An artificially-damped Fourier method for dispersive evolution equations

Computing solutions to partial differential equations using the fast Fourier transform can lead unwanted oscillatory behavior. Due periodic nature of discrete transform, waves that leave computational domain on one side reappear other and for dispersive these are typically high-velocity, high-frequency waves. However, is a very efficient numerical tool it important find way damp oscillations so this still be used. In paper, we accurately model four nonlinear an infinite by considering finite interval implementing two damping methods outside interval: solves heat equation simulates rapid exponential decay. Heat equation-based best suited small-amplitude, while decay used traveling high-amplitude oscillations. We demonstrate significant improvements in runtime well-studied when adding method.