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

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

ISSN (print)

09600779

This document is currently not available here.

Share

COinS