Extension of the class of integrable dynamical systems connected with semisimple Lie algebras

DOI10.1007/BF00398546zbMath0573.58016OpenAlexW2019159791MaRDI QIDQ1063305

V. I. Inozemtsev, D. V. Meshcheryakov

Publication date: 1985

Published in: Letters in Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf00398546

zbMATH Keywords

semisimple Lie algebrascompletely integrable systems

Mathematics Subject Classification ID

Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) Infinite-dimensional Lie (super)algebras (17B65) Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests (37J35)

Related Items (22)

TWO QUITE SIMILAR MATRIX ODES AND THE MANY-BODY PROBLEMS RELATED TO THEM ⋮ A class of Calogero type reductions of free motion on a simple Lie group ⋮ A class of completely integrable quantum systems associated with classical root systems ⋮ Duality between the trigonometricBC_nSutherland system and a completed rational Ruijsenaars–Schneider–van Diejen system ⋮ Difference Calogero–Moser systems and finite Toda chains ⋮ The finite Toda lattices ⋮ On Hamiltonian systems in two degrees of freedom with invariants quartic in the momenta of form p21p22⋅⋅⋅ ⋮ Integrability of difference Calogero–Moser systems ⋮ Takasaki’s rational fourth Painlevé-Calogero system and geometric regularisability of algebro-Painlevé equations ⋮ A family of quasi-solvable quantum many-body systems ⋮ Hamiltonian reductions in matrix Painlevé systems ⋮ Scattering theory of the hyperbolic \(BC_n\) Sutherland and the rational \(BC_n\) Ruijsenaars-Schneider-Van Diejen models ⋮ Separability and Lax pairs for the two-dimensional Hamiltonian system with a quartic potential ⋮ \(\mathfrak{sl}(M+1)\) construction of quasi-solvable quantum \(M\)-body systems. ⋮ Lax formalism for a family of integrable Calogero-Moser related \(n\)-particle systems ⋮ A many-body generalization of quasi-solvable models with type C \(\mathcal N\)-foldsupersymmetry. I: regular cases ⋮ Matrix analogues of elliptic functions ⋮ Lax representation with spectral parameter on a torus for integrable particle systems ⋮ An integrable many-body problem ⋮ A new construction of quasi-solvable quantum many-body systems of deformed Calogero-Sutherland type ⋮ On the r-matrix structure of the hyperbolic BC n Sutherland model ⋮ A new model in the Calogero-Ruijsenaars family

Cites Work

• Similarity, Bäcklund transformations and rational solutions
• Three integrable Hamiltonian systems connected with isospectral deformations
• Completely integrable classical systems connected with semisimple Lie algebras
• Some finite dimensional integrable systems and their scattering behavior
• Rational and elliptic solutions of the korteweg-de vries equation and a related many-body problem

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