This book presents several fundamental results in solving 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 which are relevant for biological
applications from the symmetry point of view providing rigorous definitions and constructive
algorithms to search for conditional symmetry (a nontrivial generalization of the well-known
Lie symmetry) of nonlinear reaction-diffusion systems. In order to present applications to
population dynamics it focuses mainly on two- and three-component diffusive Lotka-Volterra
systems. While it is primarily a valuable guide for researchers 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.
