Continuum limit for the Ablowitz--Ladik system
Analysis of PDEs
2023-06-21 v1
Abstract
We show that solutions to the Ablowitz--Ladik system converge to solutions of the cubic nonlinear Schr\"odinger equation for merely initial data. Furthermore, we consider initial data for this lattice model that excites Fourier modes near both critical points of the discrete dispersion relation and demonstrate convergence to a decoupled system of nonlinear Schr\"odinger equations.
Keywords
Cite
@article{arxiv.2206.02720,
title = {Continuum limit for the Ablowitz--Ladik system},
author = {Rowan Killip and Zhimeng Ouyang and Monica Visan and Lei Wu},
journal= {arXiv preprint arXiv:2206.02720},
year = {2023}
}