The R-matrix theory and the reduction of Poisson manifolds
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Publication:4008249
DOI10.1063/1.529747zbMath0747.58038OpenAlexW1980198810MaRDI QIDQ4008249
Publication date: 27 September 1992
Published in: Journal of Mathematical Physics (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1063/1.529747
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 (2)
New hierarchies of integrable lattice equations and associated properties: Darboux transformation, conservation laws and integrable coupling ⋮ On the simplectization of bi-Hamiltonian structures
Cites Work
- Master symmetries and r-matrices for the Toda lattice
- What is a classical r-matrix?
- Nonlinear Poisson structures and r-matrices
- Classical r-matrices and compatible Poisson brackets for coupled KdV systems
- Reduction techniques for infinite-dimensional Hamiltonian systems: some ideas and applications
- A new class of integrable systems and its relation to solitons
- Kac-Moody Lie algebras and soliton equations. II: Lax equations associated with \(A_ 1^{(1)}\)
- On a trace functional for formal pseudo-differential operators and the symplectic structure of the Korteweg-deVries type equations
- The resolvent and Hamiltonian systems
- Yang-Baxter equations and intermediate long wave hierarchies
- Integrable relativistic N-particle systems in an external potential
- R-matrices and higher Poisson brackets for integrable systems
- Some remarks on the bi-Hamiltonian structure of integral and discrete evolution equations
- Mastersymmetries, angle variables, and recursion operator of the relativistic Toda lattice
- A unified algebraic approach to integral and discrete evolution equations
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