Integrable hamiltonian hierarchies associated with the equation of heat conduction

Yufeng Zhang*, Hon Wah TAM, Jianqin Mei

*Corresponding author for this work

Research output: Contribution to journalJournal articlepeer-review

2 Citations (Scopus)


Using a 4-dimensional Lie algebra g, an isospectral Lax pair is introduced, whose compatibility condition is equivalent to a soliton hierarchy of evolution equations with three components of potential functions. Its Hamiltonian structure is obtained by employing the quadratic-form identity proposed by Guo and Zhang. In order to obtain explicit Hamiltonian functions, a detailed computing formula for the constant appearing in the quadratic-form identity is obtained. One type of reduction equations of the hierarchy is also produced, which is further reduced to the standard equation of heat conduction. By introducing a loop algebra of the Lie algebra g, we obtain a soliton hierarchy with an arbitrary parameter which can be reduced to the previous equation hierarchy obtained, whose quasi-Hamiltonian structure is also worked out by the quadratic-form identity. Finally, we extend the Lie algebra g into a higher-dimensional Lie algebra so that a new integrable Hamiltonian hierarchy, which comprise integrable couplings, is produced; its reduced equations in particular contain two arbitrary parameters.

Original languageEnglish
Pages (from-to)1573-1594
Number of pages22
JournalModern Physics Letters B
Issue number14
Publication statusPublished - 10 Jun 2010

Scopus Subject Areas

  • Statistical and Nonlinear Physics
  • Condensed Matter Physics

User-Defined Keywords

  • Hamiltonian structure
  • Lie algebra
  • Quadratic-form identity


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