"Analysis and applications of nonlinear evolution equations: waves, patterns, and singularities."

“非线性演化方程的分析和应用：波、模式和奇点。”

• 批准号: 251124-2012
• 负责人: Gustafson, Stephen
• 金额: $ 1.82万
• 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: 2012
• 资助国家: 加拿大
• 起止时间: 2012-01-01 至 2013-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=508789
• 关键词: Analysis; applications; nonlinear; evolution; equations

The aim of the proposed research is to understand fundamental mathematical equations -- called Partial Differential Equations -- which describe the behaviour of physical systems, such as ferromagnets, superfluids, superconductors, and lasers. The equations are non-linear, cannot be solved explicitly, and are often difficult to solve even with the help of a computer. So we aim instead to obtain a clear picture of how solutions behave -- to determine their essential qualitative features -- by using various mathematical techniques.

拟议研究的目的是理解基本数学方程（称为偏微分方程），它描述物理系统的行为，例如铁磁体、超流体、超导体和激光。这些方程是非线性的，无法明确求解，并且即使借助计算机也通常很难求解。因此，我们的目标是通过使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。