Promotion Talk - Marco Roque-Sol

Date: October 13, 2017

Time: 1:00PM - 2:00PM

Location: BLOC 220

Speaker: Marco Roque-Sol, Texas A&M University

Description:

Title: An introduction to Solitons.

Abstract:
The study of differential equations plays an essential role in applying mathematics to physical systems. A mathematically important aspect of these studies is the theory of integrable systems, which currently plays an important role in many branches of modern mathematics and mathematical physics, among those we can find: Oscillations in Classical Mechanics, wave equation in Electrodynamics, Schrõdinger equation in Quantum Mechanics, ( Ernst ) Ising model to explain ferromagnetism in statistical mechanics, quantum field theory (QFT), a set of quantum mechanical models of subatomic particles, Solitons, ... etc. This presentation gives a survey of the soliton theory, starting by introducing some historical remarks, basic concepts of the mathematical aspects of Soliton Theory, and later on, talking about the KdV ( Diederik Korteweg and Gustav de Vrise) equation with its traveling wave solution. The aim of this talk is to serve as an introductory session to the more advanced material related to global attraction to solitary waves where we study properties of solitary wave solutions of the form φ(x)e^{-iωt} , with ω real and φ(x) localized in space.