Year: 2023
Type: preprint
Abstract: This paper is dedicated to studying the matrix solutions to the cubic Szegő equation, introduced in Gérard--Grellier (2009) arXiv:0906.4540, leading to the cubic matrix Szegő equation on the torus, \begin{equation*} i \partial_t U = Π_{\geq 0} \left(U U ^* U \right), \quad Π_{\geq 0}: \sum_{n\in \mathbb{Z}}\hat{U}(n) e^{inx} \mapsto \sum_{n \geq 0} \hat{U}(n) e^{inx}. \end{equation*}This equation enjoys a two-Lax-pair structure, which allow every solution to be expressed explicitly in terms of the initial datum and the time $t \in \mathbb{R}$.
Source: arXiv (Cornell University)
Author: Sun, Ruoci
Institution: Georgia Institute of Technology
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Funder: Georgia Institute of Technology
OpenAlex ID: W4386977839