Algebro-geometric integration of the Q1 lattice equation via nonlinear integrable symplectic maps
Abstract
The Q1 lattice equation, a member in the Adler-Bobenko-Suris list of 3D consistent lattices, is investigated. By using the multidimensional consistency, a novel Lax pair for Q1 equation is given, which can be nonlinearized to produce integrable symplectic maps. Consequently, a Riemann theta function expression for the discrete potential is derived with the help of the Baker-Akhiezer functions. This expression leads to the algebro-geometric integration of the Q1 lattice equation, based on the commutativity of discrete phase flows generated from the iteration of integrable symplectic maps.
- Publication:
-
Nonlinearity
- Pub Date:
- May 2021
- DOI:
- 10.1088/1361-6544/abddca
- arXiv:
- arXiv:2005.12765
- Bibcode:
- 2021Nonli..34.2897X
- Keywords:
-
- Baker–Akhiezer functions;
- algebro-geometric solutions;
- integrable lattice equations;
- integrable symplectic maps;
- 37J10;
- 37K10;
- 39A14;
- Nonlinear Sciences - Exactly Solvable and Integrable Systems
- E-Print:
- doi:10.1088/1361-6544/abddca