Abstract
Abstract Reaction-diffusion equations are ubiquitous as models of pattern formation in chemistry and biology. In this paper, the invariant subspace method is used to investigate exact solutions and the corresponding patterns in a reaction-diffusion system. Several forms of the exact solutions of the one-dimensional reaction-diffusion system are presented, including complexions. Furthermore, we show several patterns the two-dimensional reaction-diffusion system, involving stripes, spots and transitions between them. Additionally, we discuss the relations between patterns and exact solutions.
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