On symmetric primitive potentials

Patrik Nabelek; Dmitry Zakharov; Vladimir Zakharov

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arXiv · 1812.10545

On symmetric primitive potentials

Patrik Nabelek·Dmitry Zakharov·Vladimir Zakharov

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Abstract

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.

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Patrik Nabelek, Dmitry Zakharov, Vladimir Zakharov. 2018-12-26. On symmetric primitive potentials. https://arxiv.org/abs/1812.10545

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