2 research outputs found
Functional representation of the Volterra hierarchy
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.Comment: 17 pages, submitted to Journal of Nonlinear Mathematical Physic