The Shigesada–Kawasaki–Teramoto model: Conditional symmetries, exact solutions and their properties

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 polymerization process is suggested and exact solutions are found in this case as well. •Q-conditional (non-classical) symmetries of the Shigesada–Kawasaki–Teramoto system are found for the first time.•New families of exact solutions are constructed.•Biological interpretation of the most interesting solutions is presented.•An alternative application of the system is suggested.