Symmetries, periodic plane waves and blow-up of λ–ω systems

Nonclassical symmetries of one-dimensional reaction diffusion equations, of the λ–ω type, have been studied. The functional forms of λ and ω for which the system admits nonclassical symmetries have been determined and the corresponding reduced systems have been obtained. Some of these reduced systems admit symmetries which lead to further reductions. Among the several classes of exact solutions that have been obtained, asymptotically periodic plane waves appear as similarity solutions of λ–ω systems. We also have obtained a family of solutions that exhibit a blow-up process.