New exact solutions of a nonlinear cross-diffusion system.
A system of two reaction-diffusion equations with cross-diffusion and quadratic nonlinearities is considered. The system contains as a particular case the well-known model proposed by Shigesada, Kawasaki and Teramoto in 1979. New non-Lie ansatze reducing the system to the ordinary differential equations system are obtained and applied for finding its exact solutions. Several families of exact solutions are constructed and their asymptotic behavior are investigated. Some biological interpretation of the solutions are provided, too.