Elliptic solutions of nonlinear equations (Q1814069)

From the introduction: Methods of the finite-gap integration enable to find exact solutions to many equations of mathematical physics (Korteweg--de Vries, Kadomtsev-Petviashvili, etc.), which can be expressed by means of theta-functions of algebraic curves. In Section 1, a method is shown for a construction of curves whose theta-functions are reduced to one-dimensional ones. The method is based on an explicit evaluation of the Prym manifolds. Solutions to nonlinear equations, which correspond to such curves, are expressed in terms of elliptic functions. In Section 2, a family of elliptic potentials is constructed, which is dense in a certain one-dimensional set of two-gap potentials.