Dissipative solitons: Present Understanding, Applications and New Developments

The concept of the dissipative soliton has received wide recognition in optics (physics in general), biology and medicine [Akhmediev & Ankiewicz, 2005, 2008]. This concept allows many diverse phenomena in nature to be understood and studied in a simple and systematic way. It represents a unifying notion in science, since it stresses common features in a variety of complicated behaviors of self-localized formations. The most prominent feature of dissipative solitons is that they exist only when there is a continuous energy supply from an external source. This energy has to be dissipated in the medium where solitons are found. Thus, their formation requires a balance between the energy supplied and lost. This balance has to be exact in order to prevent overheating or cooling down of the system and the subsequent disappearance of the soliton. The exact balance is provided by the highly involved nonlinear dynamics in the system, which implies that dissipative solitons have to be self-organized. Their shape, amplitude, width and all other parameters are unique for given external conditions. Dissipative solitons can be natural, i.e. they can exist in nature as a result of a relaxation to a localized formation under the influence of solar heating and dissipation, or they can be artificial objects created by scientists. In the latter case, they can be used in modern technology. A common misconception concerning dissipative systems is that they can only have losses and thus only decaying solutions. The name “Dissipative system” was coined by [Nikolis & Prigogine, 1977] for systems considered in nonequilibrium