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，宾夕法尼亚州立大学的Jerry Bona，田纳西大学的Ohannes Karakashian和北卡罗来纳州州立大学的William McKinney，以及两名希腊研究人员，克里特大学的乔治Akrivis和雅典国立技术大学的Vassilios Dougalis之间的合作研究。 这项合作将在希腊赫拉克利翁的应用和计算数学研究所（FORTH）进行。 研究的目标涉及三种类型的偏微分方程的数值解，这些偏微分方程模拟了非线性色散系统中波传播现象的各个方面。 研究关注的是有趣的和有用的类的非线性，色散波方程的积分的数值方案的设计和分析。 这种数值方法是至关重要的，与实验室实验结合使用，并为研究的详细结构的解决方案，包括奇点的形成。 该项目还包括实施计划的计算机代码和使用这些代码在他的调查与这类偏微分方程的理论和应用问题。

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.