Interaction of dissipative solitons: particle-like behaviour of localized structures in a three-component reaction-diffusion system

Abstract

We investigate the static and dynamic behaviour of well localized solitary solutions of a three-component reaction-diffusion model in two- and three-dimensional space. These solutions behave like particles under many aspects and we refer to them as dissipative solitons. These objects may interact with each other, and are influenced by boundaries and inhomogeneities of the parameters. Depending on parameters and initial conditions they may be generated or annihilated. Reflection, scattering and the formation of bound states is commonly observed and dissipative solitons essentially retain their identity under such interactions if these are sufficiently weak. For parameters near to the onset of propagation, the field equations are reduced to a set of ordinary differential equations describing rather well the dynamical behaviour of many aspects of isolated and interacting dissipative solitons using their center coordinates and amplitudes of certain propagator modes. The work demonstrates that dissipative solitons are a generic self-organized pattern of reaction-diffusion systems, that they are rather robust under interaction and in many circumstances can be considered as elementary constituents of patterns of higher complexity. The reduced description can be looked upon as a theoretical foundation of the concept of dissipative solitons exhibiting particle-like behaviour. In addition, for the first time these equations allow a numerical investigation of systems with large number of dissipative solitons as they are observed experimentally. It is pointed out that many of the described properties of dissipative solitons are observed in experimental systems of reaction-diffusion type.