Generalized Casorati determinant and positon-negaton-type solutions of the Toda lattice equation

Ken Ichi Maruno, Wen Xiu Ma, Masayuki Oikawa

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20 Citations (Scopus)


A set of conditions is presented for Casorati determinants to give solutions to the Toda lattice equation. It is used to establish a relation between the Casorati determinant solutions and the generalized Casorati determinant solutions. Positons, negatons and their interaction solutions of the Toda lattice equation are constructed through the generalized Casorati determinant technique. A careful analysis is also made for general positons and negatons, the resulting positons and negatons of order one being explicitly computed. The generalized Casorati determinant formulation for the two dimensional Toda lattice (2dTL) equation is presented. It is shown that positon, negaton and complexiton type solutions in the 2dTL equation exist and these solutions reduce to positon, negaton and complexiton type solutions in the Toda lattice equation by the standard reduction procedure.

Original languageEnglish
Pages (from-to)831-837
Number of pages7
Journaljournal of the physical society of japan
Issue number4
Publication statusPublished - 2004 Apr 1



  • Casorati determinant
  • Negaton
  • Positon
  • Toda lattice

ASJC Scopus subject areas

  • Physics and Astronomy(all)

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