Classical and quantum mechanical systems of Toda-lattice type. II: Solutions of the classical flows

DOI10.1007/BF01209301zbMath0592.58028WikidataQ125288638 ScholiaQ125288638MaRDI QIDQ1075665

Roe Goodman, Nolan R. Wallach

Publication date: 1984

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

zbMATH Keywords

Euler equationroot systemToda latticeequationBanach-Lie groupIwasawa decompositionLaxquantum-mechanical Hamiltonian

Mathematics Subject Classification ID

Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) Hamilton's equations (70H05) Applications of Lie groups to the sciences; explicit representations (22E70) Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests (37J35) Dynamical aspects of finite-dimensional Hamiltonian and Lagrangian systems (37J99)

Related Items (22)

Reflection positivity for the complementary series of SL(2n, \({\mathbb{C}})\) ⋮ Bogoyavlensky-Volterra and Birkhoff integrable systems ⋮ Symmetries, conserved quantities, and hierarchies for some lattice systems with soliton structure ⋮ Associated integrable systems ⋮ Relativistic Toda systems ⋮ The integration of semi-infinite Toda chain by means of inverse spectral problem ⋮ Spherically symmetric dyonic solutions for vacuum Einstein equations in 4+K dimensions ⋮ Asymptotic expansions of matrix coefficients of Whittaker vectors at irregular singularities ⋮ Lie algebraic aspects of the finite nonperiodic Toda flows ⋮ QR-type factorizations, the Yang-Baxter equation, and an eigenvalue problem of control theory ⋮ Extended Schur's \(Q\)-functions and the full Kostant-Toda hierarchy on the Lie algebra of type \(D\) ⋮ On an integrable case of Kozlov-Treshchev Birkhoff integrable potentials ⋮ Variétés de drapeaux et réseaux de Toda. (Flag manifolds and Toda lattices) ⋮ Elementary Toda orbits and integrable lattices ⋮ Unitarity of the SoV transform for the Toda chain ⋮ Toda Flows and Isospectral Manifolds ⋮ A convexity theorem for isospectral manifolds of Jacobi matrices in a compact Lie algebra ⋮ Classical and quantum mechanical systems of Toda-lattice type. III: Joint eigenfunctions of the quantized systems ⋮ Toda flows and real Hessenberg manifolds ⋮ Construction of canonical coordinates on polarized coadjoint orbits of Lie groups ⋮ Limit matrices for the Toda flow and periodic flags for loop groups ⋮ Integrable Hamiltonians with exponential potential

Cites Work

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• Classical and quantum-mechanical systems of Toda lattice type. I
• Three integrable Hamiltonian systems connected with isospectral deformations
• On a trace functional for formal pseudo-differential operators and the symplectic structure of the Korteweg-deVries type equations
• Structure and unitary cocycle representations of loop groups and the group of diffeomorphisms of the circle.
• The minimal orbit in a simple Lie algebra and its associated maximal ideal
• Explicit solutions of classical generalized Toda models

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