The concept of a primitive potential for the Schrödinger 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.
|Original language||English (US)|
|State||Published - Dec 26 2018|
- Integrable systems
- Primitive potentials
- Schrödinger equation
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