The 2015 AMMCS-CAIMS Congress

Interdisciplinary AMMCS Conference Series

Waterloo, Ontario, Canada | June 7-12, 2015

AMMCS-CAIMS 2015 Semi-Plenary Talk

On long time dynamics in nonlinear wave equations

Eduard-Wilhelm Kirr (University of Illinois at Urbana-Champaign)

Since the first description in 1834 of the "wave of translation", currently called soliton, by John Scott Russell, scientist have studied intensely such particular solutions of nonlinear wave equations i.e., coherent structures that do not change shape as they propagate. They have been put to good use in nonlinear optics and telecommunications, and play an important role in understanding the formation of large waves in oceans and in analyzing large systems of quantum particles. Moreover their importance in describing the large time behavior of nonlinear wave models is summarized by the following: Asymptotic Completeness Conjecture: any initial data of a nonlinear wave equations evolves into a superposition of coherent structures plus a part that radiates to infinity. My presentation will summarize both our current knowledge on existence of coherent structures and recent progress towards solving the asymptotic completeness conjecture.
Eduard-Wilhem Kirr is currently an associate professor in the Mathematics Department at University of Illinois Urbana-Champaign. He obtained his Ph.D. in Mathematics from University of Michigan in 2002 under the direction of Michael I. Weinstein and Anthony Bloch and was a Dickson Instructor at University of Chicago from 2002 to 2005 under the direction of Peter Constantin. During his graduate studies he was also a summer intern at Bell Laboratories. His main research interests focus on studying wave propagation and wave interaction using both theoretical methods and numerical simulations.