Download Soliton Management in Periodic Systems by Boris A. Malomed PDF

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By Boris A. Malomed

During the prior ten years, there was extensive improvement in theoretical and experimental examine of solitons in periodic media. This e-book offers a distinct and informative account of the cutting-edge within the box. the quantity opens with a overview of the life of strong solitary pulses in platforms equipped as a periodic concatenation of very various parts. one of the most renowned examples of this sort of structures are the dispersion administration in fiber-optic telecommunication hyperlinks, and (more lately) photonic crystals. a few different platforms belonging to an analogous huge type of spatially periodic strongly inhomogeneous media (such because the split-step and tandem types) have lately been pointed out in nonlinear optics, and transmission of solitary pulses in them was once investigated intimately. comparable soliton dynamics happens in temporal-domain opposite numbers of such platforms, the place they're topic to powerful time-periodic modulation (for example, the Feshbach-resonance administration in Bose-Einstein condensates). foundation effects acquired for these types of structures are reviewed within the e-book. This well timed paintings will function an invaluable source for the soliton community.

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2. SOLITONS IN PERIODIC HETEROGENEOUS MEDIA 19 are exceptional models, in the sense that any additional term, which takes into regard physical effects that were not included in the basic model, breaks the exact integrability. This circumstance suggest the necessity to investigate solitons in nonintegrable models (in a strict mathematical sense, these solutions are not "solitons", but rather "solitary waves"; however, following commonly adopted practice, they will be called solitons). In many physically relevant situations, the additional terms which break the integrability of the unperturbed model are small, making it natural to apply a perturbation theory relying on an asymptotic expansion around exact solutions provided by the 1ST in the absence of the perturbations.

L 1 L. 10: A typical example of the shape (shown on the logarithmic scale) of dispersion-managed solitons in the ideal lossless model, and in its realistic counterpart with lumped filters and amplifiers (for comparison, the solitons with equal amplitudes are taken in both cases). Each soliton is shown at a position (close to the midpoint of the anomalous-GVD segment of the DM map) where it is narrowest. 45) (the latter is usually referred to as the Gaussian transfer function with the bandpass width Aw).

It is composed of alternating BGs with opposite signs of the Kerr nonlinearity, and also gives rise to a family of robust solitons. A periodic heterogeneous system with the x^^^ nonlinearity was proposed in the form of the so-called tandem model [162], which combines linear segments and ones carrying the quadratic nonlinearity [162]. Specific solitons were revealed by numerical simulations in this model. In all these systems, stable solitons exist in the form of periodically oscillating breathers (obviously, the solitons cannot keep a permanent shape propagating through the inhomogeneous structure).

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