Two integrable coupled nonlinear systems

Hon Wah TAM*, Xing Biao Hu, Dao Liu Wang

*Corresponding author for this work

Research output: Contribution to journalJournal articlepeer-review

24 Citations (Scopus)


Motivated by Hirota and Satsuma's results on their coupled KdV equation, two integrable coupled nonlinear systems are considered. One of them is a coupled Ito system. It is shown that the coupled Ito system is a special case of the (6,2)-reduction of the two component BKP hierarchy while the other coupled system can be obtained from the (5,1)-reduction of the two component BKP hierarchy. By using MATHEMATICA, we obtain the 3- and 4-soliton solutions of the coupled Ito system. In addition, starting from bilinear equations of the other coupled system, a Bäcklund transformation is found and nonlinear superposition formulae are established. Soliton solutions and rational solutions are also derived from these results.

Original languageEnglish
Pages (from-to)369-379
Number of pages11
JournalJournal of the Physical Society of Japan
Issue number2
Publication statusPublished - Feb 1999

Scopus Subject Areas

  • Physics and Astronomy(all)

User-Defined Keywords

  • Bäcklund transformation
  • Hirota's method
  • Integrable systems
  • Solitons
  • Superposition principle


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