修正Korteweg-de Vries方程的可积离散化
On an integrable discretization of the modified Korteweg-de Vries equation
摘要：
我们发现时间离散化的两个“第二流动”的Ablowitz-Ladik hierachy。这些离散描述的局部运动方程，而不是以前已知的，由于塔哈和Ablowitz。我们的地图的某些叠加允许一个字段的减少，因此作为有效的时空离散的修改Korteweg-de Vries方程。我们期望这些离散化的性能要好得多，然后的Taha-Ablowitz计划。还指出了为我们的映射寻找插值哈密顿算子的方法，以及用矩阵分解求解初值问题。
英文摘要：
We find time discretizations for the two ''second flows'' of the Ablowitz-Ladik hierachy. These discretizations are described by local equations of motion, as opposed to the previously known ones, due to Taha and Ablowitz. Certain superpositions of our maps allow a one-field reduction and serve therefore as valid space-time discretizations of the modified Korteweg-de Vries equation. We expect the performance of these discretizations to be much better then that of the Taha-Ablowitz scheme. The way of finding interpolating Hamiltonians for our maps is also indicated, as well as the solution of an initial value problem in terms of matrix factorizations.
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