On algebraic models of dynamical systems

DOI10.1007/BF00401731zbMath0494.58021OpenAlexW2007108289MaRDI QIDQ1169192

Boris A. Kupershmidt

Publication date: 1982

Published in: Letters in Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf00401731

zbMATH Keywords

deformationsinfinitesimal automorphismsabstract Hamiltonian formalismconstruction of integralsdifferential scalar Lax systemsuniversal algebraic model for discrete dynamical systems

Mathematics Subject Classification ID

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) Dynamical aspects of finite-dimensional Hamiltonian and Lagrangian systems (37J99) Abstract differential equations (12H20) General theory for ordinary differential equations (34A99)

Related Items

Hamiltonian differencing of fluid dynamics, Canonical property of the Miura maps between the MKP and KP hierarchies, continuous and discrete, The structures of generalized noncommutative Toda lattices, Discretization of ideal fluid dynamics in the Eulerian representation, Dark Equations, On dual spaces of differential Lie algebras, Mathematics of dispersive water waves

Cites Work

• Algebraic aspects of nonlinear differential equations
• The solution to a generalized Toda lattice and representation theory
• Completely integrable systems, Euclidean Lie algebras, and curves
• Modifying Lax equations and the second Hamiltonian structure
• The spectrum of difference operators and algebraic curves
• On a trace functional for formal pseudo-differential operators and the symplectic structure of the Korteweg-deVries type equations
• Commuting flows and conservation laws for Lax equations
• On the nature of the Gardner transformation