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Functional representation of the Volterra hierarchy

V. E. Vekslerchik
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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.

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V. E. Vekslerchik. 2004-10-05. Functional representation of the Volterra hierarchy. https://doi.org/10.2991/jnmp.2005.12.3.6

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