On the Benjamin-Bona-Mahony regularization of the Korteweg-de Vries equation

2025/01/18 by Younghun Hong, Hong, Younghun, Jang, Junyeong +2 · 1 citation
Mathematics · Physics and Astronomy · #35Q53 #76B15 #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Photonic Systems #Nonlinear Waves and Solitons

paper · pdf · doi:10.48550/arxiv.2501.10899

openalex publication_date 2025/01/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The Benjamin-Bona-Mahony equation (BBM) is introduced as a regularization of the Korteweg-de Vries equation (KdV) for long water waves \citeBBM1972. In this paper, we establish the convergence from the BBM to the KdV for energy class solutions. As a consequence, employing the conservation laws, we extend the known temporal interval of validity for the BBM regularization.

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• On the steadiness of symmetric solutions to higher order perturbations of KdV

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