Integrability and Beyond

This is the official webpage for the seminar Integrability and Beyond, organized by the research group of Kenneth D. T-R. McLaughlin from the mathematics department of Tulane University. The seminar is focused on the study of integrable systems, their applications, and related topics in mathematics and physics.

The seminar is held every Tuesday at 5:00 PM in Richardson Building room 201

Inverse scattering transform for the Korteweg-de Vries equation

In this series of lecture, we focus on the inverse scattering transform (IST) method for solving the Korteweg-de Vries (KdV) equation, a fundamental nonlinear partial differential equation that describes the evolution of shallow water waves. We will explore the mathematical foundations of IST, including the Lax pair formulation, the scattering problem, and the reconstruction of solutions from scattering data. We will follow the lecture notes by Prof. Tamara Grava.

  • Lecture 1: Traveling wave solution to the KdV equation; Video
  • Lecture 2: Conserved Quantities and the Lax pais; Video
  • Lecture 3: Conserved Quantities and the linear KdV equation; Video
  • Lecture 4: Scattering Theory Part 1; Video