ИСТИНА

It is well-known that real regular mutliline soliton solutions of the Kadomtsev-Petviashvili-II equation can be constructed using two different approaches: 1) By applying the Darboux transformation associated to a point of totally non-negative Grassmannian; 2) By degenerating real regular finite-gap solutions, associated to the so-called M-curves (Riemann surfaces equipped with antiholomoprhic involution with maximal possible number of real ovals). Both objects – totally non-negative Grassmannians and M-curves arise in many areas of mathematics, but, at first sight, they are not connected. In other words, how to associate a degenerate M-curve with a divisor to a point of Grassmannian with non-negative Plücker coordinates? We show that a bridge between these two objects can be constructed using the parametrization of totally non-negative Grassmannians in terms of Le-networks suggested by Alexander Postnikov. This parametrization was, in particular, used in the study of on-shell Yang-Mills scattering amplitude.