Inverse scattering for reflectionless Schr\"odinger operators with integrable potentials and generalized soliton solutions for the KdV equation
Spectral Theory
2020-06-24 v1 Mathematical Physics
math.MP
Abstract
We give a complete characterisation of the reflectionless Schr\"odinger operators on the line with integrable potentials, solve the inverse scattering problem of reconstructing such potentials from the eigenvalues and norming constants, and derive the corresponding generalized soliton solutions of the Korteweg--de Vries equation
Keywords
Cite
@article{arxiv.2006.12782,
title = {Inverse scattering for reflectionless Schr\"odinger operators with integrable potentials and generalized soliton solutions for the KdV equation},
author = {Rostyslav Hryniv and Bohdan Melnyk and Yaroslav Mykytyuk},
journal= {arXiv preprint arXiv:2006.12782},
year = {2020}
}
Comments
35 pages