On generating integrable dynamical systems in 1+1 and 2+1 dimensions by using semisimple lie algebras

Yufeng Zhang*, Hon Wah TAM, Lixin Wu

*Corresponding author for this work

Research output: Contribution to journalJournal articlepeer-review

3 Citations (Scopus)


We deduce a set of integrable equations under the framework of zero curvature equations and obtain two sets of integrable soliton equations, which can be reduced to some new integrable equations including the generalised nonlinear Schrödinger (NLS) equation. Under the case where the isospectral functions are oneorder polynomials in the parameter λ, we generate a set of rational integrable equations, which are reduced to the loop soliton equation. Under the case where the derivative λt of the spectral parameter λ is a quadratic algebraic curve in λ, we derive a set of variable-coefficient integrable equations. In addition, we discretise a pair of isospectral problems introduced through the Lie algebra given by us for which a set of new semi-discrete nonlinear equations are available; furthermore, the semi-discrete MKdV equation and the Hirota lattice equation are followed to produce, respectively. Finally, we apply the Lie algebra to introduce a set of operator Lax pairs with an operator, and then through the Tu scheme and the binomial-residue representation method proposed by us, we generate a 2+1-dimensional integrable hierarchy of evolution equations, which reduces to a generalised 2+1-dimensional Davey-Stewartson (DS) equation.

Original languageEnglish
Pages (from-to)975-977
Number of pages3
JournalZeitschrift fur Naturforschung - Section A Journal of Physical Sciences
Issue number11
Publication statusPublished - 2015

Scopus Subject Areas

  • Mathematical Physics
  • Physics and Astronomy(all)
  • Physical and Theoretical Chemistry

User-Defined Keywords

  • Hirota lattice equation
  • Lie algebra
  • Semidiscrete equation


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