Functional Representation of the Ablowitz­Ladik Hierarchy. II

DOI

10.2991/jnmp.2002.9.2.3How to use a DOI?

Abstract

In this paper we continue studies of the functional representation of the Ablowitz­ Ladik hierarchy (ALH). Using formal series solutions of the zero-curvature condition we rederive the functional equations for the tau-functions of the ALH and obtain some new equations which provide more straightforward description of the ALH and which were absent in our previous paper. These results are used to establish relations between the ALH and the discrete-time nonlinear Schrödinger equations, to deduce the superposition formulae (Fay's identities) for the tau-functions of the hierarchy and to obtain some new results related to the Lax representation of the ALH and its conservation laws. Using the previously found connections between the ALH and other integrable systems we derive functional equations which are equivalent to the AKNS, derivative nonlinear Schrödinger and Davey­Stewartson hierarchies.

Copyright

© 2006, the Authors. Published by Atlantis Press.

Open Access

This is an open access article distributed under the CC BY-NC license (http://creativecommons.org/licenses/by-nc/4.0/).

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TY  - JOUR
AU  - V.E. Vekslerchik
PY  - 2002
DA  - 2002/05/01
TI  - Functional Representation of the Ablowitz­Ladik Hierarchy. II
JO  - Journal of Nonlinear Mathematical Physics
SP  - 157
EP  - 180
VL  - 9
IS  - 2
SN  - 1776-0852
UR  - https://doi.org/10.2991/jnmp.2002.9.2.3
DO  - 10.2991/jnmp.2002.9.2.3
ID  - Vekslerchik2002
ER  -