Roman Cherniha (Institute of Mathematics of NAS of Ukraine and Institute of Cybernetics, IRAPM, Kyiv, Ukraine)

New conditional symmetries and exact solutions of nonlinear evolution equations

A complete description of Q-conditional symmetries for two classes of reaction-diffusion-convection equations with power diffusivities is derived. It is shown that all the known results for reaction-diffusion equations with power diffusivities follow as particular cases from those obtained here but not vise versa. The symmetries obtained for constructing exact solutions of the relevant equations are successfully applied. In the particular case, new exact solutions of nonlinear reaction-diffusion-convection equations arising in application are found.

Joint work with Oleksii Pliukhin.