Bäcklund transformations between the AKNS and DNLS hierarchies

Abstract

Starting from the functional representation of the Ablowitz-Kaup-Newell-Segur (AKNS) and derivative nonlinear Schrödinger (DNLS) hierarchies and using the chains of the Miura-like transformations we derive a set of Bäcklund transformations that link solutions of these systems. It is shown that the extended AKNS and DNLS hierarchies possess common set of tau-functions and their connection with the Ablowitz-Ladik hierarchy is established. These results are another manifestation of the already known fact that the AKNS and DNLS hierarchies are closely related and can be viewed as particular cases of a more general system.

16 pages

References in corpus (3)

• Lattice representation and dark solitons of the Fokas-Lenells equation
• Functional representations of integrable hierarchies
• From AKNS to derivative NLS hierarchies via deformations of associative products

Cited by in corpus (3)

• Functional representation of the negative AKNS hierarchy
• General soliton solutions to a coupled Fokas-Lenells equation
• Functional representation of the negative DNLS hierarchy