An explicit characterization of Calogero–Moser systems

DOI10.1090/S0002-9947-05-03886-9zbMath1082.37065arXivnlin/0305057OpenAlexW1874715226MaRDI QIDQ5705525

Rudi Weikard, Karl Unterkofler, Friedrich Gesztesy

Publication date: 9 November 2005

Published in: Transactions of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/nlin/0305057

zbMATH Keywords

periodic solutionsKdV equationnonlinear evolution equationshierarchyelliptic solutionsAMM and DG lociCalogero-Moses systemsmeromorphic fundamental system

Mathematics Subject Classification ID

Periodic solutions to ordinary differential equations (34C25) Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) KdV equations (Korteweg-de Vries equations) (35Q53) Relations of infinite-dimensional Hamiltonian and Lagrangian dynamical systems with algebraic geometry, complex analysis, and special functions (37K20) Entire and meromorphic solutions to ordinary differential equations in the complex domain (34M05) Elliptic functions and integrals (33E05)

Related Items (11)

The AKNS hierarchy and finite-gap Schrödinger potentials ⋮ The inverse scattering transform for the KdV equation with step-like singular Miura initial profiles ⋮ A necessary and sufficient condition for the Darboux-Treibich-Verdier potential with its spectrum contained in $\mathbb{R}$ ⋮ Polynomial sequences related to point vortex equilibria with three strengths ⋮ Finite-gap solutions of the Fuchsian equations ⋮ A short proof of the Gaillard-Matveev theorem based on shape invariance arguments ⋮ Singular fiber of the Mumford system and rational solutions to the KdV hierarchy ⋮ On algebro-geometric simply-periodic solutions of the KdV hierarchy ⋮ On the poles of Picard potentials ⋮ Spatial Analyticity of Solutions to Integrable Systems. I. The KdV Case ⋮ Soliton Theory and Hankel Operators

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Differential equations in the spectral parameter
• Verdier elliptic solitons and the Weierstrass theory of reduction
• Tangential polynomials and elliptic solitons
• Elliptic solutions of the Korteweg-de Vries equation
• On the Darboux transformation of the second order differential operator of Fuchsian type on the Riemann sphere
• Rational solutions for the equation of commutation of differential operators
• An algebro-geometric interpretation of the Bäcklund-transformation for the Korteweg-de Vries equation
• Loop groups and equations of KdV type
• Collisions of Calogero-Moser particles and an adelic Grassmannian (with an appendix by I. G. Macdonald)
• Trace formula for a system of particles with elliptic potential
• On a class of polynomials connected with the Korteweg-de Vries equation
• Exceptional coverings and sums of 4 triangular numbers
• A system of particles equivalent to solitons
• Examples of commutative rings of differential operators
• Rational solutions of the Kadomtsev-Petviashvili equation and integrable systems of \(n\) particles on a line
• A characterization of all elliptic algebro-geometric solutions of the AKNS hierarchy
• On rational and periodic solutions of stationary KdV equations
• Spectral characteristics of elliptic solitons
• Elliptic solutions of nonlinear integrable equations and related topics
• New elliptic potentials
• On the geometry of elliptic solitons
• Reduction of theta functions and elliptic finite-gap potentials
• On the two-gap elliptic potentials
• Finite-gap elliptic solutions of the KdV equation
• Integrable systems: the Verdier memorial conference. Actes du colloque international de Luminy, France, July 1-5, 1991
• Picard potential and Hill's equation on a torus
• Matrix elliptic solitons
• Reflectionless Schrödinger operators, the dynamics of zeros, and the solitonic Sato formula
• Pole dynamics for elliptic solutions of the Korteweg-de Vries equation
• On a theorem of Halphen and its application to integrable systems
• Elliptic families of solutions of the Kadomtsev-Petviashvili equation, and the field analogue of the elliptic Calogero-Moser system
• Elliptic solutions of nonlinear equations
• On Picard potentials
• Treibich-Verdier potentials and the stationary (m)KdV hierarchy
• Bispectral KP solutions and linearization of Calogero-Moser particle systems
• Varieties of elliptic solitons
• Solitons and rational solutions of nonlinear evolution equations
• Isospectral deformations of elliptic potentials
• An Example of Blow-Up, for the Complex K<scp>d</scp>V Equation and Existence Beyond the Blow-Up
• Meromorphic solutions of nonlinear partial differential equations and many-particle completely integrable systems
• Rational and elliptic solutions of the korteweg-de vries equation and a related many-body problem
• Elliptic algebro-geometric solutions of the KdV and AKNS hierarchies - an analytic approach
• Rational solutions of the Kadomtsev–Petviashvili hierarchy and the dynamics of their poles. I. New form of a general rational solution
• Calogero–Moser hierarchy and KP hierarchy
• Au-delà des potentiels et revêtements tangentiels hyperelliptiques exceptionnels
• On a theorem of Picard
• Elliptic Calogero–Moser systems and isomonodromic deformations
• On the explicit solutions of the elliptic Calogero system
• Darboux-type transformations and hyperelliptic curves
• Floquet theory for linear differential equations with meromorphic solutions
• (m)KdV solitons on the background of quasi-periodic finite-gap solutions
• Lamé Potentials and the Stationary (m)KdV Hierarchy
• On the two-gap locus for the elliptic Calogero-Moser model
• Abelian solitons
• The dynamics of zeros of finite-gap solutions of the Schrödinger equation

This page was built for publication: An explicit characterization of Calogero–Moser systems