Continuum limit for the Ablowitz–Ladik system
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 …