Symmetry reduction method and surfaces in life algebras for nonlinear phenomena in physics

物理非线性现象的生命代数中的对称约简方法和曲面

• 批准号: 36257-2009
• 负责人: Grundland, AlfredMichel
• 金额: $ 2.62万
• 依托单位: Université du Québec à Trois-Rivières
• 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=521345
• 关键词: Symmetry; reduction; method; surfaces; life

The proposed research concentrates on analytical methods for solving systems of nonlinear PDEs which appear in various branches of Mathematical Physics. The subject of this investigation involves symmetry reduction methods and geometric methods based on the analysis of surfaces immersed in Lie algebras. Certain applications to the equations of nonlinear field theory and fluid dynamics will be studied. The development of these methods provides us with new tools for dealing with nonlinear phenomena in physics, especially the ones which are described by multidimensional systems of PDEs and which so far have not been approached successfully by other methods. This program includes the following projects:

建议的研究集中在解决系统的非线性偏微分方程出现在数学物理的各个分支的分析方法。本次调查的主题涉及对称性约化方法和几何方法的基础上分析沉浸在李代数的表面。某些应用的非线性场论和流体动力学方程将进行研究。这些方法的发展为我们处理物理学中的非线性现象提供了新的工具，特别是那些由多维偏微分方程系统描述的，迄今为止还没有成功地接近其他方法的非线性现象。该方案包括以下项目：