2018/12/26 by Nabelek, Patrik, Zakharov, Dmitry, Zakharov, Vladimir · 1 citation
#Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Physical sciences
paper · doi:10.48550/arxiv.1812.10545
The concept of a primitive potential for the Schroedinger operator on the line was introduced in [2,3,4]. Such a potential is determined by a pair of positive functions on a finite interval, called the dressing functions, which are not uniquely determined by the potential. The potential is constructed by solving a contour problem on the complex plane. In this paper, we consider a reduction where the dressing functions are equal. We show that in this case, the resulting potential is symmetric, and describe how to analytically compute the potential as a power series. In addition, we establish that if the dressing functions are both equal to one, then the resulting primitive potential is the elliptic one-gap potential.