Nonlinear Reaction-Diffusion Systems

This book presents several fundamental results insolving nonlinear reaction-diffusion equations and systems using symmetry-based methods. Reaction-diffusion systems are fundamental modeling tools for mathematical biology with applications to ecology, population dynamics, pattern formation, morphogenesis, enzymatic reactions and chemotaxis. The book discusses the properties of nonlinear reaction-diffusion systems, whichare relevant for biological applications,from the symmetry point of view, providing rigorous definitionsand constructive algorithmstosearch for conditional symmetry (a nontrivial generalization of the well-known Lie symmetry)ofnonlinear reaction-diffusion systems. In order to presentapplications to population dynamics,it focuses mainlyontwo- and three-component diffusive Lotka-Volterra systems.While it is primarily a valuable guideforresearchers working with reaction-diffusion systems and those developing the theoretical aspects of conditional symmetry conception, parts of the book can also be used in master's level mathematical biology courses.