The matrix Szegő equation

2023/09/21 by Ruoci Sun, Sun, Ruoci
Mathematics · Physics and Astronomy · #37K10 #47B35 #Advanced Algebra and Geometry #Algebraic structures and combinatorial models #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Waves and Solitons

paper · pdf · doi:10.48550/arxiv.2309.12136

openalex publication_date 2023/09/21 · openalex created_date 2023/09/23 · openalex updated_date 2026/07/28

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, i ∂_t U = Π_{≥ 0} (U U ^* U ), Π_{≥ 0}: ∑_{n∈ ℤ}U(n) e^inx ↦ ∑_{n ≥ 0} U(n) e^inx.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 ∈ ℝ.

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