论文标题
在任意尺寸晶格上具有相互关系的离散KDV类型方程
Coprimeness-preserving discrete KdV type equation on an arbitrary dimensional lattice
论文作者
论文摘要
我们引入了在多维晶格上定义的方程式，该方程可被视为在我们以前的论文中的扩展范围的扩展。该方程也被解释为Hietarinta-Viallet方程的高维类似物，该方程以其奇异性限制性质而闻名，同时具有指数性的增长。作为主要定理，我们证明了劳伦（Laurent）和方程式的“ tau功能”形式的不可约性特性。从定理中，方程的共同点随后。 在附录中，我们回顾了具有共同度的离散KDV等方程，它是我们主系统的基本方程式，并证明了诸如共有性之类的属性。
We introduce an equation defined on a multi-dimensional lattice, which can be considered as an extension to the coprimeness-preserving discrete KdV like equation in our previous paper. The equation is also interpreted as a higher-dimensional analogue of the Hietarinta-Viallet equation, which is famous for its singularity confining property while having an exponential degree growth. As the main theorem we prove the Laurent and the irreducibility properties of the equation in its "tau-function" form. From the theorem the coprimeness of the equation follows. In Appendix we review the coprimeness-preserving discrete KdV like equation whichis a base equation for our main system and prove the properties such as the coprimeness.
