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

Abenda, Simonetta ; Grinevich, Petr G.

Selecta mathematica (Basel, Switzerland), 2019-08, Vol.25 (3), p.1-64, Article 43 [Periódico revisado por pares]

Cham: Springer International Publishing

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  • Título:
    Reducible M-curves for Le-networks in the totally-nonnegative Grassmannian and KP-II multiline solitons
  • Autor: Abenda, Simonetta ; Grinevich, Petr G.
  • Assuntos: Algebra ; Mathematics ; Mathematics and Statistics ; Networks ; Parameterization ; Solitary waves
  • É parte de: Selecta mathematica (Basel, Switzerland), 2019-08, Vol.25 (3), p.1-64, Article 43
  • Descrição: 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 G r TNN ( k , n ) . In [ 3 ] we were able to construct real algebraic–geometric data for soliton data in the main cell G r TP ( k , n ) only. Here we do not just extend that construction to all points in G r TNN ( k , n ) , but we also considerably simplify it, since both the reducible rational M -curve Γ and the real regular KP divisor on Γ are directly related to the parametrization of positroid cells in G r TNN ( k , n ) via the Le-networks introduced in [ 63 ]. In particular, the direct relation of our construction to the Le-networks guarantees that the genus of the underlying smooth M -curve is minimal and it coincides with the dimension of the positroid cell in G r TNN ( k , n ) to which the soliton data belong to. Finally, we apply our construction to soliton data in G r TP ( 2 , 4 ) and we compare it with that in [ 3 ].
  • Editor: Cham: Springer International Publishing
  • Idioma: Inglês
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