Integrable discretization of soliton equations via bilinear method and Bäcklund transformation

Ying Nan Zhang*, Xiang Ke Chang, Juan Hu, Xing Biao Hu, Hon Wah TAM

*Corresponding author for this work

Research output: Contribution to journalJournal articlepeer-review

11 Citations (Scopus)


We present a systematic procedure to derive discrete analogues of integrable PDEs via Hirota’s bilinear method. This approach is mainly based on the compatibility between an integrable system and its Bäcklund transformation. We apply this procedure to several equations, including the extended Korteweg-de-Vries (KdV) equation, the extended Kadomtsev-Petviashvili (KP) equation, the extended Boussinesq equation, the extended Sawada-Kotera (SK) equation and the extended Ito equation, and obtain their associated semi-discrete analogues. In the continuum limit, these differential-difference systems converge to their corresponding smooth equations. For these new integrable systems, their Bäcklund transformations and Lax pairs are derived.

Original languageEnglish
Pages (from-to)279-296
Number of pages18
JournalScience China Mathematics
Issue number2
Publication statusPublished - 17 Jan 2015

Scopus Subject Areas

  • Mathematics(all)

User-Defined Keywords

  • Bilinear method
  • Bäcklund transformation
  • Integrable discretization


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