Hyperelliptic tangential covers and finite-gap potentials

This paper is devoted to the study of finite-gap potentials that can be expressed in terms of elliptic functions. New elliptic finite-gap potentials and new elliptic solitons of the KdV equation are found. A step is taken towards the study of relationships connecting elliptic KdV solitons, elliptic finite-gap potentials, and the Jacobians of the associated spectral curves.