Bäcklund equations on Kac-Moody-Lie algebras and integrable systems

DOI10.1016/0393-0440(84)90002-0zbMath0579.58012OpenAlexW1971372618MaRDI QIDQ1067274

B. George

Publication date: 1984

Published in: Journal of Geometry and Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0393-0440(84)90002-0

zbMATH Keywords

evolution equationsKac-Moody Lie algebracompletely integrable systemsinverse sequence of Poisson spaces

Mathematics Subject Classification ID

Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) Infinite-dimensional Lie (super)algebras (17B65) Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests (37J35) Partial differential equations of mathematical physics and other areas of application (35Q99)

Related Items (4)

Kac-Moody Lie algebras and soliton equations. II: Lax equations associated with \(A_ 1^{(1)}\) ⋮ On the ubiquitous Gelfand-Levitan-Marčenko (GLM) equation ⋮ Isospectral Hamiltonian flows in finite and infinite dimensions. I: Generalized Moser systems and moment maps into loop algebras ⋮ Completely integrable systems of the KdV type related to isospectral periodic regular difference operators

Cites Work

• Kac-Moody Lie algebras and soliton equations. III: Stationary equations associated with \(A_ 1^{(1)}\)
• Completely integrable systems, Euclidean Lie algebras, and curves
• Modifying Lax equations and the second Hamiltonian structure
• Systems of Toda type, inverse spectral problems, and representation theory
• Conservation laws and symmetries of generalized sine-Gordon equations
• Infinite-dimensional algebras, Dedekind's \(\eta\)-function, classical Möbius function and the very strange formula
• On a trace functional for formal pseudo-differential operators and the symplectic structure of the Korteweg-deVries type equations
• Completely integrable systems of the KdV type related to isospectral periodic regular difference operators
• The modified Lax and two-dimensional Toda lattice equations associated with simple Lie algebras
• Prolongation structures of nonlinear evolution equations
• HOMOGENEOUS SPACES OF INFINITE-DIMENSIONAL LIE ALGEBRAS AND CHARACTERISTIC CLASSES OF FOLIATIONS
• Nonlinear Partial Differential Equations and Computing
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