Mastersymmetries, angle variables, and recursion operator of the relativistic Toda lattice
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Publication:3477706
DOI10.1063/1.528497zbMath0699.58042OpenAlexW2044368405MaRDI QIDQ3477706
Benno Fuchssteiner, Hong-Wei Zhang, Walter Oevel
Publication date: 1989
Published in: Journal of Mathematical Physics (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1063/1.528497
Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests (37J35)
Related Items (26)
INTEGRABLE DISCRETIZATIONS FOR LATTICE SYSTEM: LOCAL EQUATIONS OF MOTION AND THEIR HAMILTONIAN PROPERTIES ⋮ \(N\)-fold Darboux transformation and soliton solutions for the relativistic Toda lattice equation ⋮ The negative relativistic Toda hierarchy Poisson brackets ⋮ Algebro-geometric solutions for the Ruijsenaars-Toda hierarchy ⋮ Symmetries, conserved quantities, and hierarchies for some lattice systems with soliton structure ⋮ R-matrices and higher Poisson brackets for integrable systems ⋮ Relativistic Toda systems ⋮ The R-matrix theory and the reduction of Poisson manifolds ⋮ Variational bihamiltonian cohomologies and integrable hierarchies. III: Linear reciprocal transformations ⋮ Multiple Hamiltonian structures for Toda-type systems ⋮ Representations of \(\mathfrak{sl}(2,\mathbb{C})\) in category \(\mathcal{O}\) and master symmetries ⋮ Nonlinear integrable systems containing the canonical subsystems of distinct physical origins ⋮ Darboux transformations and recursion operators for differential-difference equations ⋮ Lax pairs, symmetries and conservation laws of a differential-difference equation -- Sato's approach ⋮ On bi-Integrable Natural Hamiltonian Systems on Riemannian Manifolds ⋮ Affine collineations in Riemannian spaces ⋮ On the geometry of extended self-similar solutions of the Airy shallow water equations ⋮ Discrete time Toda systems ⋮ Nonlocal symmetries of the KdV equation ⋮ Algebraic structure of discrete zero curvature equations and master symmetries of discrete evolution equations ⋮ Rational recursion operators for integrable differential-difference equations ⋮ Four-component integrable systems inspired by the Toda and the Davydov-Kyslukha models ⋮ Generalized Legendre transformations ⋮ A unified construction for the algebro-geometric quasiperiodic solutions of the Lotka-Volterra and relativistic Lotka-Volterra hierarchy ⋮ On an integrable system related to the relativistic Toda lattice – Bäcklund transformation and integrable discretization ⋮ The negative Toda hierarchy and rational Poisson brackets
Cites Work
- Symplectic structures, their Bäcklund transformations and hereditary symmetries
- A new class of integrable systems and its relation to solitons
- Computer-algebra methods for investigation of hereditary operators of higher order soliton equations
- Integrable relativistic N-particle systems in an external potential
- Mastersymmetries, Higher Order Time-Dependent Symmetries and Conserved Densities of Nonlinear Evolution Equations
- R structures, Yang–Baxter equations, and related involution theorems
- The periodic relativistic Toda lattice: direct and inverse problem
- Multisolitons, or the discrete eigenfunctions of the recursion operator of nonlinear evolution equations: II. Background
- Application of hereditary symmetries to nonlinear evolution equations
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