Three Sources and Three Component Parts of the Concept of Dissipative Solitons

Abstract

We explain the notion of dissipative solitons within a historical perspective. We show that the ideas of the theory of dissipative solitons emerge from several fields, including classical soliton theory, nonlinear dynamics, with its theory of bifurcations, and Prigogine's concept of self-organization. A new notion, emerging from this three-part foundation, allows us to build the novel concept of the dissipative soliton. We also show that reductions to lower dimensional systems have to be done carefully and should always include a comparison of the results with numerical simulations of the original equations.