Abstract We show that solutions to the Ablowitz–Ladik system converge of cubic nonlinear Schrödinger equation for merely L 2 initial data. Furthermore, we consider data this lattice model excites Fourier modes near both critical points discrete dispersion relation and demonstrate convergence a decoupled equations.

Scientists have observed and studied diffusive waves in contexts as disparate population genetics cell signaling. Often, these are propagated by discrete entities or agents, such individual cells the case of For a broad class waves, we characterize transition between collective propagation -- which wave speed is well-described continuum theory agents. We show that this depends heavily on dimens...