On the KdV approximation for a Boussinesq equation posed on the infinite necklace graph

2023/11/09 by Wolf‐Patrick Düll, Düll, Wolf-Patrick, Guido Schneider +3 · 1 citation
Engineering · Mathematics · Physics and Astronomy · #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #Electromagnetic Simulation and Numerical Methods #FOS: Mathematics #Nonlinear Photonic Systems

paper · pdf · doi:10.48550/arxiv.2311.05489

openalex publication_date 2023/11/09 · openalex created_date 2023/11/11 · openalex updated_date 2026/07/28

Abstract

We consider a Boussinesq equation posed on the infinite periodic necklace graph. For the description of long wave traveling waves we derive the KdV equation and establish the validity of this formal approximation by providing estimates for the error. The proof is based on suitable energy estimates.

Cited by

• Traveling waves in periodic metric graphs via spatial dynamics

Related

• On the Korteweg-de Vries limit for the Boussinesq equation
• Reductive Perturbation Method, Multiple-Time Solutions and the KdV Hierarchy
• Mathematical properties of Klein-Gordon-Boussinesq systems
• Boussinesq equation
• Schrodinger equation and wave equation on finite graphs