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Abstract In the Korteweg–de Vries equation (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 same benefits as the classical binary Darboux transformation does.
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The binary Darboux transformation revisited and KdV solitons on arbitrary short‐range backgrounds
Abstract In the KdV context, we revisit the classical Darboux transformation in the framework of the vector Riemann–Hilbert problem. This readily yields a version of the binary Darboux transformation providing a short‐cut to explicit formulas for solitons traveling on a wide range of background solutions. Our approach also links the binary Darboux transformation and the double commutation method.
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- Award ID(s):
- 2009980
- PAR ID:
- 10361295
- Publisher / Repository:
- Wiley-Blackwell
- Date Published:
- Journal Name:
- Studies in Applied Mathematics
- Volume:
- 148
- Issue:
- 1
- ISSN:
- 0022-2526
- Page Range / eLocation ID:
- p. 141-153
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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