Functional representation of the negative AKNS hierarchy

Abstract

This paper is devoted to the negative flows of the AKNS hierarchy. The main result of this work is the functional representation of the extended AKNS hierarchy, composed of both positive (classical) and negative flows. We derive a finite set of functional equations, constructed by means of the Miwa's shifts, which contains all equations of the hierarchy. Using the obtained functional representation we convert the nonlocal equations of the negative subhierarchy into local systems of higher order, derive the generating function of the conservation laws and the N-dark-soliton solutions for the extended AKNS hierarchy. As an additional result we obtain the functional representation of the Landau-Lifshitz hierarchy.

arXiv comment20 pages

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Cited by in corpus (5)

• A vectorial binary Darboux transformation of the first member of the negative part of the AKNS hierarchy
• Soliton Fay identities. II. Bright soliton case
• Soliton Fay identities. I. Dark soliton case
• Explicit solutions for a (2+1)-dimensional Toda-like chain
• Functional representation of the negative DNLS hierarchy