Symmetry analysis, conservation laws, field equations and hamiltonian flows

对称分析、守恒定律、场方程和哈密顿流

• 批准号: 227381-2009
• 负责人: Anco, Stephen
• 金额: $ 1.31万
• 依托单位: Brock University
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2013
• 资助国家: 加拿大
• 起止时间: 2013-01-01 至 2014-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=523963
• 关键词: Symmetry; analysis; conservation; laws; field

Symmetries, conservation laws, and related analysis of differential equations has attracted a high level of flourishing activity in the last 10 years while also expanding in interesting new directions. At the same time, there has been a surge of work in geometric integrability of partial differential equations, in particular deriving soliton equations, recursion operators, and Hamiltonian structures from flows of curves and surfaces in differential geometry. My research proposal involves several major directions of work in these two areas, with the aim being to solve open problems, address important applications, and produce new results having a wide mathematical impact.

在过去的10年里，对微分方程的对称性、守恒定律和相关的分析吸引了高度活跃的活动，同时也向有趣的新方向扩展。与此同时，在偏微分方程的几何可积性方面也有了大量的工作，特别是从微分几何中的曲线和曲面的流动中推导出孤子方程、递归算子和哈密顿结构。我的研究提案涉及这两个领域的几个主要工作方向，目的是解决公开问题，解决重要应用，并产生具有广泛数学影响的新结果。