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

该奖项支持宾夕法尼亚州立大学的Jerry Bona、田纳西大学的Ohannes karakashan和北卡罗莱纳州立大学的William McKinney三位美国研究人员以及克里特大学的George Akrivis和雅典国立技术大学的Vassilios Dougalis两位希腊研究人员之间的合作研究。这项合作将在希腊伊拉克利翁的应用和计算数学研究所进行。研究的目的是研究三种类型的偏微分方程的数值解，这些方程模拟了非线性色散系统中波传播现象的各个方面。本研究的重点是设计和分析有趣的和有用的非线性色散波动方程的积分的数值格式。这种数值方法对于结合实验室实验和研究包括奇点形成在内的解的详细结构至关重要。该项目还包括将这些方案作为计算机代码实施，并将这些代码用于研究与这类偏微分方程相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.