## Abstract

An isospectral problem is introduced, a spectral radius of the corresponding spectral matrix is obtained, which enlightens us to set up an isospectral problem whose compatibility condition gives rise to a zero curvature equation in formalism, from which a Lax integrable soliton equation hierarchy with constraints of potential functions is generated along with 5 parameters, whose reduced cases present three integrable systems, i.e., AKNS hierarchy, Levi hierarchy and D-AKNS hierarchy. Enlarging the above Lie algebra into two bigger ones, the two integrable couplings of the hierarchy are derived, one of them has Hamiltonian structure by employing the quadratic-form identity or variational identity. The corresponding integrable couplings of the reduced systems are obtained, respectively. Finally, as comparing study for generating expanding integrable systems, a Lie algebra of antisymmetric matrices and its corresponding loop algebra are constructed, from which a great number of enlarging integrable systems could be generated, especially their Hamiltonian structure could be computed by the trace identity.

Original language | English |
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Pages (from-to) | 4855-4879 |

Number of pages | 25 |

Journal | International Journal of Modern Physics B |

Volume | 23 |

Issue number | 24 |

DOIs | |

Publication status | Published - 30 Sept 2009 |

## Scopus Subject Areas

- Statistical and Nonlinear Physics
- Condensed Matter Physics

## User-Defined Keywords

- Hamiltonian structure
- Integrable couplings
- Lie algebra
- Spectral radius analysis