Reducible M-curves for Le-networks in the totally-nonnegative Grassmannian and KP-II multiline solitons

@article{Abenda2018ReducibleMF,
  title={Reducible M-curves for Le-networks in the totally-nonnegative Grassmannian and KP-II multiline solitons},
  author={Simonetta Abenda and P. G. Grinevich},
  journal={Selecta Mathematica},
  year={2018},
  volume={25},
  pages={1-64}
}
We associate real and regular algebraic–geometric data to each multi-line soliton solution of Kadomtsev–Petviashvili II (KP) equation. These solutions are known to be parametrized by points of the totally non-negative part of real Grassmannians $$Gr^{\mathrm{TNN}}(k,n)$$GrTNN(k,n). In [3] we were able to construct real algebraic–geometric data for soliton data in the main cell $$Gr^{\mathrm{TP}} (k,n)$$GrTP(k,n) only. Here we do not just extend that construction to all points in $$Gr^{\mathrm… 

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