Date: Monday, September 27, 2021
Location: ZOOM ID: 926 6491 9790 Virtual (4:00 PM to 5:00 PM)
Title: Weakly Nonlinear Longwave Models and Solitons
Abstract: In this talk I will discuss (1+1) D completely integrable partial differential equations that; in particular, I will consider the Korteweg--de Vries equation and the Kaup--Broer system with both weak and strong capillarity. I will discuss solitary waves or 1-soliton solutions to these equations, discuss a nonlinear superposition principal that allows the calculation of what are called N-soliton solutions, and then consider various classes of solutions that can be produced as a limit of these solutions and N goes to infinity. I will also discuss the periodic and quasiperiodic solutions. I will discuss recent approaches based on the theory of Riemann--Hilbert problems and singular integral equations. I will give some motivation for this work based on the goal of modeling a soliton gas, and provide a brief literature review of some recent experimental results on soliton gasses in hydrodynamics.
A recording can be found here.
Files:
Speaker: Patrik Nabelek
Institution: Oregon State University
Event Organizer: Ahmad Barhoumi barhoumi@umich.edu
|
