A novel numerical approach to simulating nonlinear Schrödinger equations with varying coefficients Original Research Article

We describe a novel numerical approach to simulations of nonlinear Schrödinger equations with varying coefficients, based on the discovery of a new and intrinsic conservation law for varying coefficient nonlinear Schrödinger equations. The approach is shown to preserve some crucial classical conservations, such as the spatial ergodicity, and utilized in numerical simulations of periodically and quasi-periodically solitary waves for nonlinear Schrödinger equations with periodic or quasi-periodic coefficients. Some numerical experiments are presented to illustrate the conservative property.