Title:
Time: 2:30 - 3:20pm
Place: Condon Room 311 (next to the Design Coffee Shop)
Abstract. Soliton solutions to PDEs are unique in that structure of the waveform is barely changed by interaction with another soliton wave. In fact, the only distinction between the wave before and after the interaction is a phase shift. Despite this simplicity, during the interaction of two solitons, the process is very complicated. In 1974, Kruskal proposed looking at this complicated interaction as a "parade of poles" in the complex plane in order to glean more details of the interaction from a new perspective.
In this talk, I will discuss the history of research in this area, as well as dynamics of the poles for soliton solutions to the Nonlinear Schrodinger equations. I will make remarks about extending this perspective to other solution forms (rational solutions, elliptic solutions) in order to gain additional information about how the solutions behave over finite time.
Everyone welcome!