Bäcklund transformations between the AKNS and DNLS hierarchies

Details Bäcklund transformations between the AKNS and DNLS hierarchies Bäcklund transformations between the AKNS and DNLS hierarchies

2011-10-24

arxiv.org/abs/1110.5163v1

Nonlinear Sciences

Exactly Solvable and Integrable Systems

16 pages

Scientific paper

Starting from the functional representation of the Ablowitz-Kaup-Newell-Segur (AKNS) and derivative nonlinear Schr\"odinger (DNLS) hierarchies and using the chains of the Miura-like transformations we derive a set of B\"acklund 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.

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