A few new higher-dimensional Lie algebras and two types of coupling integrable couplings of the AKNS hierarchy and the KN hierarchy

Yu Feng Zhang*, Hon Wah TAM

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

9 Citations (Scopus)

Abstract

Four higher-dimensional Lie algebras are introduced. With the help of their different loop algebras and the block matrices of Lax pairs for the zero curvature representations of two given integrable couplings, the two types of coupling integrable couplings of the AKNS hierarchy and the KN hierarchy are worked out, respectively, which fill up the consequences obtained by Ma and Gao (2009) [9]. The coupling integrable couplings of the AKNS hierarchy obtained in the paper again reduce to the coupling integrable couplings of the nonlinear Schrödinger equation and the modified KdV (mKdV) equation, which are different from the resulting results given by Ma and Gao.

Original languageEnglish
Pages (from-to)76-85
Number of pages10
JournalCommunications in Nonlinear Science and Numerical Simulation
Volume16
Issue number1
DOIs
Publication statusPublished - Jan 2011

Scopus Subject Areas

  • Numerical Analysis
  • Modelling and Simulation
  • Applied Mathematics

User-Defined Keywords

  • Integrable couplings
  • Lie algebra
  • Zero curvature equation

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