Multiple Hamiltonian structures for Toda-type systems
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Publication:4327252
DOI10.1063/1.530763zbMath0822.58017arXiv1410.0191OpenAlexW3099753492MaRDI QIDQ4327252
Publication date: 5 April 1995
Published in: Journal of Mathematical Physics (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1410.0191
KdV equations (Korteweg-de Vries equations) (35Q53) Dynamical aspects of finite-dimensional Hamiltonian and Lagrangian systems (37J99)
Related Items (30)
R-matrix theory, formal Casimirs and the periodic Toda lattice ⋮ The negative relativistic Toda hierarchy Poisson brackets ⋮ Integrable cluster dynamics of directed networks and pentagram maps ⋮ On the continuous limit of integrable lattices. I: The Kac-Moerbeke system and KdV theory ⋮ Volterra's realization of the KM-system ⋮ MULTIPLE HAMILTONIAN STRUCTURE OF BOGOYAVLENSKY–TODA LATTICES ⋮ A trihamiltonian extension of the Toda lattice ⋮ Lax pairs, symmetries and recursion operators for Toda lattices ⋮ \(\mathfrak{so}(p,q)\) Toda systems ⋮ Lax formalism for a family of integrable Toda-related n-particle systems ⋮ Comment to: ``Two hierarchies of lattice soliton equations associated with a new discrete eigenvalue problem and Darboux transformation [Phys. Lett. A 338 (2005) 117] ⋮ Nonlinear integrable systems containing the canonical subsystems of distinct physical origins ⋮ Reduction and realization in Toda and Volterra ⋮ Bi-Hamiltonian structures and singularities of integrable systems ⋮ From the Toda lattice to the Volterra lattice and back ⋮ On an integrable case of Kozlov-Treshchev Birkhoff integrable potentials ⋮ The Toda\(_2\) chain ⋮ Intermediate Toda systems ⋮ Dynamical symmetries, bi-Hamiltonian structures, and superintegrable n=2 systems ⋮ The modular hierarchy of the Toda lattice ⋮ Toda systems and exponents of simple Lie groups ⋮ Noether and master symmetries for the Toda lattice ⋮ Separation of variables in the Jacobi identities ⋮ Poisson brackets on rational functions and multi-Hamiltonian structure for integrable lattices ⋮ Algebraic properties of compatible Poisson brackets ⋮ Multiple Hamiltonian Structures and Lax Pairs for BogoyavlenskyVolterra Systems ⋮ On the Continuous Limit of Integrable Lattices II. Volterra Systems and SP(N) Theories ⋮ Separability of the Toda lattice ⋮ New four-dimensional solutions of the Jacobi equations for Poisson structures ⋮ The negative Toda hierarchy and rational Poisson brackets
Cites Work
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- Nonlinear Poisson structures and r-matrices
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- R-matrices and higher Poisson brackets for integrable systems
- Relativistic Toda systems
- Mastersymmetries, Higher Order Time-Dependent Symmetries and Conserved Densities of Nonlinear Evolution Equations
- Some remarks on the bi-Hamiltonian structure of integral and discrete evolution equations
- Mastersymmetries, angle variables, and recursion operator of the relativistic Toda lattice
- The toda flow on a generic orbit is integrable
- Symmetries and Integrability
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- A simple model of the integrable Hamiltonian equation
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- On the Toda Lattice. II: Inverse-Scattering Solution
- The Toda lattice. II. Existence of integrals
- Explicit solutions of classical generalized Toda models
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