Calogero-Moser hierarchy and KP hierarchy

Abstract

The space of solutions of the rational Calogero-Moser hierarchy, and the space of solutions of the KP hierarchy whose tau functions are monic polynomials in $t_1$ with coefficients depending on $t_n$, $n>1$, are identified, generalizing earlier results of Airault-McKean-Moser and Krichever.

8pages

Cited by in corpus (35)

• On Double-Elliptic Integrable Systems. 1. A Duality Argument for the case of SU(2)
• Generalized orthogonal polynomials, discrete KP and Riemann-Hilbert problems
• Bispectral KP Solutions and Linearization of Calogero-Moser Particle Systems
• Commuting Hamiltonians from Seiberg-Witten Theta-Functions
• Kadomtsev-Petviashvili turning points and CKP hierarchy
• Elliptic solutions to integrable nonlinear equations and many-body systems
• Affine Toda Solitons and Systems of Calogero-Moser Type
• The master T-operator for the Gaudin model and the KP hierarchy
• Dynamics of KPI lumps
• Spin Calogero Particles and Bispectral Solutions of the Matrix KP Hierarchy
• Supersymmetric quantum spin chains and classical integrable systems
• Rational Ruijsenaars-Schneider hierarchy and bispectral difference operators
• On complete solution of the quantum Dell system
• Constrained Toda hierarchy and turning points of the Ruijsenaars-Schneider model
• The Master T-Operator for Inhomogeneous XXX Spin Chain and mKP Hierarchy
• KP hierarchy and trigonometric Calogero-Moser hierarchy
• Bethe ansatz and Hirota equation in integrable models
• D-Bundles and Integrable Hierarchies
• Spin generalization of the Calogero-Moser hierarchy and the matrix KP hierarchy
• Time discretization of the spin Calogero-Moser model and the semi-discrete matrix KP hierarchy
• From solitons to many-body systems
• Elliptic solutions to the KP hierarchy and elliptic Calogero-Moser model
• Toda lattice hierarchy and trigonometric Ruijsenaars-Schneider hierarchy
• Elliptic solutions to matrix KP hierarchy and spin generalization of elliptic Calogero-Moser model
• Calogero-Moser pairs and the Airy and Bessel bispectral involutions
• Matrix KP hierarchy and spin generalization of trigonometric Calogero-Moser hierarchy
• Quantum Gaudin model and classical KP hierarchy
• Incarnations of XXX $\widehat{{\mathfrak{sl}}_N}$ Bethe ansatz equations and integrable hierarchies
• Elliptic solutions to Toda lattice hierarchy and elliptic Ruijsenaars-Schneider model
• An Explicit Characterization of Calogero--Moser Systems
• On a Theorem of Halphen and its Application to Integrable Systems
• Elliptic Algebro-Geometric Solutions of the KdV and AKNS Hierarchies - An Analytic Approach
• Higher-order heat equation and the Gelfand-Dickey hierarchy
• On the Quantization of a Self-Dual Integrable System
• Cusps and $\D$-Modules