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

提出的研究集中于求解非线性偏微分方程系统的解析方法，这些系统出现在数学物理的各个分支中。本研究的主题包括对称约简方法和基于李代数表面分析的几何方法。将研究非线性场论和流体动力学方程的某些应用。这些方法的发展为我们处理物理中的非线性现象提供了新的工具，特别是那些由偏微分方程的多维系统描述的，迄今为止还没有被其他方法成功地处理过的现象。该计划包括以下项目：

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: