Finite dimensional integrable systems and differential geometry

有限维可积系统和微分几何

• 批准号: DP210100951
• 负责人: Dr Yuri Nikolayevsky
• 金额: $ 27.43万
• 依托单位: La Trobe University
• 依托单位国家: 澳大利亚
• 项目类别: Discovery Projects
• 财政年份: 2022
• 资助国家: 澳大利亚
• 起止时间: 2022-03-09 至 2025-03-08
• 项目状态: 未结题
• 来源: https://dataportal.arc.gov.au/RGS/Web/Grants/DP210100951
• 关键词: Finite; dimensional; integrable; systems; differential

Mathematical models of many processes in science (physics, engineering) and in the real world (nature, economics) are governed by complicated systems of differential equations. An important, distinguished class of such models is described by integrable systems, the systems for which one can provide a comprehensive qualitative picture, and in many cases, a complete solution. Using recently developed, powerful methods of integrable systems and differential geometry, this project will focus on a range of important, interconnected theoretical problems in both disciplines. The expected outcomes will provide new, deep, mathematically and physically significant results which will lead to applications and developments across a range of fields.

科学（物理学、工程学）和真实的世界（自然、经济学）中许多过程的数学模型都是由复杂的微分方程系统控制的。一个重要的，杰出的一类这样的模型是由可积系统，系统，其中一个可以提供一个全面的定性图片，并在许多情况下，一个完整的解决方案。使用最近开发的，强大的可积系统和微分几何的方法，这个项目将集中在一系列重要的，在这两个学科相互关联的理论问题。预期的结果将提供新的，深入的，数学和物理上重要的结果，这将导致在一系列领域的应用和发展。