Integrable Lattice Equations

可积格方程

• 批准号: DP0985615
• 负责人: Prof Nalini Joshi
• 金额: $ 19.25万
• 依托单位: The University of Sydney
• 依托单位国家: 澳大利亚
• 项目类别: Discovery Projects
• 财政年份: 2009
• 资助国家: 澳大利亚
• 起止时间: 2009-02-10 至 2012-11-26
• 项目状态: 已结题
• 来源: https://dataportal.arc.gov.au/RGS/Web/Grants/DP0985615
• 关键词: Integrable; Lattice; Equations

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.

当在计算机上模拟数学模型时，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网格上演化。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。我们的目标是开发技术解决一类这样的方程的初值问题。我们的例子包括可积晶格方程，在模拟许多物理问题，从浅水波的进展，在光纤中的信号。