Hilbert problem and yields a new explicit formula for perturbation of the negative spectrum of a wide class of step-type potentials without changing the rest of the scattering data. This extends the previously known formulas for inserting/removing finitely many bound states to arbitrary sets of negative spectrum of arbitrary nature. In the KdV context our method offers the same benefits as the classical binary Darboux transformation does.

This talk is part of the Isaac Newton Institute Seminar Series series.

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