We consider the su(n) spin chains with long range interactions and the spin generalization of the Calogero-Sutherland models. We show that their properties derive from a transfer matrix obeying the Yang-Baxter equation. We obtain the expression of the conserved quantities and we diagonalise them. 01/93 1 Laboratoire de la Direction de Sciences de la Matière du Commissariat à l’énergie atomique.

In this paper many soliton-like solutions with the arbitrary functions of y and t are obtained for the 1+2D Calogero-Bogoyavlenskii-Schif equation by means of some generalized ansatz and symbolic computation. Some new exact solutions are also presented from the obtained soliton-like solutions. Shock wave solution is only a special case.

We consider the Calogero–Degasperis–Ibragimov–Shabat depending on the local variables and on the integral of the only local conserved density of the equation in question. The resulting Lie algebra of these symmetries turns out to be a central extension of that of local symmetries.

We briefly explain some simple arguments based on pseudo Hermiticity, supersymmetry and PT -symmetry which explain the reality of the spectrum of some non-Hermitian Hamiltonians. Subsequently we employ PT -symmetry as a guiding principle to construct deformations of some integrable systems, the Calogero-Moser-Sutherland model and the Korteweg deVries equation. Some properties of these models ar...

We introduce 3N × 3N Lax pair with spectral parameter for Calogero-Inozemtsev model. The one degree of freedom case appears to have 2 × 2 Lax representation. We derive it from the elliptic Gaudin model via some reduction procedure and prove algebraic integrability. This Lax pair provides elliptic linear problem for the Painlevé VI equation in elliptic form.

Schiffbase was obtained by condensation of camphor with 4-amino-phenol .The charge transfer complex of the Schiff base as a donor molecule with picric acid as acceptor molecule in methanol were estimated. Schiff-base compound and charge transfer complex were identified by elemental analysis, infrared spectra and UV-visible spectra.The physical parameters of the CT complex were calculated by app...

Abstract We show that the configuration in phase space of elliptic Calogero–Moser model when particles stick together pairs is stable under third Hamiltonian flow model. The equations motion for coincide with poles solutions to B-version Kadomtsev–Petviashvili equation.

The Calogero equation is used to illustrate the following two aspects of the Painlevé analysis of PDEs: (i) the singular expansions of solutions around characteristic hypersurfaces are neither single-valued functions of independent variables nor single-valued functionals of data; (ii) the truncated singular expansions not necessarily lead to the simplest, elementary, Bäcklund autotransformation...

We give a new derivation and characterisation of the generalised elliptic genus of Krichever-Höhn by means of a functional equation. Introduction Functional equations provide a common thread to several investigations in mathematics and physics: our focus in this article will particularly be on the areas of topology and integrable systems where it is still unclear whether the threads before us f...