From solitons to many-body systems

DOI10.4310/PAMQ.2008.v4.n2.a3zbMath1153.37031arXivmath/0310490MaRDI QIDQ930812

David Ben-Zvi, Thomas A. Nevins

Publication date: 1 July 2008

Published in: Pure and Applied Mathematics Quarterly (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0310490

zbMATH Keywords

noncommutative geometrysolitonsHamiltonian systemmany-body systemKP hierarchyLax operatornoncommutative instantonsCalogero-Moser system\(\mathcal{D}\)-modules

Mathematics Subject Classification ID

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) Soliton equations (35Q51) Groups and algebras in quantum theory and relations with integrable systems (81R12) Relations of infinite-dimensional Hamiltonian and Lagrangian dynamical systems with algebraic geometry, complex analysis, and special functions (37K20) (n)-body problems (70F10)

Related Items

On the geometry of the Calogero-Moser system, Suzuki functor at the critical level, Elliptic Springer theory, Spin generalization of the Calogero–Moser hierarchy and the matrix KP hierarchy, Quantum Lax pairs via Dunkl and Cherednik operators, Time discretization of the spin Calogero-Moser model and the semi-discrete matrix KP hierarchy, On rational solutions of multicomponent and matrix KP hierarchies, Ideals of rings of differential operators on algebraic curves (with an appendix by George Wilson)., On a relative Fourier-Mukai transform on genus one fibrations, Geometry of Calogero-Moser systems, The geometry of Calogero-Moser systems.