Dissipative Solitons in Reaction Diffusion Systems

Dissipative solitons are local excitations of nonlinear continuous systems which emerge due to a flux of energy or matter. Although they are continuous entities, dissipative solitons in reaction diffusion systems behave like particles: They are generated or annihilated as a whole, propagate with a well-defined velocity and interact with each other, which can lead to the formation of bound states, e.g. This book introduces dissipative solitons in the context of pattern formation, discusses experimental findings in chemical and physical systems, deduces a phenomenological model of dissipative solitons from basic principles, analyzes their dynamics and interaction from a theoretical point of view and verifies these finding in an experimental system by means of stochastic data analysis. Finally, the mechanisms of annihilation and generation are explained on the basis of simulations. Theoretical considerations focus on a certain family of reaction diffusion models with the result such that basic and advanced analytical methods can be introduced from scratch and can be followed down to computational results.