## Abstract

In this paper, a generalized Zakharov-Shabat equation (g-ZS equation), which is an isospectral problem, is introduced by using a loop algebra G. From the stationary zero curvature equation we define the Lenard gradients {g _{j}} and the corresponding generalized AKNS (g-AKNS) vector fields {X_{j}} and X_{k} flows. Employing the nonlinearization method, we obtain the generalized Zhakharov-Shabat Bargmann (g-ZS-B) system and prove that it is Liouville integrable by introducing elliptic coordinates and evolution equations. The explicit relations of the X_{k} flows and the polynomial integrals {H_{k}} are established. Finally, we obtain the finite-band solutions of the g-ZS equation via the Abel-Jacobian coordinates. In addition, a soliton hierarchy and its Hamiltonian structure with an arbitrary parameter k are derived.

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

Pages (from-to) | 968-976 |

Number of pages | 9 |

Journal | Chaos, Solitons and Fractals |

Volume | 44 |

Issue number | 11 |

DOIs | |

Publication status | Published - Nov 2011 |

## Scopus Subject Areas

- Statistical and Nonlinear Physics
- Mathematics(all)
- Physics and Astronomy(all)
- Applied Mathematics