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，结果是一个部分差异方程的系统，其解决方案在时空和时间上的晶格上以离散的步骤演化。尽管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。我们旨在开发解决此类方程式的初始值问题的技术。我们的示例包括在模拟许多物理问题中出现的可集成晶格方程，从浅水波的进展到光纤中的信号。