Inverse scattering problem for third order differential operators on the whole axis
Classical Analysis and ODEs
2024-06-13 v1 Mathematical Physics
math.MP
Abstract
Inverse scattering problem for an operator, which is a sum of the operator of the third derivative and of an operator of multiplication by a real function, is solved. The main closed system of equations of inverse problem is obtained. This system contains scattering coefficients and bound state elements as independent parameters. Form of the simplest reflectionless potential (analogous to soliton) is found.
Cite
@article{arxiv.2406.07947,
title = {Inverse scattering problem for third order differential operators on the whole axis},
author = {V. A. Zolotarev},
journal= {arXiv preprint arXiv:2406.07947},
year = {2024}
}