Affiliation:
1. Department of Mathematics and Statistics University of Alaska Fairbanks Fairbanks Alaska USA
Abstract
AbstractIn 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.
Funder
National Science Foundation
Isaac Newton Institute for Mathematical Sciences
Engineering and Physical Sciences Research Council
Reference57 articles.
1. Solitons, Nonlinear Evolution Equations and Inverse Scattering
2. Explicit solutions to the Korteweg–de Vries equation on the half line
3. The binary Darboux transform for the Toda lattice;Babich MV;Zap. Nauchn. Sem. Leningrad. Otdel. Mat. Inst. Steklov. (LOMI),1985
4. Algebraic construction of the Darboux matrix revisited;Cieslinski JL.;J Phys A,2009
5. Nonuniqueness for solutions of the Korteweg-de Vries equation