New Frontiers and Advances in Discrete Integrable Systems

离散可积系统的新领域和进展

• 批准号: DP140100383
• 负责人: Prof John Roberts
• 金额: $ 28.1万
• 依托单位: The University of New South Wales
• 依托单位国家: 澳大利亚
• 项目类别: Discovery Projects
• 财政年份: 2014
• 资助国家: 澳大利亚
• 起止时间: 2014-01-01 至 2020-06-20
• 项目状态: 已结题
• 来源: https://dataportal.arc.gov.au/RGS/Web/Grants/DP140100383
• 关键词: New; Frontiers; Advances; Discrete; Integrable

Integrable systems boast a long and venerable history, and have such famous members as the Kepler system, the Korteweg-de Vries equation, and the sine-Gordon equation. More recently, interest in integrable systems has expanded to include systems with discrete time, that is, ordinary difference equations (or maps) and integrable partial difference equations. These discrete integrable systems are arguably more fundamental than the continuous-time ones. Based upon recent breakthroughs this study will combine analysis, geometry, and computer algebra to expand and systematise this new interdisciplinary field of discrete integrable systems.

可积系统有着悠久的历史，其中著名的有Kepler系统、Korteweg-de弗里斯方程和sine-Gordon方程。最近，对可积系统的兴趣已经扩展到包括离散时间系统，即常差分方程（或映射）和可积偏差分方程。这些离散的可积系统可以说比连续时间系统更基本。基于最近的突破，这项研究将结合联合收割机分析，几何和计算机代数，扩展和系统化这一新的跨学科领域的离散可积系统。