Direct methods for ultradiscrete systems

研究所谓的离散可积系统的代数结构--它可以通过适当的离散化技术从连续可积系统中得到--证明了阐明某些被称为“超离散可积系统”的细胞自动机的对称结构是可能的。因此，我得到了一个新的技术来解决所谓的超离散KdV方程，这是典型的超离散可积系统。此外，某些类型的离散可积系统的分类不仅导致了它们之间意想不到的关系的发现，而且在低维情况下，将先前已知的离散可积系统的几何结构扩展到几类新的离散系统。

Studying the algebraic structure of so-called discrete integrable systems-which can be obtained from continuous integrable systems by appropriate discretisation techniques-it proved possible to elucidate the symmetry structure of certain cellular automata known as "ultradiscrete integrable systems". As a result I obtained a novel technique for solving the so-called ultradiscrete KdV equation, which is the prototypical ultradiscrete integrable system. Moreover, the classification of certain types of discrete integrable systems not only led to the discovery of unexpected relations among them, but also, in the lower dimensional case, to extensions of the geometric structures of previously known discrete integrable systems to several new classes of discrete systems.