From the Toda lattice to the Volterra lattice and back

DOI10.1016/S0034-4877(02)80066-0zbMath1038.37046arXivmath-ph/0202037MaRDI QIDQ1429205

Pantelis A. Damianou, Rui Loja Fernandes

Publication date: 18 May 2004

Published in: Reports on Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math-ph/0202037

zbMATH Keywords

Hamiltonian structurePoisson bracketToda latticesLax pairsVolterra lattices

Mathematics Subject Classification ID

Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests (37J35) Discrete version of topics in analysis (39A12) Completely integrable systems and methods of integration for problems in Hamiltonian and Lagrangian mechanics (70H06) Lattice dynamics; integrable lattice equations (37K60)

Related Items

Lotka-Volterra systems satisfying a strong Painlevé property ⋮ Bogoyavlensky-Volterra and Birkhoff integrable systems ⋮ MULTIPLE HAMILTONIAN STRUCTURE OF BOGOYAVLENSKY–TODA LATTICES ⋮ Invariant critical sets of conserved quantities ⋮ Orthogonal polynomial interpretation of \(q\)-Toda and \(q\)-Volterra equations ⋮ Dubrovin method and the Toda chain ⋮ On the Links between Miura Transformations of Bogoyavlensky Lattices and Inverse Spectral Problems for Band Operators ⋮ Integrable reductions of the Bogoyavlenskij-Itoh Lotka-Volterra systems ⋮ Reduction and realization in Toda and Volterra ⋮ Extended mixed function method and its application for solving two classic Toda lattice equations ⋮ On generalized Volterra systems ⋮ Inverse Spectral Problems for Second-Order Difference Operators and Their Application to the Study of Volterra Type Systems ⋮ Characterizations of \(\Delta\)-Volterra lattice: a symmetric orthogonal polynomials interpretation ⋮ Nijenhuis forms on Lie-infinity algebras associated to Lie algebroids ⋮ Reductions of the Volterra lattice ⋮ Poisson integrators for Volterra lattice equations ⋮ Integrability and conservation laws for two systems of hydrodynamic type derived from the Toda and Volterra systems ⋮ The matrix Toda equations for coefficients of a matrix three-term recurrence relation ⋮ Multiple Hamiltonian Structures and Lax Pairs for BogoyavlenskyVolterra Systems

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• The local structure of Poisson manifolds
• Master symmetries and r-matrices for the Toda lattice
• Hamiltonian interpretation of the Volterra model
• The Toda lattice, Dynkin diagrams, singularities and Abelian varieties
• Theory of nonlinear lattices.
• Three integrable Hamiltonian systems connected with isospectral deformations
• On an explicitly soluble system of nonlinear differential equations related to certain Toda lattices
• On a trace functional for formal pseudo-differential operators and the symplectic structure of the Korteweg-deVries type equations
• On algebro-geometric Poisson brackets for the Volterra lattice
• Integrability of the periodic KM system
• Multiple Hamiltonian structures for Toda systems of type \(A\)-\(B\)-\(C\)
• On the master symmetries and bi-Hamiltonian structure of the Toda lattice
• Multiple Hamiltonian structures for Toda-type systems
• Dirac Manifolds
• Tata lectures on theta. II: Jacobian theta functions and differential equations. With the collaboration of C. Musili, M. Nori, E. Previato, M. Stillman, and H. Umemura
• Toda systems and exponents of simple Lie groups
• Integrable systems in the realm of algebraic geometry.
• Hyperelliptic Prym varieties and integrable systems