Journal ArticleDOI
On the motion of classical integrable systems of interacting particles in an external field
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TLDR
New classical systems with a hamiltonian of the form H = σ i=1 N [ 1 2 p i 2 + W(x i )] + σ ǫ i>j N V (x i − x j ) (N ⩾ 2) possessing N independent integrals of motion are found within the isospectral deformation method as mentioned in this paper.About:
This article is published in Physics Letters A.The article was published on 1983-10-31. It has received 39 citations till now. The article focuses on the topics: Hamiltonian (quantum mechanics) & Isospectral.read more
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Direct methods for the search of the second invariant
TL;DR: In this paper, the authors discuss the direct methods that can be used to search for the second invariant of a system defined by the Hamiltonian H = 1 2 (p x 2 ) + p y 2 + A(x, y)p x + B(x and y), p y + V(x, y).
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Lax representation with spectral parameter on a torus for integrable particle systems
TL;DR: In this paper, complete integrability for the most general class of systems of interacting particles on a straight line with the Hamiltonian including elliptic functions of coordinates, depending on seven arbitrary parameters and having the structure defined by the root systems of the classical Lie algebras is proved.
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The finite Toda lattices
TL;DR: In this paper, a connection between one-dimensional Toda lattices, constructed on the basis of the systems of simple roots of classical and affine Lie algebras, and other integrable systems of interacting particles is established.
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Quantum Inozemtsev model, quasi-exact solvability and -fold supersymmetry
Ryu Sasaki,Kanehisa Takasaki +1 more
TL;DR: In this paper, the authors show that quantum Inozemtsev models can be deformed to be a wide class of quasi-exactly solvable (or quasi-equivalent) multi-particle dynamical systems.
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Extension of the Class of Integrable Dynamical Systems Connected With Semisimple Lie Algebras
TL;DR: In this paper, a new class of completely integrable systems connected with semisimple Lie algebras is introduced, which generalizes most of the previously-considered integrability systems describing a one-dimensional motion of interacting particles.
References
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Journal ArticleDOI
Three integrable Hamiltonian systems connected with isospectral deformations
TL;DR: In this paper, three integrable hamiltonian systems connected with isospectral deformations are discussed, where wave solutions of a nonlinear partial differential equation have a strong stability behavior.
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Some finite dimensional integrable systems and their scattering behavior
TL;DR: In this article, a class of Hamiltonian systems which posses integrals expressible in terms of the eigenvalues of some associate matrices is considered and their scattering behavior investigated using additional associated matrices whose eigen values change in time during a flow.
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Completely integrable classical systems connected with semisimple Lie Algebras, III
TL;DR: In this paper, a new proof is given that the integrals of motion for all with no exception classical systems previously considered in papers [1, 8] are in evolution, which is the same proof given in this paper.