  The quantum and classical aspects of a deformed $c=1$ matrix model proposed
by Jevicki and Yoneya are studied. String equations are formulated in the
framework of Toda lattice hierarchy. The Whittaker functions now play the role
of generalized Airy functions in $c<1$ strings. This matrix model has two
distinct parameters. Identification of the string coupling constant is thereby
not unique, and leads to several different perturbative interpretations of this
model as a string theory. Two such possible interpretations are examined. In
both cases, the classical limit of the string equations, which turns out to
give a formal solution of Polchinski's scattering equations, shows that the
classical scattering amplitudes of massless tachyons are insensitive to
deformations of the parameters in the matrix model.
