  We study a simplification of the well-known Shigesada-Kawasaki-Teramoto
model, which consists of two nonlinear reaction-diffusion equations with
cross-diffusion. A complete set of Q-conditional (nonclassical) symmetries is
derived using an algorithm adopted for the construction of conditional
symmetries. The symmetries obtained are applied for finding a wide range of
exact solutions, possible biological interpretation of some of which being
presented. Moreover, an alternative application of the simplified model related
to the polymerisation process is suggested and exact solutions are found in
this case as well.
