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.
