Localized Structures in Dissipative Nonlinear Systems - Abstract
Purwins, Hans-Georg
In the first part of the talk an attempt is made to give a definition of what may be referred to as a “Dissipative Soliton (DS)”. Thereby the starting point is the particle-like behavior of many self-organized localized structures in dissipative systems. The proposed definition allows for some general conclusions with respect to the properties of DSs.
There follows a critical overview of the experimental observations of DSs in various physical, chemical and biological systems. Peculiarities of the concrete experimental systems are pointed out. It is concluded that the formation of DSs is a generic phenomenon.
The subject of the third part of the presentation is related to the quantitative description of experimental DS patterns. In some cases a semi-quantitative agreement between theory and experiment seems to be possible. However, it is obvious that in general one is confronted with severe difficulties. The latter are attributed to the sensitive dependence of nonlinear systems on parameters and on initial conditions.
In the present talk often reaction-diffusion systems of activator-inhibiter type are used to illustrate general statements. This class of DS carrying systems is fairly large. Also there is a simple intuitive excess to the understanding of the mechanisms of the DS formation. Last not least, for such systems a simple mathematical foundation can be given for the particle-like behavior of DSs.
Literature:
“Dissipative Solitons” by H.-G. Purwins, H. U. Bödeker and Sh. Amiranashvili, accepted for publication in Advances in Physics (2010)
http://physik.uni-muenster.de/AP/Purwins/