Negaton and positon solutions of the soliton equation with self-consistent sources

Yunbo Zeng*, Yijun Shao, Weimin Xue

*Corresponding author for this work

Research output: Contribution to journalJournal articlepeer-review

57 Citations (Scopus)


The Korteweg-de Vries (KdV) equation with self-consistent sources (KdVES) is used as a model to illustrate this method. We present a generalized binary Darboux transformation (GBDT) with an arbitrary time-dependent function for the KdVES as well as the formula for N-times repeated GBDT. This GBDT provides non-auto-Bäcklund transformation between two KdV equations with different degrees of sources and enables us to construct more general solutions with N arbitrary t-dependent functions. By taking the special t-function, we obtain multisoliton, multipositon, multinegaton, multisoliton-positon, multinegaton-positon and multisoliton-negaton solutions of the KdVES.

Original languageEnglish
Pages (from-to)5035-5043
Number of pages9
JournalJournal of Physics A: Mathematical and General
Issue number18
Publication statusPublished - 9 May 2003
Externally publishedYes

Scopus Subject Areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics
  • Physics and Astronomy(all)


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