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.

Author Bio

Yu Wan is a senior undergraduate student at the University of Minnesota, Twin Cities. At the time of this writing, he is pursuing a BS degree in Mathematics and a BA degree in Computer Science. He completed this work under the guidance of Dr. Anila Yadavalli during the academic year 2020-2021.