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.

20 pages

References in corpus (6)

• On a novel integrable generalization of the nonlinear Schrödinger equation
• Functional representations of integrable hierarchies
• Systematic method of generating new integrable systems via inverse Miura maps
• From AKNS to derivative NLS hierarchies via deformations of associative products
• A singular integrable equation from short capillary-gravity waves
• On the One Class of Hyperbolic Systems