scholarly journals Periodic solutions to a coupled two-dimensional lattice presented by Blaszak and Szum with Riemann–theta function

2018 ◽  
Vol 2018 (1) ◽  
Author(s):  
Ting Su
2016 ◽  
Vol 71 (7) ◽  
pp. 639-645
Author(s):  
Lihua Wu ◽  
Xianguo Geng

AbstractWith the help of the characteristic polynomial of Lax matrix for the K(−2, −2) hierarchy, we define a hyperelliptic curve 𝒦n+1 of arithmetic genus n+1. By introducing the Baker–Akhiezer function and meromorphic function, the K(−2, −2) hierarchy is decomposed into Dubrovin-type differential equations. Based on the theory of hyperelliptic curve, the explicit Riemann theta function representation of meromorphic function is given, and from which the quasi-periodic solutions to the K(−2, −2) hierarchy are obtained.


1991 ◽  
Vol 06 (39) ◽  
pp. 3591-3600 ◽  
Author(s):  
HIROSI OOGURI ◽  
NAOKI SASAKURA

It is shown that, in the three-dimensional lattice gravity defined by Ponzano and Regge, the space of physical states is isomorphic to the space of gauge-invariant functions on the moduli space of flat SU(2) connections over a two-dimensional surface, which gives physical states in the ISO(3) Chern–Simons gauge theory. To prove this, we employ the q-analogue of this model defined by Turaev and Viro as a regularization to sum over states. A recent work by Turaev suggests that the q-analogue model itself may be related to an Euclidean gravity with a cosmological constant proportional to 1/k2, where q=e2πi/(k+2).


2007 ◽  
Vol 21 (02n03) ◽  
pp. 139-154 ◽  
Author(s):  
J. H. ASAD

A first-order differential equation of Green's function, at the origin G(0), for the one-dimensional lattice is derived by simple recurrence relation. Green's function at site (m) is then calculated in terms of G(0). A simple recurrence relation connecting the lattice Green's function at the site (m, n) and the first derivative of the lattice Green's function at the site (m ± 1, n) is presented for the two-dimensional lattice, a differential equation of second order in G(0, 0) is obtained. By making use of the latter recurrence relation, lattice Green's function at an arbitrary site is obtained in closed form. Finally, the phase shift and scattering cross-section are evaluated analytically and numerically for one- and two-impurities.


1992 ◽  
Vol 68 (13) ◽  
pp. 2027-2030 ◽  
Author(s):  
Jean-Christophe Toussaint ◽  
Jean-Marc Debierre ◽  
Loïc Turban

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