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Dalhousie-AARMS AAMP Seminar: Manuela Girotti (Saint Mary’s Uni.)
March 25, 2022 @ 4:00 pm - 5:00 pm
Title: Asymptotic Analysis of the Interaction Between a Soliton and a Regular Gas of Solitons (a.k.a. Gulliver and the Lilliputians)
Abstract: N. Zabusky coined the word “soliton” in 1965 to describe a curious feature he and M. Kruskal observed in their numerical simulations of the initial-value problem for a simple nonlinear PDE. The first part of the talk will be a broad introduction to the theory of solitons/solitary waves and integrable PDEs (the KdV and modified KdV equation in particular), describing classical results in the field.
The second part will focus on some new developments and growing interest into a special case of solitons defined as “solitonic gas” or “integrable turbulence”. In particular, we will discuss a recent work on long-time asymptotic behaviour of such type of solitons. We will achieve our results by first framing the problem in the setting of a Riemann–Hilbert problem and then by rigorously analyzing it using the powerful technique of nonlinear steepest descent.
This is a joint work with Tamara Grava (U. Bristol/SISSA), Bob Jenkins (UCF), Ken McLaughlin (CSU) and Alexander Minakov (U. Karlova).
The Dalhousie-AARMS Analysis-Applied Math-Physics Seminar takes place on Fridays from 4 – 5 pm Atlantic Time over Zoom. If you would like to attend, please email the organizers for connection details.