Functional representation of the Volterra hierarchy
Exactly Solvable and Integrable Systems
2012-11-09 v1
Abstract
In this paper I study the functional representation of the Volterra hierarchy (VH). Using the Miwa's shifts I rewrite the infinite set of Volterra equations as one functional equation. This result is used to derive a formal solution of the associated linear problem, a generating function for the conservation laws and to obtain a new form of the Miura and Backlund transformations. I also discuss some relations between the VH and KP hierarchy.
Keywords
Cite
@article{arxiv.nlin/0410003,
title = {Functional representation of the Volterra hierarchy},
author = {V. E. Vekslerchik},
journal= {arXiv preprint arXiv:nlin/0410003},
year = {2012}
}
Comments
17 pages, submitted to Journal of Nonlinear Mathematical Physics