Integrable Lattice Equations

当数学模型在计算机上模拟时，结果是一个偏差分方程系统，其解在空间和时间上以离散步骤在晶格上演化。虽然已经开发了许多工具来研究连续方程，但很少有数学技术可用于分析非线性晶格方程。我们的目标是发展解决这类方程的初值问题的技术。我们的例子包括在许多物理问题的模拟中出现的可积晶格方程，从浅水波浪的进展到光纤中的信号。

When mathematical models are simulated on a computer, the result is a system of partial difference equations, whose solutions evolve with discrete steps on a lattice in space and time. While many tools have been developed to study continuous equations, very few mathematical techniques are available for analysing non-linear lattice equations. We aim to develop techniques of solving the initial-value problem for a class of such equations. Our examples include integrable lattice equations that arise in the simulation of many physical problems ranging from the progression of shallow water waves to signals in an optical fibre.