Discretization effects in the nonlinear Schrödinger equation Original Research Article

We show that discretization effects in finite-difference simulations of blowup solutions of the nonlinear Schrödinger equation (NLS) initially accelerate self focusing but later arrest the collapse, resulting instead in focusing–defocusing oscillations. The modified equation of the semi-discrete NLS, which is the NLS with high-order anisotropic dispersion, captures the arrest of collapse but not the subsequent oscillations. Discretization effects in perturbed NLS equations are also discussed.