On Liouville integrability of zero-curvature equations and the Yang hierarchy
- 7 July 1989
- journal article
- Published by IOP Publishing in Journal of Physics A: General Physics
- Vol. 22 (13), 2375-2392
- https://doi.org/10.1088/0305-4470/22/13/031
Abstract
Sufficient conditions for a zero-curvature equation Ut-Vx+(U,V)=0 being Liouville integrable are investigated. In the case that the equation is integrable an explicit formula of the Poisson bracket (H( lambda ),H( mu )) for Hamiltonians H is proposed. The Yang hierarchy is derived and shown to be Liouville integrable.Keywords
This publication has 13 references indexed in Scilit:
- The trace identity, a powerful tool for constructing the Hamiltonian structure of integrable systemsJournal of Mathematical Physics, 1989
- A hierarchy of systems of non-linear equationsJournal of Physics A: General Physics, 1986
- Hamiltonian Hierarchies on Semisimple Lie AlgebrasStudies in Applied Mathematics, 1985
- A hamiltonian structure from gauge transformations of the Zakharov-Shabat systemPhysics Letters A, 1984
- Kac-moody lie algebras and soliton equationsPhysica D: Nonlinear Phenomena, 1983
- Symplectic structures, their Bäcklund transformations and hereditary symmetriesPhysica D: Nonlinear Phenomena, 1981
- The modified Lax and two-dimensional Toda lattice equations associated with simple Lie algebrasErgodic Theory and Dynamical Systems, 1981
- Application of hereditary symmetries to nonlinear evolution equationsNonlinear Analysis, 1979
- Integrability of Nonlinear Hamiltonian Systems by Inverse Scattering MethodPhysica Scripta, 1979
- A Lie algebra structure in a formal variational calculationFunctional Analysis and Its Applications, 1976