Journal ArticleDOI
Reduction of Hamiltonian systems, affine Lie algebras and Lax equations
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This article is published in Inventiones Mathematicae.The article was published on 1979-02-01. It has received 258 citations till now. The article focuses on the topics: Affine Lie algebra & Adjoint representation of a Lie algebra.read more
Citations
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Classical integrable finite-dimensional systems related to Lie algebras
TL;DR: In this article, a review of the results obtained in this field during the last few years is presented, and some new results both of physical and mathematical interest are also presented, as well as some generalizations of these models, naturally suggested by their association with Lie algebras.
Book ChapterDOI
Quantum spectral transform method. recent developments
Petr P. Kulish,E. K. Sklyanin +1 more
Journal ArticleDOI
Discrete versions of some classical integrable systems and factorization of matrix polynomials
TL;DR: In this article, a Lax-pair representation of the Euler-Arnold equation is used to show the integrability of the Heisenberg chain with classical spins and a new discrete system on the Stiefel manifold.
Journal ArticleDOI
Completely Integrable Systems, Euclidean Lie-algebras, and Curves
TL;DR: In this paper, the authors discuss the relationship between polynomials in the indeterminate h, h-l, with coefficients in one of the simple Lie algebras and complete integrability of Hamiltonian systems.
References
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Book
Mathematical Methods of Classical Mechanics
TL;DR: In this paper, Newtonian mechanics: experimental facts investigation of the equations of motion, variational principles Lagrangian mechanics on manifolds oscillations rigid bodies, differential forms symplectic manifolds canonical formalism introduction to pertubation theory.
Journal ArticleDOI
On a trace functional for formal pseudo-differential operators and the symplectic structure of the Korteweg-devries type equations
TL;DR: In this article, the Lie geometric structure behind the Hamiltonian structure of the Korteweg deVries type equations was studied and the authors showed that it is the same as the Lie geometry behind the Lie structure of a Hamiltonian lattice.
Journal ArticleDOI
Non-linear equations of korteweg-de vries type, finite-zone linear operators, and abelian varieties
TL;DR: In this paper, a broad class of periodic and almost-periodic solutions of non-linear equations of mathematical physics to which (in the rapidly decreasing case) the method of the inverse scattering problem is applicable is presented.