Abstract
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. These results are used to derive a formal solution of the associated linear problem and 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 other integrable systems.
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© 2004 Kluwer Academic Publishers
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Vekslerchik, V. (2004). Miwa’s Representation of the Volterra Hierarchy. In: Abdullaev, F.K., Konotop, V.V. (eds) Nonlinear Waves: Classical and Quantum Aspects. NATO Science Series II: Mathematics, Physics and Chemistry, vol 153. Springer, Dordrecht. https://doi.org/10.1007/1-4020-2190-9_42
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DOI: https://doi.org/10.1007/1-4020-2190-9_42
Publisher Name: Springer, Dordrecht
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