Abstract
A constructive method for obtaining new exact solutions of nonlinear evolution equations is further developed. The method is based on the consideration of a fixed nonlinear partial differential equation together with an additional generating condition in the form of a linear high-order ordinary differential equation. Using this method new non-Lie ansatze and exact solutions are obtained for two classes of diffusion equations with power and exponential nonlinearities, which describe real processes in physics, chemistry, and biology. The analysis of the found solutions and the relation of the proposed method to some approaches, which have been suggested in several recently published papers, are presented.
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