für Naturforschung in cooperation with the Max Planck Society for the Advancement of Science under a Creative Commons Attribution 4.0 International License. Dieses Werk wurde im Jahr 2013 vom Verlag Zeitschrift für Naturforschung in Zusammenarbeit mit der Max-Planck-Gesellschaft zur Förderung der Wissenschaften e.V. digitalisiert und unter folgender Lizenz veröffentlicht: Creative Commons Namen...

Quantum mechanics of a general one dimensional dissipative system investigated by it’s coupling to a Klein-Gordon field as the environment using a minimal coupling method. Heisenberg equation for such a dissipative system containing a dissipative term proportional to velocity obtained. As an example, quantum dynamics of a damped harmonic oscillator as the prototype of some important one dimensi...

A posteriori L error estimates (in the sense of [12, 23]) are derived for both well-balanced (WB) and fractional-step (FS) numerical approximations of the unique weak solution of the Cauchy problem for the 1D semilinear damped wave equation. For setting up the WB algorithm, we proceed by rewriting it under the form of an elementary 2 × 2 system which linear convective structure allows to reduce...

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-...

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 o...