On the Benjamin-Bona-Mahony regularization of the Korteweg-de Vries equation
Younghun Hong, Junyeong Jang, Changhun Yang
TL;DR
This paper proves that solutions of the Benjamin-Bona-Mahony (BBM) equation converge to those of the Korteweg-de Vries (KdV) equation for energy class solutions, extending the validity period of the BBM regularization.
Contribution
It establishes the convergence of BBM solutions to KdV solutions and extends the temporal validity of the BBM regularization using conservation laws.
Findings
Proves convergence of BBM to KdV for energy class solutions
Extends the time interval of validity for BBM regularization
Utilizes conservation laws to support the analysis
Abstract
The Benjamin-Bona-Mahony equation (BBM) is introduced as a regularization of the Korteweg-de Vries equation (KdV) for long water waves \cite{BBM1972}. 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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Taxonomy
TopicsAdvanced Mathematical Physics Problems · Nonlinear Waves and Solitons · Nonlinear Photonic Systems