Numerical Methods for the Study of Some Nonlinear Wave Equations

该奖项将支持由宾夕法尼亚州立大学曾傑瑞·博纳教授和希腊克里特大学瓦西利奥斯·A·杜加利斯教授领导的类似小组之间的美希合作研究。合作者打算对求解两个重要的非线性偏微分方程组的数值方法进行计算和理论研究：非线性薛定谔方程和Korteweg-de Vries方程。在过去的几年里，合作者们发表了几篇关于上述偏微分方程数值解的重要论文。这些方程之所以有价值，是因为它们有助于对水波、等离子体物理和非线性光学等应用领域中发生的某些非线性波动现象进行建模。通过支持这些经验丰富和富有成效的合作者的互动，该奖项将有助于促进我们对非线性现象的理解。

This award will support U.S.-Greece cooperative research between a group headed by Prof. Jerry Bona of Penn State University and a similar group headed by Prof. Vassilios A. Dougalis of the University of Crete, Greece. The collaborators intend to conduct computational and theoretical research on numerical methods for solving two important nonlinear partial differential equations: the nonlinear Schroedinger equation and the Korteweg-de Vries equation. Over the past few years the collaborators have produced several important papers on the numerical solution of the mentioned partial differential equations. These equations are valued because they help to model certain nonlinear wave phenomena that occur in areas of applications such as water waves, plasma physics and nonlinear optics. By supporting the interaction of these experienced and productive collaborators, this award will help to advance our understanding of nonlinear phenomena.