Seminar Event Detail


Integrable Systems and Random Matrix Theory

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

 

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