  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.
