New Conditional Symmetries and Exact Solutions of a Class of Nonlinear Reaction-Diffusion-Convection Equations

Abstract:
A theorem  giving a complete description  $Q$-conditional symmetries of a class of  nonlinear reaction-diffusion-convection equations is presented. The $Q$-conditional symmetries found are further applied for finding exact solutions of the Murray and generalized Newell-Whitehead equations. Moreover new exact solutions of these equations are constructed using the method of additional generating conditions. Finally, the main results of the paper are summarized and compared with those obtained earlier.