Document Type

Journal Article

Department/Unit

Department of Computer Science

Title

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

Language

English

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. © 2011 Elsevier Ltd. All rights reserved.

Publication Date

2011

Source Publication Title

Chaos, Solitons and Fractals

Volume

44

Issue

11

Start Page

968

End Page

976

Publisher

Elsevier

DOI

10.1016/j.chaos.2011.07.014

Link to Publisher's Edition

http://dx.doi.org/10.1016/j.chaos.2011.07.014

ISSN (print)

09600779

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