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Reducible M-curves for Le-networks in the totally-nonnegative Grassmannian and KP-II multiline solitonsстатья
- Авторы: Abenda Simonetta, Grinevich Petr G.
- Журнал: Selecta Mathematica
- Том: 25
- Номер: 3
- Год издания: 2019
- DOI: 10.1007/s00029-019-0488-5
- Аннотация: 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^{TNN}(k, n). In [3] we were able to construct real algebraic–geometric data for soliton data in the main cell Gr TP (k, n) only. Here we do not just extend that construction to all points in Gr^{TNN}(k, n), but we also considerably simplify it, since both the reducible rational M-curve Gamma and the real regular KP divisor on Gamma are directly related to the parametrization of positroid cells in Gr^{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 Gr^{TNN}(k, n) to which the soliton data belong to. Finally, we apply our construction to soliton data in Gr^{TP}(2, 4) and we compare it with that in [3].
- Добавил в систему: Гриневич Петр Георгиевич