Two enlarged loop algebras for obtaining new integrable hierarchies

Yufeng Zhang*, Hon Wah TAM, Wei Jiang

*Corresponding author for this work

Research output: Contribution to journalJournal articlepeer-review


Taking a loop algebra B̄2 we obtain an integrable soliton hierarchy which is similar to the well-known KaupNewell (KN) hierarchy, but it is not. We call it a modified KN (mKN) hierarchy. Then two new enlarged loop algebras of the loop algebra B̄2 are established, respectively, which are used to establish isospectral problems. Thus, two various types of integrable soliton-equation hierarchies along with multi-component potential functions are obtained. Their Hamiltonian structures are also obtained by the variational identity. The second hierarchy is integrable couplings of the mKN hierarchy. This paper provides a clue for generating loop algebras, specially, gives an approach for producing new integrable systems. If we obtain a new soliton hierarchy, we could deduce its symmetries, conserved laws, Darboux transformations, soliton solutions and so on. Hence, the way presented in the paper is an important aspect to obtain new integrable systems in soliton theory.

Original languageEnglish
Pages (from-to)2637-2656
Number of pages20
JournalInternational Journal of Modern Physics B
Issue number19
Publication statusPublished - 30 Jul 2011

Scopus Subject Areas

  • Statistical and Nonlinear Physics
  • Condensed Matter Physics

User-Defined Keywords

  • Hamiltonian structure
  • integrable system
  • Loop algebra


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