On the semi-dynamical reflection equation: solutions and structure matrices
نویسندگان
چکیده
Explicit solutions of the non-constant semi-dynamical reflection equation are constructed, together with suitable parametrizations of their structure matrices. Considering the semi-dynamical reflection equation with rational non-constant Arutyunov-Chekhov-Frolov structure matrices, and a specific meromorphic ansatz, it is found that only two sets of the previously found constant solutions are extendible to the non-constant case. In order to simplify future constructions of spin-chain Hamiltonians, a parametrization procedure is applied explicitly to all elements of the semi-dynamical reflection equation available. Interesting expressions for ‘twists’ and Rmatrices entering the parametrization procedure are found. In particular, some expressions for the R-matrices seem to appear here for the first time. In addition, a new set of consistent structure matrices for the semi-dynamical reflection equation is obtained. E-mail: [email protected] E-mail: [email protected]
منابع مشابه
Analyzing dynamical snap-through of a size dependent nonlinear micro-resonator via a semi-analytic method
In the present paper, the dynamical snap-through of a preloaded micro-sensor is analyzed. This behavior is linked to analyzing bifurcation behavior of the micro structure in a suitable framework. Effec...
متن کامل1 8 M ay 2 00 0 Lectures on the dynamical Yang - Baxter equations
This paper arose from a minicourse given by the first author at MIT in the Spring of 1999, when the second author extended and improved his lecture notes of this minicourse. It contains a systematic and elementary introduction to a new area of the theory of quantum groups – the theory of the classical and quantum dynamical Yang-Baxter equations. The quantum dynamical Yang-Baxter equation is a g...
متن کاملDynamical distance as a semi-metric on nuclear conguration space
In this paper, we introduce the concept of dynamical distance on a nuclear conguration space. We partition the nuclear conguration space into disjoint classes. This classification coincides with the classical partitioning of molecular systems via the concept of conjugacy of dynamical systems. It gives a quantitative criterion to distinguish dierent molecular structures.
متن کاملDynamics of higher order rational difference equation $x_{n+1}=(alpha+beta x_{n})/(A + Bx_{n}+ Cx_{n-k})$
The main goal of this paper is to investigate the periodic character, invariant intervals, oscillation and global stability and other new results of all positive solutions of the equation$$x_{n+1}=frac{alpha+beta x_{n}}{A + Bx_{n}+ Cx_{n-k}},~~ n=0,1,2,ldots,$$where the parameters $alpha$, $beta$, $A$, $B$ and $C$ are positive, and the initial conditions $x_{-k},x_{-k+1},ldots,x_{-1},x_{0}$ are...
متن کاملNew Solutions for Singular Lane-Emden Equations Arising in Astrophysics Based on Shifted Ultraspherical Operational Matrices of Derivatives
In this paper, the ultraspherical operational matrices of derivatives are constructed. Based on these operational matrices, two numerical algorithms are presented and analyzed for obtaining new approximate spectral solutions of a class of linear and nonlinear Lane-Emden type singular initial value problems. The basic idea behind the suggested algorithms is basically built on transforming the eq...
متن کامل