Generalized primitive potentials
Abstract
In our previous work, we introduced a new class of bounded potentials of the onedimensional Schrödinger operator on the real axis, and a corresponding family of solutions of the KdV hierarchy. These potentials, which we call primitive, are obtained as limits of rapidly decreasing reflectionless potentials, or multisoliton solutions of KdV. In this note, we introduce generalized primitive potentials, which are obtained as limits of all rapidly decreasing potentials of the Schrödinger operator. These potentials are constructed by solving a contour problem, and are determined by a pair of positive functions on a finite interval and a functional parameter on the real axis.
 Publication:

arXiv eprints
 Pub Date:
 July 2019
 DOI:
 10.48550/arXiv.1907.05038
 arXiv:
 arXiv:1907.05038
 Bibcode:
 2019arXiv190705038Z
 Keywords:

 Nonlinear Sciences  Exactly Solvable and Integrable Systems
 EPrint:
 10 pages