Integrable discretization of 'time' and its application on the Fourier pseudospectral method to the Korteweg-de Vries equation

Yingnan Zhang*, Hon Wah TAM, Xingbiao Hu

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

5 Citations (Scopus)

Abstract

This paper presents a new integrable discretization of the Korteweg-de Vries (KdV) equation. Different from other discrete analogues, we discretize the variable 'time' and obtain an integrable differential-difference system. This system has the original KdV equation as a standard limit when the step size tends to zero. The main idea is based on Hirota's bilinear method and Bäcklund transformation and can be applied to other integrable systems. By applying the Fourier pseudospectral method to the space variable, we derive a new numerical scheme for the KdV equation. Numerical results are found to agree with the exact solution and the first five conservation quantities are preserved quite well.

Original languageEnglish
Article number045202
JournalJournal of Physics A: Mathematical and Theoretical
Volume47
Issue number4
DOIs
Publication statusPublished - 31 Jan 2014

Scopus Subject Areas

  • Statistical and Nonlinear Physics
  • Statistics and Probability
  • Modelling and Simulation
  • Mathematical Physics
  • Physics and Astronomy(all)

User-Defined Keywords

  • Fourier pseudospectral method
  • integrable discretization
  • KdV equation

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