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Families of analytical solutions are found for symmetric and antisymmetric solitons in a dual-core system with Kerr nonlinearity and parity-time (PT)-balanced gain and loss. The crucial issue is stability of the solitons. A stability region is obtained in an analytical form, and verified by simulations, for the PT-symmetric solitons. For the antisymmetric ones, the stability border is found in a numerical form. Moving solitons of both types collide elastically. The two soliton species merge into one in the "supersymmetric" case, with equal coefficients of gain, loss, and intercore coupling. These solitons feature a subexponential instability, which may be suppressed by periodic switching ("management"). 相似文献
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We consider polarization dynamics of solitons in the split-step system (SSM), built as a periodic concatenation of dispersive and nonlinear segments. The model is based on coupled equations for two polarizations, which include birefringence and PMD (polarization-mode dispersion) in the form of random misalignments of the principal polarization axes at junctions between fiber segments. By means of direct simulations, we identify a full stability region for solitons (RZ signals) in the system, and compare it with that in the regular SSM. Beyond the stability border, pulses suffer splitting (which is a characteristic feature of the SSM). Considering co-transmission of soliton pairs, we conclude that the minimum separation between the RZ signals necessary to prevent their interaction increases by ?25% in comparison with the regular (single-polarization) SSM. 相似文献
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B. V. Gisin R. Driben B. A. Malomed I. M. Merhasin 《Theoretical and Mathematical Physics》2005,144(2):1246-1165
We consider spatial solitons in a channel waveguide or in a periodic array of rectangular potential wells (the Kronig-Penney
(KP) model) in the presence of the uniform cubic-quintic (CQ) nonlinearity. Using the variational approximation and numerical
methods, we. nd two branches of fundamental (single-humped) soliton solutions. The soliton characteristics, in the form of
the integral power Q (or width w) vs. the propagation constant k, reveal a strong bistability with two different solutions
found for a given k. Violating the known Vakhitov-Kolokolov criterion, the solution branches with dQ/dk > 0 and dQ/dk < 0
are simultaneously stable. Various families of higher-order solitons are also found in the KP version of the model: symmetric
and antisymmetric double-humped solitons, three-peak solitons with and without the phase shift π between the peaks, etc. In
a relatively shallow KP lattice, all the solitons belong to the semi-infinite gap beneath the linear band structure of the
KP potential, while finite gaps between the bands remain empty (solitons in the finite gaps can be found if the lattice is
much deeper). But in contrast to the situation known for the model combining a periodic potential and the self-focusing Kerr
nonlinearity, the fundamental solitons fill only a finite zone near the top of the semi-infinite gap, which is a manifestation
of the saturable character of the CQ nonlinearity.
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Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 144, No. 2, pp. 324–335, August, 2005.
An erratum to this article is available at . 相似文献
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R. Driben B. A. Malomed 《The European Physical Journal D - Atomic, Molecular, Optical and Plasma Physics》2008,50(3):317-323
It is known that optical-lattice (OL) potentials can stabilize solitons and
solitary vortices against the critical collapse, generated by cubic
attractive nonlinearity in the 2D geometry. We demonstrate that OLs can also
stabilize various species of fundamental and vortical solitons against the
supercritical collapse, driven by the double-attractive cubic-quintic
nonlinearity (however, solitons remain unstable in the case of the pure
quintic nonlinearity). Two types of OLs are considered, producing similar
results: the 2D Kronig-Penney “checkerboard”, and the sinusoidal potential.
Soliton families are obtained by means of a variational approximation, and
as numerical solutions. The stability of all families, which include
fundamental and multi-humped solitons, vortices of oblique and straight
types, vortices built of quadrupoles, and supervortices, strictly
obeys the Vakhitov-Kolokolov criterion. The model applies to optical media
and BEC in “pancake” traps. 相似文献
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A brief introduction is given to the concept of the soliton management, i.e., stable motion of localized pulses in media with strong periodic (or, sometimes, random) inhomogeneity, or conditions for the survival of solitons in models with strong time‐periodic modulation of linear or nonlinear coefficients. It is demonstrated that a class of systems can be identified, in which solitons remain robust inherently coherent objects in seemingly “hostile” environments. Most physical models belonging to this class originate in nonlinear optics and Bose‐Einstein condensation, although other examples are known too (in particular, in hydrodynamics). In this paper, the complexity of the soliton‐management systems, and the robustness of solitons in them are illustrated using a recently explored fiber‐optic setting combining a periodic concatenation of nonlinear and dispersive segments (the split‐step model) for bimodal optical signals (i.e., ones with two polarizations of light), which includes the polarization mode dispersion, i.e., random linear mixing of the two polarization components at junctions between the fiber segment. © 2008 Wiley Periodicals, Inc. Complexity, 2008 相似文献
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