Matrix generalization of the cubic Szegő equation

Analysis Seminar
Wednesday, March 27, 2024 - 2:00pm for 1 hour (actually 50 minutes)
Skiles 005
Ruoci Sun – Georgia Tech
Benjamin Jaye

This presentation is devoted to studying matrix solutions of the cubic Szegő equation, leading to the matrix Szegő equation on the 1-d torus and on the real line. The matrix Szegő equation enjoys a Lax pair structure, which is slightly different from the Lax pair structure of the cubic scalar Szegő equation introduced in Gérard-Grellier [arXiv:0906.4540]. We can establish an explicit formula for general solutions both on the torus and on the real line of the matrix Szegő equation. This presentation is based on the works Sun [arXiv:2309.12136arXiv:2310.13693].