Multisoliton KP-2 solutions and degenerate M-curves

Multiline solitons of the KP-2 equations can be constructed using the Darboux transformations. But they also can be obtained as degeneration of the finite-gap solutions. If one wants to obtain physically relevant regular real-valued solutions it is necessary to use totally-positive Grassmannians in the Darboux transformation and M-curves in the finite-gap approach. We construct a bridge between these two approaches.