The linearized Korteweg-de-Vries equa- tion on general metric graphs

2017/11/02 by Christian Seifert, Seifert, Christian
Mathematics · #Analysis of PDEs (math.AP) #FOS: Mathematics #FOS: Physical sciences #Functional Analysis (math.FA) #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Mathematical Physics (math-ph) #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.1711.00703

openalex publication_date 2017/11/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider the linearized Korteweg-de-Vries equa- tions, sometimes called Airy equation, on general metric graphs with edge lengths bounded away from zero. We show that pro- perties of the induced dynamics can be obtained by studying boundary operators in the corresponding boundary space indu- ced by the vertices of the graph. In particular, we characterize unitary dynamics and contractive dynamics. We demonstrate our results on various special graphs, including those recently treated in the literature.

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