New conditional symmetries and exact solutions of reaction–diffusion–convection equations with exponential nonlinearities

A complete description of QQ-conditional symmetries for a class of reaction–diffusion–convection equations with exponential diffusivities is derived. It is shown that all the known results for reaction–diffusion equations with exponential diffusivities follow as particular cases from those obtained here but not vice versa. The symmetries obtained for constructing exact solutions of the relevant equations are successfully applied. The exact solutions are compared with those found earlier by means of different approaches. An application of the solutions for solving a boundary-value problem arising in population dynamics is presented.