Mathematical Sciences: Stability and Instability of Nonlinear Waves

首席研究员将开发和改进方法 理解非线性波作为解的稳定性 的偏微分方程，出现在一些 科学领域。 在一个特定的情况下，他将使用他的想法， 最近发展到建立指数衰减率 孤立波问题中的非线性扰动KdV- 类型方程。 这类系统非线性波的定性分析 具有重要的科学意义，因为它广泛分布在 这种现象在真实的世界中的发生。

The principal investigator will develop and improve methods for understanding the stability of nonlinear waves as solutions of partial differential equations which arise in a number of scientific fields. In one particular case, he will use ideas he has recently developed to establish the exponential decay rate for nonlinear perturbations in solitary wave problems for KdV- type equations. The qualitative analysis of nonlinear waves for such systems is of significant scientific interest in view of the wide spread occurrence of such phenomena in real world situations.