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arXiv · 2005.12765

Algebro-geometric integration of the Q1 lattice equation via nonlinear integrable symplectic maps

Xiaoxue Xu·Cewen Cao·Frank W Nijhoff
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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 nonlinearised 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.

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Xiaoxue Xu, Cewen Cao, Frank W Nijhoff. 2020-05-26. Algebro-geometric integration of the Q1 lattice equation via nonlinear integrable symplectic maps. https://doi.org/10.1088/1361-6544/abddca

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