Non-compact symmetric spaces and the Toda molecule equations

DOI10.1007/BF01240353zbMath0583.58013OpenAlexW2015349784MaRDI QIDQ1069189

David I. Olive, Luiz Agostinho Ferreira

Publication date: 1985

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

Full work available at URL: https://doi.org/10.1007/bf01240353

zbMATH Keywords

symmetric spacesintegrabilityYang-Baxter equationsToda equationsfundamental Poisson bracket relation

Mathematics Subject Classification ID

Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests (37J35) Partial differential equations of mathematical physics and other areas of application (35Q99)

Related Items

Regularization of Toda lattices by Hamiltonian reduction, Black holes as generalised Toda molecules, Black holes in supergravity and integrability, Generalised Eisenhart lift of the Toda chain, Exact vortex solutions in a \(\mathbb{CP}^{N}\) Skyrme-Faddeev type model, Solutions to higher Hamiltonians in the Toda hierarchies, Solitons, \(\tau\)-functions and Hamiltonian reduction for non-abelian conformal affine Toda theories., Kac-Moody construction of Toda type field theories., Construction of trigonometric Toda \(r\)-matrices via a Hamiltonian reduction of the cotangent bundle over loop groups

Cites Work

• Unnamed Item
• Unnamed Item
• Representation of zero curvature for the system of nonlinear partial differential equations \(x_{\alpha,z\bar z}=\exp(kx)_\alpha\) and its integrability
• Solitons and infinite dimensional Lie algebras
• The solution to a generalized Toda lattice and representation theory
• Partition function of the eight-vertex lattice model
• Some Exact Results for the Many-Body Problem in one Dimension with Repulsive Delta-Function Interaction
• Integrals of nonlinear equations of evolution and solitary waves
• Explicit solutions of classical generalized Toda models