U.S.-Greece Cooperative Research: Numerical Studies of Nonlinear, Dispersive Wave Equations

该奖项支持三名美国研究人员之间的合作研究，他们是宾夕法尼亚州立大学的曾傑瑞·博纳、田纳西大学的Ohannes Karakashian和北卡罗来纳州立大学的威廉·麦金尼，以及克里特大学的George Akrivis和雅典国家技术大学的Vassilios Dougalis。合作将在希腊伊拉克利安的应用和计算数学研究所(FORTH)进行。这项研究的目的是关于三类偏微分方程组的数值解，这些偏微分方程组模拟了非线性色散系统中波传播现象的各个方面。这项研究致力于设计和分析数值格式，用于积分有趣和有用的非线性色散波动方程。这种数值方法对于结合实验室实验使用以及研究包括奇点形成在内的解的详细结构至关重要。该项目还包括将格式实现为计算机代码，并将这些代码用于研究与这类偏微分方程组有关的理论和应用问题。

This award supports cooperative research between three U.S. researchers, Jerry Bona at the Pennsylvania State University, Ohannes Karakashian at the University of Tennessee, and William McKinney at North Carolina State University, and two Greek researchers, George Akrivis at the University of Crete and Vassilios Dougalis at the National Technical University in Athens. The collaboration will occur at the Institute of Applied and Computational Mathematics (FORTH) in Heraklion, Greece. The objective of the research concerns the numerical solution of three types of partial differential equations that model various aspects of wave propagation phenomena in nonlinear dispersive systems. The research is concerned with the design and analysis of numerical schemes for the integration of interesting and useful classes of nonlinear, dispersive wave equations. Such numerical methods are crucially important for use in conjunction with laboratory experiments and for the study of the detailed structure of solutions including singularity formation. The project also includes implemen tation of the schemes as computer codes and the use of these codes int he investigation of theoretical and applied issues connected with this class of partial differential equations.