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Additional Fay Identities Of The Extended Toda Hierarchy, Yu Wan
Additional Fay Identities Of The Extended Toda Hierarchy, Yu Wan
Rose-Hulman Undergraduate Mathematics Journal
The focus of this paper is the extended Toda Lattice hierarchy, an infinite system of partial differential equations arising from the Toda lattice equation. We begin by giving the definition of the extended Toda hierarchy and its explicit bilinear equation, following Takasaki’s construction. We then derive a series of new Fay identities. Finally, we discover a general formula for one type of Fay identity.