An (2+1)-dimensional expanding model of the Davey-stewartson hierarchy as well as its hamiltonian structure

Yufeng Zhang*, Wenjuan Rui, Hon Wah TAM

*Corresponding author for this work

Research output: Contribution to journalJournal articlepeer-review

5 Citations (Scopus)


Introducing a new 6-dimensional Lie algebra aims at generating a Lax pair whose compatibility condition gives rise to (1+1)-dimensional integrable hierarchy of equationswhich can reduce to the nonlinear Schrödinger equation and two sets of nonlinear integrable equations by taking various parameters. The Hamiltonian structure of the (1+1)-dimensional hierarchy is also obtained by using the trace identity. The reason for generating the above (1+1)-dimensional integrable hierarchy lies in obtaining (2+1)-dimensional equation hierarchy. That is to say, with the hep of the higher dimensional Lie algebra, we introduce two 4×4 matrix operators in an associative algebra A (ξ) for which a new (2+1)-dimensional hierarchy of equations is derived by using the TAH scheme and the Hamiltonian operator in the case of 1+1 dimensions, which generalizes the results presented by Tu, that is, the reduced case of the hierarchy obtained by us can be reduced to the Davey-Stewartson (DS) hierarchy. Finally, the Hamiltonian structure of the (2+1)-dimensional hierarchy is produced by the trace identity used for 2+1 dimensions, which was proposed by Tu. As we have known that there is no paper involving such the problem on generating expanding models of (2+1)-dimensional integrable hierarchy.

Original languageEnglish
Pages (from-to)427-434
Number of pages8
JournalDiscontinuity, Nonlinearity, and Complexity
Issue number4
Publication statusPublished - 2014

Scopus Subject Areas

  • Statistical and Nonlinear Physics
  • Computational Mechanics
  • Discrete Mathematics and Combinatorics
  • Control and Optimization

User-Defined Keywords

  • Hamiltonian structure
  • Integrable hierarchy
  • Lax pair


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