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

DOI10.1007/s00029-019-0488-5zbMath1426.37052arXiv1805.05641OpenAlexW2963397360WikidataQ127636112 ScholiaQ127636112MaRDI QIDQ2424714

Simonetta Abenda, Petr G. Grinevich

Publication date: 25 June 2019

Published in: Selecta Mathematica. New Series (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1805.05641

zbMATH Keywords

Baker-Akhiezer functionGrassmannianssolitonstotal positivityDarboux transformationKP hierarchyYoung diagramsPlücker coordinatesSchubert cellsIts-Matveev formulaplanar bicolored networksPostnikov networksSato divisor

Mathematics Subject Classification ID

Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) Grassmannians, Schubert varieties, flag manifolds (14M15) Plane and space curves (14H50) Soliton equations (35Q51) Relationships between algebraic curves and integrable systems (14H70) Relations of infinite-dimensional Hamiltonian and Lagrangian dynamical systems with algebraic geometry, complex analysis, and special functions (37K20) Soliton theory, asymptotic behavior of solutions of infinite-dimensional Hamiltonian systems (37K40) Postnikov systems, (k)-invariants (55S45) Synthetic treatment of fundamental manifolds in projective geometries (Grassmannians, Veronesians and their generalizations) (51M35) Soliton solutions (35C08)

Related Items

On reducible degeneration of hyperelliptic curves and soliton solutions ⋮ Edge vectors on plabic networks in the disk and amalgamation of totally non-negative Grassmannians ⋮ Nonlinear algebra and applications ⋮ The direct scattering problem for perturbed Kadomtsev–Petviashvili multi line solitons ⋮ Real soliton lattices of the Kadomtsev-Petviashvili II equation and desingularization of spectral curves: the \(\mathrm{Gr}^{\mathrm{TP}}(2, 4)\) case ⋮ Kasteleyn theorem, geometric signatures and KP-II divisors on planar bipartite networks in the disk ⋮ Real regular KP divisors on \({\texttt{M}}\)-curves and totally non-negative Grassmannians

Cites Work

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• KP solitons and total positivity for the Grassmannian
• Matching polytopes, toric geometry, and the totally non-negative Grassmannian.
• Combinatorial geometries, convex polyhedra, and Schubert cells
• Spectral theory of finite-zone nonstationary Schrödinger operators. A nonstationary Peierls model
• Some comments on the rational solutions of the Zakharov-Schabat equations
• The periodic problem for the Korteweg-de Vries equation
• A scheme for integrating the nonlinear equations of mathematical physics by the method of the inverse scattering problem. I
• Integration of nonlinear equations by the methods of algebraic geometry
• An algebraic cell decomposition of the nonnegative part of a flag variety
• Rational degenerations of \({\mathtt M}\)-curves, totally positive Grassmannians and KP2-solitons
• Real soliton lattices of the Kadomtsev-Petviashvili II equation and desingularization of spectral curves: the \(\mathrm{Gr}^{\mathrm{TP}}(2, 4)\) case
• On a family of KP multi-line solitons associated to rational degenerations of real hyperelliptic curves and to the finite non-periodic Toda hierarchy
• Riemann-Roch and Abel-Jacobi theory on a finite graph
• On some properties of KP-II soliton divisors in \(Gr^{\mathrm{TP}} (2,4)\)
• The Deodhar decomposition of the Grassmannian and the regularity of KP solitons
• Moduli spaces of local systems and higher Teichmüller theory
• Dimers and amoebae
• Towards an inverse scattering theory for non-decaying potentials of the heat equation
• Cluster algebras I: Foundations
• Grassmannian Geometry of Scattering Amplitudes
• On determinants of modified Bessel functions and entire solutions of double confluent Heun equations
• Singular spectral curves in finite-gap integration
• KP solitons in shallow water
• KP line solitons and Tamari lattices
• Geometry of Algebraic Curves
• Soliton solutions of the Kadomtsev-Petviashvili II equation
• Spectral theory of two-dimensional periodic operators and its applications
• A Formula for Plucker Coordinates Associated with a Planar Network
• Classification of the line-soliton solutions of KPII
• Soliton Solutions of the KP Equation and Application to Shallow Water Waves
• Soliton solutions of the Korteweg de Vries and the Kadomtsev-Petviashvili equations: the Wronskian technique
• Combinatorial geometries and torus strata on homogeneous compact manifolds
• REAL THETA-FUNCTION SOLUTIONS OF THE KADOMTSEV–PETVIASHVILI EQUATION
• A class of exact solutions of the Kadomtsev-Petviashvili equation
• THE TOPOLOGY OF REAL PROJECTIVE ALGEBRAIC VARIETIES
• Double Bruhat cells and total positivity
• The τ‐function of the universal whitham hierarchy, matrix models and topological field theories
• Moduli of real algebraic surfaces, and their superanalogues. Differentials, spinors, and Jacobians of real curves
• Twistor theory at fifty: from contour integrals to twistor strings
• Young diagrams and N-soliton solutions of the KP equation
• Toric topology of the complex Grassmann manifolds
• Vertex dynamics in multi-soliton solutions of Kadomtsev–Petviashvili II equation
• Total positivity, Grassmannian and modified Bessel functions
• Topology and geometry of the canonical action of $T^4$ on the complex Grassmannian $G_{4,2}$ and the complex projective space $CP^{5}$
• Dimers and cluster integrable systems
• Tropical algebraic geometry
• Dynamical systems. IV. Symplectic geometry and its applications. Transl. from the Russian by G. Wassermann.