Non-Lie non-classical symmetry solutions of a class of nonlinear reaction–diffusion equations

Nonlinear one-dimensional reaction–diffusion equations are useful for modeling processes in science and engineering. Non-classical symmetry analysis with a vanishing coefficient of $\frac{\partial }{\partial t}$ 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 $\frac{\partial }{\partial t}$. A solution is presented as a potential model for population growth in biology.