Explicit solutions of classical generalized Toda models

DOI10.1007/BF01390233zbMath0419.58008MaRDI QIDQ5904180

A. M. Perelomov, Mikhail A. Olshanetsky

Publication date: 1979

Published in: Inventiones Mathematicae (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/142682

zbMATH Keywords

generalized Toda modelsgeodesic flows on symmetric spacesN-body Toda modelroot systems of simple Lie algebras

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) Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests (37J35) Dynamical aspects of finite-dimensional Hamiltonian and Lagrangian systems (37J99) Geometric quantization (53D50) (n)-body problems (70F10)

Related Items

Multidimensional classical and quantum cosmology with intersecting p-branes, Bogoyavlensky-Volterra and Birkhoff integrable systems, Duality identities for moduli functions of generalized Melvin solutions related to classical Lie algebras of rank 4, Relativistic Toda systems, MULTIPLE HAMILTONIAN STRUCTURE OF BOGOYAVLENSKY–TODA LATTICES, Integrability of multicomponent models in multidimensional cosmology, The finite Toda lattices, Lax pairs, symmetries and recursion operators for Toda lattices, Action-angle map and duality for the open Toda lattice in the perspective of Hamiltonian reduction, Multiple Hamiltonian structures for Toda-type systems, On generalized Melvin's solutions for Lie algebras of rank 2, Integrable pseudo-Euclidean Toda-like systems in multidimensional cosmology with multicomponent perfect fluid, Reduction and realization in Toda and Volterra, On an integrable case of Kozlov-Treshchev Birkhoff integrable potentials, Classical and quantum-mechanical systems of Toda lattice type. I, The Toda lattice, Dynkin diagrams, singularities and Abelian varieties, Black brane solutions governed by fluxbrane polynomials, Intermediate Toda systems, Variétés de drapeaux et réseaux de Toda. (Flag manifolds and Toda lattices), On generalized Melvin solutions for Lie algebras of rank 3, Moduli space theory for the Allen-Cahn equation in the plane, Unnamed Item, Toda systems and exponents of simple Lie groups, Multidimensional gravity, flux and black brane solutions governed by polynomials, Non-integrability of Gross-Neveu systems, On multidimensional analogs of Melvin's solution for classical series of Lie algebras, Reduction of Hamiltonian systems, affine Lie algebras and Lax equations, Integrable Hamiltonian systems connected with graded Lie algebras, Explicit solutions of superized Toda lattices, Group theory approach to the \(\tau\)-function and its quantization, On brane solutions with intersection rules related to Lie algebras, Affine Toda solitons and vertex operators, Non-compact symmetric spaces and the Toda molecule equations, Integrable Hamiltonians with exponential potential, Classical and quantum mechanical systems of Toda-lattice type. II: Solutions of the classical flows

Cites Work

• On an explicitly soluble system of nonlinear differential equations related to certain Toda lattices
• Completely integrable Hamiltonian systems connected with semisimple Lie algebras
• On a trace functional for formal pseudo-differential operators and the symplectic structure of the Korteweg-deVries type equations
• Integrals of the Toda lattice
• On the Toda Lattice. II: Inverse-Scattering Solution
• The Toda lattice. II. Existence of integrals
• Unnamed Item
• Unnamed Item
• Unnamed Item