2010
DOI: 10.1103/physreva.82.053833
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Self-similar interaction of slowly oscillating dispersion-managed solitons

Abstract: We present an investigation of the interaction of solitons in dispersion-managed fibers beyond the regime of formation of stable pairs (soliton molecules). There is a nonlinear resonance between a slow (compared to the dispersion map period) oscillation of the pulse shape and the typical distance of bouncing of the pulses off each other. Parameter ranges for either repetitive bouncing or a final split of the pair are shown to be organized in a self-similar pattern. Predictions of a theoretical model agree well… Show more

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Cited by 14 publications
(10 citation statements)
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“…3(c) subsequent behavior, and the complex interplay may result in a self-similar (fractal) structure of the parameter space. This behavior has been studied before [48]. With a view to applications of soliton molecules for data transmission, the energy region near E sol ≈ 11-16 pJ is preferred.…”
Section: A Global Parameter Dependencementioning
confidence: 99%
“…3(c) subsequent behavior, and the complex interplay may result in a self-similar (fractal) structure of the parameter space. This behavior has been studied before [48]. With a view to applications of soliton molecules for data transmission, the energy region near E sol ≈ 11-16 pJ is preferred.…”
Section: A Global Parameter Dependencementioning
confidence: 99%
“…A Gaussian ansatz as an approximation to a DM soliton shape captures the central part quite well and is therefore almost universally adopted (e.g., [42,43]); it is a reasonable ansatz to describe the ground state of soliton molecules [23,29]. It meets its limitations, however, when details of the wings count: The tails of Gaussian, sech, and "true-soliton" pulses are quite different, and any conclusions about higherorder equilibria or interactions between adjacent solitons are affected considerably.…”
Section: And a Metric Of The Nonlinearity Allocationmentioning
confidence: 99%
“…In this paper, we endeavor to draw a more complete picture. We use a perturbative treatment similar to that in [23,29], but with a refinement, to calculate interaction forces and equilibrium separations of adjacent solitons. We find conditions under which symmetric in-phase and opposite-phase DM soliton pairs of the same energy can have more than a single equilibrium separation.…”
Section: Introductionmentioning
confidence: 99%
“…Thus, solitary wave solutions behave like solitons, with the characteristics described above. In a more complex scenario, when the NLS equation presents nonintegrability, collision of solitary waves can show a complex structure since the collision outcome can depend on the initial conditions, presenting a fractal pattern [19][20][21][22][23][24][25][26]. Fractal structures in solitons' collisions are also reported in systems described by other equations, such as, in the ϕ 4 model [27,28], the sine-Gordon model [29][30][31][32][33], etc.…”
Section: Introductionmentioning
confidence: 99%