270 research outputs found
Tau function and Hirota bilinear equations for the Extended bigraded Toda Hierarchy
In this paper we generalize the Sato theory to the extended bigraded Toda
hierarchy (EBTH). We revise the definition of the Lax equations,give the Sato
equations, wave operators, Hirota bilinear identities (HBI) and show the
existence of function . Meanwhile we prove the validity of its
Fay-like identities and Hirota bilinear equations (HBEs) in terms of vertex
operators whose coefficients take values in the algebra of differential
operators. In contrast with HBEs of the usual integrable system, the current
HBEs are equations of product of operators involving and
.Comment: 29 pages, to appear Journal of Mathematical Physics(2010
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