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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...

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...

Application of the phenomenon of self-organization for the development of wear resistant materials has been reviewed. For this purpose the term of self-organization and dissipative structures as applied to tribology have been discussed. The applications of this phenomenon have been shown in order to develop new wear resistantand antifriction materials. Specific examples have been shown for the ...

This paper proposes geometric Ricci–flow as a general model for reaction–diffusion systems and dissipative solitons in mathematical biology.

In this paper show that dissipative mechanical systems can be represented as Hamiltonian formalism. We have defined an expanded Hamiltonian function that leads to a unique conservative system for every phase flow of a dissipative mechanical system. We have demonstrated, whether the class of dissipative mechanical system has an analytical solution or not, it can be represented as an infinite num...

≥ λ||dM ||2 − λ2 (2π)(2 + ε). ∗Received by the editors October 20, 2002; accepted for publication November 26, 2002; published electronically May 12, 2003. http://www.siam.org/journals/sinum/41-2/41653.html †Department of Mathematics, Penn State University, 307 McAllister Bldg., State College, PA 16802 ([email protected]). ‡Department of Mathematics, Shanghai Normal University, 100 Guilin Road, ...

Article history: Received 29 August 2013 Received in revised form 10 December 2013 Accepted 3 February 2014 Available online 10 February 2014