Nonlinear evolution equations: localized structures, singularities, and asymptotic dynamics

非线性演化方程：局域结构、奇点和渐近动力学

• 批准号: 251124-2007
• 负责人: Gustafson, Stephen
• 金额: $ 1.46万
• 依托单位: University of British Columbia
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2011
• 资助国家: 加拿大
• 起止时间: 2011-01-01 至 2012-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=479656
• 关键词: Nonlinear; evolution; equations; localized; structures

The aim of the proposed research is to understand basic mathematical equations which describe physical systems such as ferromagnets and superconductors. The equations are non-linear and cannot be solved analytically (and often are difficult to solve even with the help of a computer). So we hope instead to obtain a clear picture of how solutions behave -- to determine their essential qualitative features -- by utilizing a variety of mathematical techniques.

拟议研究的目的是理解描述铁磁体和超导体等物理系统的基本数学方程。这些方程是非线性的，无法解析求解（即使在计算机的帮助下通常也很难求解）。因此，我们希望通过利用各种数学技术来清楚地了解解决方案的行为方式，以确定其基本的定性特征。