Fundamental- and first-order localized states in a cubic-quintic reaction-diffusion system

This article analyzes the properties of rotationally symmetric self-localized solutions with different radial quantum numbers in the simplest one- and two-component reaction-diffusion systems. The consideration is made in one and two dimensions with the focus on the fundamental and first higher-order solutions showing zero and one intersections of the radial profile with zero. It is demonstrated that the solution with one intersection does not exist for the case of the quadratic-cubic nonlinearity, while the cubic-quintic extension of the models does allow existence. I show additionally that the cubic-quintic reaction diffusion system supports the existence and stability of the states with zero quantum numbers, as well as their antistates, state-antistate pairs, and clusters, which can be interpreted as the states with nonzero azimuthal quantum number.