# A continuous analog of the binary Darboux transformation for the Korteweg-de Vries equation

@inproceedings{Rybkin2022ACA, title={A continuous analog of the binary Darboux transformation for the Korteweg-de Vries equation}, author={Alexei Rybkin}, year={2022} }

In the KdV context we put forward a continuous version of the binary Darboux transformation (aka the double commutation method). Our appraoch 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…

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