## Abstract

Using a 4-dimensional Lie algebra g, an isospectral Lax pair is introduced, whose compatibility condition is equivalent to a soliton hierarchy of evolution equations with three components of potential functions. Its Hamiltonian structure is obtained by employing the quadratic-form identity proposed by Guo and Zhang. In order to obtain explicit Hamiltonian functions, a detailed computing formula for the constant appearing in the quadratic-form identity is obtained. One type of reduction equations of the hierarchy is also produced, which is further reduced to the standard equation of heat conduction. By introducing a loop algebra of the Lie algebra g, we obtain a soliton hierarchy with an arbitrary parameter which can be reduced to the previous equation hierarchy obtained, whose quasi-Hamiltonian structure is also worked out by the quadratic-form identity. Finally, we extend the Lie algebra g into a higher-dimensional Lie algebra so that a new integrable Hamiltonian hierarchy, which comprise integrable couplings, is produced; its reduced equations in particular contain two arbitrary parameters.

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

Pages (from-to) | 1573-1594 |

Number of pages | 22 |

Journal | Modern Physics Letters B |

Volume | 24 |

Issue number | 14 |

DOIs | |

Publication status | Published - 10 Jun 2010 |

## Scopus Subject Areas

- Statistical and Nonlinear Physics
- Condensed Matter Physics

## User-Defined Keywords

- Hamiltonian structure
- Lie algebra
- Quadratic-form identity