Journal ArticleDOI
A Bäcklund transformation for a generalised Calogero-Moser system
TLDR
A Backlund transformation for a generalised Calogero-Moser system, in which the particles posses extra, internal, degrees of freedom, is given in this paper, which is shown to be a canonical transformation and its generating function is given explicitly.About:
This article is published in Physics Letters A.The article was published on 1983-03-21. It has received 9 citations till now. The article focuses on the topics: Degrees of freedom & Generating function (physics).read more
Citations
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Random-matrix theories in quantum physics : common concepts
TL;DR: A review of the development of random-matrix theory (RMT) during the last fifteen years is given in this paper, with a brief historical survey of the developments of RMT and of localization theory since their inception.
Journal ArticleDOI
Random Matrix Theories in Quantum Physics: Common Concepts
TL;DR: It is suggested that the current development of random-matrix theory signals the emergence of a new “statistical mechanics”: Stochasticity and general symmetry requirements lead to universal laws not based on dynamical principles.
Journal ArticleDOI
Few remarks on Backlund transformations for many-body systems
V B Kuznetsov,E K Sklyanin +1 more
TL;DR: In this article, the basic properties of the Backlund transformations (BT's) from the Hamiltonian point of view were revised from the perspective of the periodic Toda lattice and the relativistic generalization due to Ruijsenaars of the elliptic Calogero-Moser system.
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On Bäcklund transformations for many-body systems
TL;DR: In this paper, the basic properties of the Backlund transformations (BTs) from the Hamiltonian point of view were revised using the n-particle periodic Toda lattice and the relativistic generalization due to Ruijsenaars of the elliptic Calogero-Moser system.
Journal ArticleDOI
Spin generalizations of the Benjamin–Ono equation
TL;DR: In this paper , a spin generalization of the Benjamin-Ono (BO) equation and the recently introduced non-chiral intermediate long-wave (ncILW) equation is presented.
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.
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
A generalisation of the Calogero-Moser system
John Gibbons,Theo Hermsen +1 more
TL;DR: In this paper, a generalised Calogero-Moser many-body system is introduced and solved by the method of Olshanetsky and Perelomov, and the hierarchy of flows commuting with this system is obtained from a hierarchy of linear systems possessing SL( N ) symmetry.
Journal ArticleDOI
Explicit solution of the Calogero model in the classical case and geodesic flows on symmetric spaces of zero curvature
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Sur les systèmes a plusieurs particules avec potentiel an 1/r 2 , l’équation de Riccatti et les systèmes complètement intégrables relies a l’équation de Schrödinger
TL;DR: In this article, it is shown that for finite number of aligned particles interacting via the potential 1/..gamma/sup 2/ there exists Baecklund transformation, which is expressed using Riccatti equation for associated S turm-Liouville problem.