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
Copyright Status
Unknown
Socpus ID
84934966632 (Scopus)
Source API URL
https://api.elsevier.com/content/abstract/scopus_id/84934966632
STARS Citation
Baxter, Mathew; Roy Choudhury, S.; and Van Gorder, Robert A., "Zero Curvature Representation, Bi-Hamiltonian Structure, And An Integrable Hierarchy For The Zakharov-Ito System" (2015). Scopus Export 2015-2019. 178.
https://stars.library.ucf.edu/scopus2015/178