A generalized Zakharov-Shabat equation with finite-band solutions and a soliton-equation hierarchy with an arbitrary parameter

Yufeng Zhang*, Hon Wah TAM, Binlu Feng

*Corresponding author for this work

Research output: Contribution to journalJournal articlepeer-review

8 Citations (Scopus)

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 {Xj} and Xk 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 Xk flows and the polynomial integrals {Hk} 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 languageEnglish
Pages (from-to)968-976
Number of pages9
JournalChaos, Solitons and Fractals
Volume44
Issue number11
DOIs
Publication statusPublished - Nov 2011

Scopus Subject Areas

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

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