Integrable discretization of nonlinear Schrödinger equation and its application with Fourier pseudo-spectral method

Y. Zhang*, X. B. Hu, Hon Wah TAM

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

2 Citations (Scopus)

Abstract

A new integrable discretization of the nonlinear Schr¨odinger (NLS) equation is presented. Different from the one given by Ablowitz and Ladik, we discretize the time variable in this paper. The new discrete system converges to the NLS equation when we take a standard limit and has the same scattering operator as the original NLS equation. This indicates that both the new system and the NLS equation possess the same set of infinite conservation quantities. By applying the Fourier pseudo-spectral method to the space variable, we calculate the first five conservation quantities at different times. The numerical results indeed verify the conservation properties.

Original languageEnglish
Pages (from-to)839-862
Number of pages24
JournalNumerical Algorithms
Volume69
Issue number4
DOIs
Publication statusPublished - 30 Aug 2015

Scopus Subject Areas

  • Applied Mathematics

User-Defined Keywords

  • Fourier pseudo-spectral method
  • Infinite conservation quantities
  • Integrable discretization
  • NLS equation

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