Zero Curvature Representation, Bi-Hamiltonian Structure, And An Integrable Hierarchy For The Zakharov-Ito System

Abstract

In the present paper, we present an integrable hierarchy for the Zakharov-Ito system. We first construct the Lenard recursion sequence and zero curvature representation for the Zakharov-Ito system, following Cao's method as significantly generalized by other authors. We then construct the bi-Hamiltonian structures employing variational trace identities but woven together with the Lenard recursion sequences. From this, we are in a position to construct an integrable hierarchy of equations from the Zakharov-Ito system, and we obtain the recursion operator and Poisson brackets for constructing this hierarchy. Finally, we demonstrate that the obtained hierarchy is indeed Liouville integrable.

Publication Date

6-1-2015

Publication Title

Journal of Mathematical Physics

Volume

56

Issue

6

Document Type

Article

Personal Identifier

scopus

DOI Link

https://doi.org/10.1063/1.4922361

Socpus ID

84934966632 (Scopus)

Source API URL

https://api.elsevier.com/content/abstract/scopus_id/84934966632

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