## Abstract

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 language | English |
---|---|

Pages (from-to) | 427-434 |

Number of pages | 8 |

Journal | Discontinuity, Nonlinearity, and Complexity |

Volume | 3 |

Issue number | 4 |

DOIs | |

Publication status | Published - 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