Spectral radius analysis of matrices and the associated with integrable systems

Hon Wah TAM*, Yufeng Zhang

*Corresponding author for this work

Research output: Contribution to journalJournal articlepeer-review

2 Citations (Scopus)


An isospectral problem is introduced, a spectral radius of the corresponding spectral matrix is obtained, which enlightens us to set up an isospectral problem whose compatibility condition gives rise to a zero curvature equation in formalism, from which a Lax integrable soliton equation hierarchy with constraints of potential functions is generated along with 5 parameters, whose reduced cases present three integrable systems, i.e., AKNS hierarchy, Levi hierarchy and D-AKNS hierarchy. Enlarging the above Lie algebra into two bigger ones, the two integrable couplings of the hierarchy are derived, one of them has Hamiltonian structure by employing the quadratic-form identity or variational identity. The corresponding integrable couplings of the reduced systems are obtained, respectively. Finally, as comparing study for generating expanding integrable systems, a Lie algebra of antisymmetric matrices and its corresponding loop algebra are constructed, from which a great number of enlarging integrable systems could be generated, especially their Hamiltonian structure could be computed by the trace identity.

Original languageEnglish
Pages (from-to)4855-4879
Number of pages25
JournalInternational Journal of Modern Physics B
Issue number24
Publication statusPublished - 30 Sept 2009

Scopus Subject Areas

  • Statistical and Nonlinear Physics
  • Condensed Matter Physics

User-Defined Keywords

  • Hamiltonian structure
  • Integrable couplings
  • Lie algebra
  • Spectral radius analysis


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