Non-Lie Non-Classical Symmetry Solutions of a Class of Nonlinear Reaction-Diffusion Equations

Nonlinear one-dimensional reaction-diffusion equations are useful for modelling processes in science and engineering. Non-classical symmetry analysis with a vanishing coefficient of ∂∂t is applied to search for non-Lie solutions of a class of nonlinear reaction-diffusion equations. The analysis leads to two non-classical symmetries. Each symmetry gives a solution that cannot be constructed using classical symmetries or non-classical symmetries with a non-vanishing coefficient of ∂∂t. A solution is applied in a potential model for population growth in biology.