Numerical investigation of the stability of the rational solutions of the nonlinear Schrödinger equation
作者：
Highlights：
• Hightlights
• A broad numerical investigation involving large ensembles of perturbed initial data indicates the Peregrine and second order rational solutions of the NLS equation are linearly unstable.
• A highly accurate Chebyshev pseudo-spectral method is developed for solving the NLS equation that uses the map x=cotθ in combination with the Fast Fourier Transform to approximate uxx on an infinite domain.
• A modified Fourier spectral method that can treat initial data with discontinuous derivatives over periodic domains is developed for solving the NLS equation, of which the resolution of the Peregrine solution is a particular example.
摘要
Hightlights•A broad numerical investigation involving large ensembles of perturbed initial data indicates the Peregrine and second order rational solutions of the NLS equation are linearly unstable.•A highly accurate Chebyshev pseudo-spectral method is developed for solving the NLS equation that uses the map x=cotθ in combination with the Fast Fourier Transform to approximate uxx on an infinite domain.•A modified Fourier spectral method that can treat initial data with discontinuous derivatives over periodic domains is developed for solving the NLS equation, of which the resolution of the Peregrine solution is a particular example.
论文关键词：Rogue waves,Peregrine solution,Stability,Spectral splitting,Chebyshev spectral methods,Spectral methods
论文评审过程：Received 29 July 2016, Revised 9 December 2016, Accepted 30 January 2017, Available online 17 February 2017, Version of Record 17 February 2017.
论文官网地址：https://doi.org/10.1016/j.amc.2017.01.060
