  New classes of conditionally integrable systems of nonlinear
reaction-diffusion equations are introduced. They are obtained by extending a
well known nonclassical symmetry of a scalar partial differential equation to a
vector equation. New exact solutions of nonlinear predator-prey systems,
related to the diffusive Lotka-Volterra system, are constructed. An infinite
dimensional class of exact solutions is made available. Unlike in the standard
Lotka-Volterra system, in the absence of predators, the prey population has a
finite carrying capacity, as in the Fisher equation.
