On some zero-front solutions of an evolution parabolic system

We present an existence and uniqueness theorem for a nontrivial analytical zero-front solution of a problem for a nonlinear evolution parabolic predator-prey system. In special cases, we construct exact solutions by reduction to the Cauchy problem for a system of ordinary differential equations, which inherits all features of the original problem. We propose an algorithm for the numerical solution of the problem based on the method of specific solutions and present the result of computational experiments.