ar X iv : n lin / 0 61 10 18 v 3 [ nl in . S I ] 6 J an 2 00 7 GENERALIZED ISOTHERMIC LATTICES

نویسنده

  • ADAM DOLIWA
چکیده

We study multidimensional quadrilateral lattices satisfying simultaneously two inte-grable constraints: a quadratic constraint and the projective Moutard constraint. When the lattice is two dimensional and the quadric under consideration is the Möbius sphere one obtains, after the stereographic projection, the discrete isothermic surfaces defined by Bobenko and Pinkall by an algebraic constraint imposed on the (complex) cross-ratio of the circular lattice. We derive the analogous condition for our generalized isthermic lattices using Steiner's projective structure of conics and we present basic geometric constructions which encode integrability of the lattice. In particular we introduce the Darboux transformation of the generalized isothermic lattice and we derive the corresponding Bianchi permutability principle. Finally, we study two dimensional generalized isothermic lattices, in particular geometry of their initial boundary value problem.

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

ar X iv : n lin / 0 61 10 18 v 2 [ nl in . S I ] 1 1 N ov 2 00 6 GENERALIZED ISOTHERMIC LATTICES

We study multidimensional quadrilateral lattices satisfying simultaneously two inte-grable constraints: a quadratic constraint and the projective Moutard constraint. When the lattice is two dimensional and the quadric under consideration is the Möbius sphere one obtains, after the stereographic projection, the discrete isothermic surfaces defined by Bobenko and Pinkall by an algebraic constrain...

متن کامل

ar X iv : n lin / 0 60 40 34 v 1 [ nl in . S I ] 1 7 A pr 2 00 6 Integrable inhomogeneous Lakshmanan - Myrzakulov equation

Abstract. The integrable inhomogeneous extension of the Lakshmanan-Myrzakulov equation is constructed by using the prolongation structure theory. The corresponding L-equivalent counterpart is also given, which is the (2+1)-dimensional generalized NLSE. PACS: 02.30.Ik, 02.40.Hw, 75.10.Hk

متن کامل

ar X iv : n lin / 0 00 40 13 v 1 [ nl in . S I ] 9 A pr 2 00 0 The critical A ( 1 ) n − 1 chain

(1) n−1 chain Abstract We study the A (1) n−1 spin chain at the critical regime |q| = 1. We give the free boson realizations of the type-I vertex operators and their duals. Using these free boson realizations, we give the integral representations for the correlation functions.

متن کامل

ar X iv : n lin / 0 50 20 61 v 1 [ nl in . C G ] 2 6 Fe b 20 05 Two Cellular Automata for the 3 x + 1 Map

Two simple Cellular Automata, which mimic the Collatz-Ulam iterated map (3x + 1 map), are introduced. These Cellular Automata allow to test efficiently the Collatz conjecture for very large numbers.

متن کامل

ar X iv : n lin / 0 50 50 19 v 1 [ nl in . S I ] 7 M ay 2 00 5 Bazhanov - Stroganov model from 3 D approach

We apply a 3-dimensional approach to describe a new parametrization of the L-operators for the 2-dimensional Bazhanov-Stroganov (BS) integrable spin model related to the chiral Potts model. This parametrization is based on the solution of the associated classical discrete integrable system. Using a 3-dimensional vertex satisfying a modified tetrahedron equation, we construct an operator which g...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 2007