35 citations · 235 across the 38 of their papers we have counts for
39 papers
Parametrization of positroid cells by Dubrovin-Natanzon Cartier divisors on maximal Mumford curves
Simonetta Abenda, Petr G. Grinevich
We prove that each totally positive Schubert cell is a real component of Jacobian of the maximal Mumford () curve corresponding to the Le-graph of such cell. At this a…
The finite gap method and the periodic Cauchy problem of dimensional anomalous waves for the focusing Davey-Stewartson 2 equation
P. G. Grinevich, P. M. Santini
The focusing Nonlinear Schrödinger (NLS) equation is the simplest universal model describing the modulation instability (MI) of dimensional quasi monochromatic waves in weakl…
Geometric nature of relations on plabic graphs and totally non-negative Grassmannians
Simonetta Abenda, Petr G. Grinevich
The standard parametrization of totally non-negative Grassmannians was obtained by A. Postnikov [45] introducing the boundary measurement map in terms of discrete path integration…
Internal edge vectors on plabic networks in the disk and a generalization of Talaska formula
Simonetta Abenda, Petr G. Grinevich
Following [42], positroid cells ${\mathcal S}_{\mathcal M}^{\mbox{TNN}}$ in totally non-negative Grassmannians ${Gr^{\mbox{TNN}} (k,n)}$ admit parametrizations by positive weights…
The linear and nonlinear instability of the Akhmediev breather
P. G. Grinevich, P. M. Santini
The Akhmediev breather (AB) and its M-soliton generalization are exact solutions of the focusing NLS equation periodic in space and exponentially localized in time over the…
Real regular KP divisors on -curves and totally non-negative Grassmannians
Simonetta Abenda, Petr G. Grinevich
In this paper we construct an explicit map from planar bicolored (plabic) trivalent graphs representing a given irreducible positroid cell in the totally non-negative Grassmann…