New symmetries for a model of fast diffusion

In this Letter we prove that, for some partial differential equations that model diffusion, by using the nonclassical method we obtain several new sol utions which are not invariant under any Lie group admitted by the equation s and consequently which are not obtainable through the classical Lie metho d. For these partial differential equations that model fast diffusion new c lasses of symmetries are derived. These nonclassical potential symmetries a llow us to increase the number of exact explicit solutions of these nonline ar diffusion equations. These solutions are neither nonclassical solutions of the diffusion equation nor solutions arising from classical potential sy mmetries. Some of these solutions exhibit an interesting behavior as a shri nking pulse formed out of the interaction of two kinks. (C) 2001 Elsevier S cience B.V. All rights reserved.