  We present a tachyon field, which simply connects to the calculus of the
tachyon condensation. The tachyon field acts on any bare boundary state: the
Neumann or the Dirichlet state, and generates the boundary state suggested by
S.P. de Alwis, which leads to the correct ratio between D-brane tensions. On
the other hand we generalize the Hirota-Miwa equation to the case where there
are two boundaries. We show that correlation functions made from only the
integrand of the tachyon field satisfy the generalized Hirota-Miwa equation.
Using the formulation based on this evidence, we suggest that the coordinates
in which there exist tachyons on an unstable D-brane be identified as the
soliton coordinates in integrable systems. We also evaluate these correlation
functions, which have not yet been integrated, to obtain the local information
about the tachyons on unstable D-branes. We further see how these amplitudes
are affected through the tachyon condensation by integrating the correlators
over the tachyon momenta and taking the on-shell limit.
