论文标题
Q1晶格方程的代数几何整合通过非线性整合符号图
Algebro-geometric integration of the Q1 lattice equation via nonlinear integrable symplectic maps
论文作者
论文摘要
研究了Q1晶格方程，是Adler-Bobenko-Suris列表的3D一致晶格列表中的成员。通过使用多维一致性，给出了一种用于Q1方程的新型LAX对，可以非线性化以产生可集成的符号图。因此，借助面包师 - 阿基耶尔（Baker-Akhiezer）功能，得出了离散电势的Riemann theta函数表达。该表达式基于从可集成的符号图的迭代产生的离散相流的交换性，导致Q1晶格方程的代数几何积分。
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.
