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

Nonclassical symmetries of one-dimensional reaction diffusion equations, of the lambda-omega type, have been studied. The functional forms of lambda and omega 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 lambda-omega systems. We also have obtained a family of solutions that exhibit a blow-up process. (C) 2000 Elsevier Science B.V. All rights reserved.