R-matrix approach to lattice integrable systems
- 1 September 1994
- journal article
- Published by AIP Publishing in Journal of Mathematical Physics
- Vol. 35 (9), 4661-4682
- https://doi.org/10.1063/1.530807
Abstract
An r‐matrix formalism is applied to the construction of the integrable lattice systems and their bi‐Hamiltonian structure. Miura‐like gauge transformations between the hierarchies are also investigated. In the end the ladder of linear maps between generated hierarchies is established and described.Keywords
This publication has 9 references indexed in Scilit:
- An $r$-Matrix Approach to Nonstandard Classes of Integrable EquationsPublications of the Research Institute for Mathematical Sciences, 1993
- A trace identity and its applications to the theory of discrete integrable systemsJournal of Physics A: General Physics, 1990
- R-matrices and higher poisson brackets for integrable systemsPhysica A: Statistical Mechanics and its Applications, 1989
- R structures, Yang–Baxter equations, and related involution theoremsJournal of Mathematical Physics, 1989
- Mastersymmetries and Multi-Hamiltonian Formulations for Some Integrable Lattice SystemsProgress of Theoretical Physics, 1989
- Mathematics of dispersive water wavesCommunications in Mathematical Physics, 1985
- The local structure of Poisson manifoldsJournal of Differential Geometry, 1983
- The solution to a generalized Toda lattice and representation theoryAdvances in Mathematics, 1979
- On a trace functional for formal pseudo-differential operators and the symplectic structure of the Korteweg-devries type equationsInventiones Mathematicae, 1978