Continuum limit for the Ablowitz--Ladik system

Abstract

We show that solutions to the Ablowitz--Ladik system converge to solutions of the cubic nonlinear Schrödinger equation for merely $L^2$ 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 Schrödinger equations.

Cited by in corpus (2)

• Continuum limit for discrete NLS with memory effect
• Asymptotics for small data solutions of the Ablowitz-Ladik equation