Master symmetries and r-matrices for the Toda lattice
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Publication:751332
DOI10.1007/BF00398275zbMath0714.70014MaRDI QIDQ751332
Publication date: 1990
Published in: Letters in Mathematical Physics (Search for Journal in Brave)
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) Dynamic lattice systems (kinetic Ising, etc.) and systems on graphs in time-dependent statistical mechanics (82C20) Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs arising in equilibrium statistical mechanics (82B20)
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Cites Work
- Unnamed Item
- The local structure of Poisson manifolds
- What is a classical r-matrix?
- The solution to a generalized Toda lattice and representation theory
- On a trace functional for formal pseudo-differential operators and the symplectic structure of the Korteweg-deVries type equations
- Mastersymmetries, Higher Order Time-Dependent Symmetries and Conserved Densities of Nonlinear Evolution Equations
- Evolution equations possessing infinitely many symmetries
- A simple model of the integrable Hamiltonian equation
- The Toda lattice. II. Existence of integrals