2008
DOI: 10.1007/978-3-540-78217-9_1
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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 sho… Show more

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Cited by 66 publications
(72 citation statements)
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“…7 Recently, the soliton pairs named bound states or soliton molecules have been extensively demonstrated, both in experiments and theories. [9][10][11][12][13] Grapinet and Grelu have given the vibrating soliton pairs in a mode-locked laser cavity which coincide with the experimental results. 9 Ortaç et al 10 have given the soliton molecules with independently evolving phase in a mode-locked fiber laser in experiments, which conforms the theory demonstrated by Zavyalov et al 11 In a normal dispersion regime, dissipative solitons and dissipative soliton molecules have also been reported, both in experiments and numerical analysis.…”
Section: Introductionsupporting
confidence: 74%
“…7 Recently, the soliton pairs named bound states or soliton molecules have been extensively demonstrated, both in experiments and theories. [9][10][11][12][13] Grapinet and Grelu have given the vibrating soliton pairs in a mode-locked laser cavity which coincide with the experimental results. 9 Ortaç et al 10 have given the soliton molecules with independently evolving phase in a mode-locked fiber laser in experiments, which conforms the theory demonstrated by Zavyalov et al 11 In a normal dispersion regime, dissipative solitons and dissipative soliton molecules have also been reported, both in experiments and numerical analysis.…”
Section: Introductionsupporting
confidence: 74%
“…Theoretically predicted in Ref. [4] and first reported to spontaneously form in microresonators made from crystalline MgF 2 , DKS have been observed in different types of material systems including silica-on-silicon [22] and silicon nitride [6] (Si 3 N 4 ) as well as silicon [23]. Of particular interest are single-soliton states, which consist of only one ultra-short pulse circulating around the cavity, leading to a broadband comb spectrum with a smooth and numerically predictable [3] envelope given by…”
mentioning
confidence: 88%
“…Here, we show that solitons may experience a comeback in optical communications, this time not as a competitor, but as a key element of massively parallel WDM. Instead of encoding data on the soliton itself, we exploit continuously circulating dissipative Kerr solitons (DKS) in a microresonator [3,4]. DKS are generated in an integrated silicon nitride microresonator [5] by four-photon interactions mediated by Kerr nonlinearity, leading to low-noise, spectrally smooth and broadband optical frequency combs [6].…”
mentioning
confidence: 99%
“…In parallel, spatially localized structures in dissipative systems have been a subject of intense research in different physical systems such as granular media [6], gas discharge [7] and biological [8] or optical systems (see [9] and references therein). Their fundamental properties, bistability and mutual independence (ie, several such structures can be present or not independently of others depending only on initial conditions), are related to the presence of dissipation, and therefore they often receive, in optics, the name of cavity solitons.…”
mentioning
confidence: 99%