Dissipative soliton resonances

Dissipative soliton resonances in laser models with parameter management

Dissipative soliton resonance (DSR) is a phenomenon where the energy of a soliton in a dissipative system increases without limit at certain values of the system parameters. We have found that the DSR phenomenon is robust and does not disappear when perturbations are introduced into the model. In particular, parameter management is benign to DSR: the resonance property remains intact even when ...

Soliton Resonances for Mkp-ii

Using the second flow the Derivative Reaction-Diffusion system, and the third one of the dissipative SL(2,R) Kaup-Newell hierarchy, we show that the product of two functions, satisfying those systems is a solution of the modified Kadomtsev-Petviashvili equation in 2+1 dimension with negative dispersion (MKP-II). We construct Hirota’s bilinear representation for both flows and combine them toget...

Dissipative soliton resonances in the anomalous dispersion regime

We have numerically calculated the resonance curve and the region of existence of high-energy dissipative solitons in systems governed by the complex cubic-quintic Ginzburg-Landau equation. The calculations are carried out for negative reactive quintic nonlinearity. This choice allows the resonance curve to be continued into the region of positive net dispersion, thus showing that high-energy p...

Chirped Dissipative Solitons

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

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...