  We analyze two extended versions [the Ishimori model (IM) and a related
system, which will be called modified Ishimori model (mIM)] of the continuous
Heisenberg model in (2+1)-dimensions within the complex Hirota scheme. The IM,
proposed in 1984, is an integrable (2+1)-dimensional topological spin field
model which has been studied in many theoretical frameworks. The mIM has been
introduced quite recently by some of the present authors [Phys. Rev. {\bf B
49}, 12915 (1994)]. Using the same stereographic variable in the Hirota
formulation, we build up some new exact solutions both for the IM and the mIM
in the compact and noncompact case. For the IM new configurations are a class
of static solutions related to a special third Painlev\'e equation,
time-dependent solutions linked to an other kind of the third Painlev\'e
transcendent, and asympotic time-dependent solutions whose energy density
behaves as Yukawa potential. For the mIM, new configurations are a class of
exact solutions expressed in terms of elliptic functions, and a class of
time-dependent solutions related to a particular form of the double sine-Gordon
and the double sinh-Gordon equations with variable coefficients. We discuss the
new configurations and certain known solutions which clarify the different
possible phenomenological role played by the considered topological spin field
models.
