4 papers · 1 filter
Long-time validity of the Korteweg-de Vries approximation for the Boussinesq equation
Younghun Hong, Junyeong Jang
We consider the Korteweg-de Vries (KdV) approximation for the good Boussinesq equation. Building upon the low-regularity local-in-time justification established by Hong and Yang \c…
Long-time reduction for the biharmonic nonlinear Schrödinger equation
Younghun Hong, Junyeong Jang
In this article, we study the reduction of the one-dimensional biharmonic nonlinear Schrödinger equation to the cubic nonlinear Schrödinger equation in the vanishing higher-order d…
Long-time Korteweg-de Vries approximation for the Fermi-Pasta-Ulam-Tsingou system
Younghun Hong, Junyeong Jang
We prove that, as the lattice spacing tends to zero, general solutions to the infinite Fermi--Pasta--Ulam--Tsingou (FPUT) system can be approximated in by two counter-pro…
On the Benjamin-Bona-Mahony regularization of the Korteweg-de Vries equation
Younghun Hong, Junyeong Jang, Changhun Yang
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 t…