Explicit integration of the full symmetric Toda hierarchy and the sorting property

DOI10.1007/BF00400137zbMath0853.58062arXivsolv-int/9502006MaRDI QIDQ1915193

Yuji Kodama, Kenneth T.-R. McLaughlin

Publication date: 5 January 1997

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

Full work available at URL: https://arxiv.org/abs/solv-int/9502006

zbMATH Keywords

symmetryintegrationToda lattice hierarchysorting property

Mathematics Subject Classification ID

Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) Explicit solutions, first integrals of ordinary differential equations (34A05) Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests (37J35)

Related Items

Bruhat order in the full symmetric \(\mathfrak{sl}_n\) Toda lattice on partial flag space, Toda hierarchy with indefinite metric, Iso-spectral deformations of general matrix and their reductions on Lie algebras, Extensions of the finite nonperiodic Toda lattices with indefinite metrics, Generalizations of the finite nonperiodic Toda lattice and its Darboux transformation, The full integration of black hole solutions to symmetric supergravity theories, Laguerre ensemble: correlators, Hurwitz numbers and Hodge integrals, Black holes in supergravity and integrability, The full Kostant-Toda hierarchy on the positive flag variety, Integral and integrable algorithms for a nonlinear shallow-water wave equation, Fifty years of the finite nonperiodic Toda lattice: a geometric and topological viewpoint, Bruhat order in full symmetric Toda system, Toda lattices with indefinite metric. II: Topology of the iso-spectral manifolds

Cites Work

• The QR algorithm and scattering for the finite nonperiodic Toda lattice
• Ordinary Differential Equations and the Symmetric Eigenvalue Problem
• The toda flow on a generic orbit is integrable
• Isospectral Flows and Abstract Matrix Factorizations
• Finitely many mass points on the line under the influence of an exponential potential -- an integrable system
• On the Toda Lattice. II: Inverse-Scattering Solution