Functional representation of the Volterra hierarchy

Details Functional representation of the Volterra hierarchy Functional representation of the Volterra hierarchy

2004-10-05

arxiv.org/abs/nlin/0410003v1

Nonlinear Sciences

Exactly Solvable and Integrable Systems

17 pages, submitted to Journal of Nonlinear Mathematical Physics

Scientific paper

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.

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