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Автор: Grafiati

Опубліковано: 4 червня 2021

Оновлено: 20 лютого 2023

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1

Abolarinwa, Abimbola. "Gap theorems for compact almost Ricci-harmonic solitons." International Journal of Mathematics 30, no. 08 (July 2019): 1950040. http://dx.doi.org/10.1142/s0129167x1950040x.

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Almost Ricci-harmonic solitons are generalization of Ricci-harmonic solitons, almost Ricci solitons and harmonic-Einstein metrics. The main focus of this paper is to establish necessary and sufficient conditions for a gradient shrinking almost Ricci-harmonic soliton on a compact domain to be almost harmonic-Einstein.

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2

Katti, Aavishkar, and Chittaranjan P. Katti. "Gap solitons supported by an optical lattice in biased photorefractive crystals having both the linear and quadratic electro-optic effect." Zeitschrift für Naturforschung A 75, no. 8 (September 25, 2020): 749–56. http://dx.doi.org/10.1515/zna-2020-0075.

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AbstractWe investigate the existence and stability of gap solitons supported by an optical lattice in biased photorefractive (PR) crystals having both the linear and quadratic electro-optic effect. Such PR crystals have an interesting interplay between the linear and quadratic nonlinearities. Gap solitons are predicted for the first time in such novel PR media. Taking a relevant example (PMN-0.33PT), we find that the gap solitons in the first finite bandgap are single humped, positive and symmetric solitons while those in the second finite band gap are antisymmetric and double humped. The power of the gap soliton depends upon the value of the axial propagation constant. We delineate three power regimes and study the gap soliton profiles in each region. The gap solitons in the first finite band gap are not linearly stable while those in the second finite band gap are found to be stable against small perturbations. We study their stability properties in detail throughout the finite band gaps. The interplay between the linear and quadratic electro-optic effect is studied by investigating the spatial profiles and stability of the gap solitons for different ratios of the linear and quadratic nonlinear coefficients.

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3

WANG, D. L., and X. H. YAN. "SOLITON ON THE SEMI-INFINITE BAND GAP OF BEC IN AN OPTICAL LATTICE." International Journal of Modern Physics B 25, no. 06 (March 10, 2011): 781–93. http://dx.doi.org/10.1142/s0217979211058250.

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By developing a multiple-scale method, we study analytically the dynamics of the soliton inside the semi-infinite band gap (SIBG) of quasi-one-dimensional Bose–Einstein condensates trapped in an optical lattice. In the linear case, a stable condition of soliton formation is obtained. For a weak nonlinearity, whether there occurs a spatially propagating or localized gap soliton is determined by the lattice depth. Meanwhile, we predict the existence of the dark (bright) gap solitons for the repulsive (attractive) interactions in the SIBG, different from that of the gap solitons in other energy gaps. And the collision of two dark (or bright) solitons is nearly elastic under a safe range of atomic numbers. An experimental protocol is further designed for observing these phenomena.

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4

Winful, Herbert G., and Victor Perlin. "Raman Gap Solitons." Physical Review Letters 84, no. 16 (April 17, 2000): 3586–89. http://dx.doi.org/10.1103/physrevlett.84.3586.

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5

Konotop, V. V. "Vector gap solitons." Physical Review A 51, no. 5 (May 1, 1995): R3422—R3425. http://dx.doi.org/10.1103/physreva.51.r3422.

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6

Gorbach, A. V., B. A. Malomed, and D. V. Skryabin. "Gap polariton solitons." Physics Letters A 373, no. 34 (August 2009): 3024–27. http://dx.doi.org/10.1016/j.physleta.2009.06.036.

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7

ALATAS, H., A. A. ISKANDAR, M. O. TJIA, and T. P. VALKERING. "DARK, ANTIDARK SOLITON-LIKE SOLUTIONS AND THEIR CONNECTION IN A FINITE DEEP NONLINEAR BRAGG GRATING WITH A MIRROR." Journal of Nonlinear Optical Physics & Materials 13, no. 02 (June 2004): 259–74. http://dx.doi.org/10.1142/s0218863504001827.

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Анотація:

We report the results of our study on the in-gap soliton-like solutions in a system of a uniform finite deep nonlinear Bragg grating with a mirror and continuous light source on the opposite sides of the grating. The system was shown to exhibit a new feature consisting of homoclinic and heteroclinic orbits in phase plane associated with the in-gap bright and dark/antidark solitons respectively. The multi-valued connection between the dark and antidark solitons was explicitly displayed. It was further demonstrated that a transition from dark to antidark soliton could be affected by either changing the mirror position or changing the source intensity.

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8

Alatas, H., A. A. Iskandar, M. O. Tjia, and T. P. Valkering. "Analytic Study of Stationary Solitons in Deep Nonlinear Bragg Grating." Journal of Nonlinear Optical Physics & Materials 12, no. 02 (June 2003): 157–73. http://dx.doi.org/10.1142/s0218863503001304.

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Анотація:

A study of nonlinear Bragg grating has been carried out using a modified scheme of approximation originally proposed by Iizuka and de Sterke. A complete classification of the solitonic solutions in the system was given. We further demonstrated in this work the existence of in-gap dark and antidark soliton, in addition to the out-gap solutions reported previously. We also found at the boundaries in the bifurcation diagram, the large-amplitude out-gap antidark soliton and broad in-gap dark soliton.

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9

Chen, W. H., Y. J. He, and H. Z. Wang. "Surface defect gap solitons." Optics Express 14, no. 23 (2006): 11271. http://dx.doi.org/10.1364/oe.14.011271.

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10

Peyraud, J., and J. Coste. "Dynamics of gap solitons." Physical Review B 40, no. 18 (December 15, 1989): 12201–8. http://dx.doi.org/10.1103/physrevb.40.12201.

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11

Longhi, S. "Gap solitons in metamaterials." Waves in Random and Complex Media 15, no. 1 (February 2005): 119–26. http://dx.doi.org/10.1080/17455030500053294.

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12

Kivshar, Yuri S. "Self-induced gap solitons." Physical Review Letters 70, no. 20 (May 17, 1993): 3055–58. http://dx.doi.org/10.1103/physrevlett.70.3055.

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13

He, Y. J., W. H. Chen, H. Z. Wang, and Boris A. Malomed. "Surface superlattice gap solitons." Optics Letters 32, no. 11 (April 25, 2007): 1390. http://dx.doi.org/10.1364/ol.32.001390.

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14

CONTI, CLAUDIO, GAETANO ASSANTO, and STEFANO TRILLO. "GAP SOLITONS AND SLOW LIGHT." Journal of Nonlinear Optical Physics & Materials 11, no. 03 (September 2002): 239–59. http://dx.doi.org/10.1142/s0218863502001000.

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Анотація:

Optical nonlinearity and feedback through Bragg periodicity are the basic ingredients for light localization into gap solitons. We review the basic concepts and model equations for gap solitons in Kerr and quadratic nonlinear media encompassing a one-dimensional Bragg resonance. With specific regard to frequency doubling media, we generalize the concept of a photonic crystal to band-gaps of a nonlinear origin, and finally address the slow character of quadratic gap-solitons with reference to their excitation.

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15

Fang, Limin, Jie Gao, Xing Zhu, Zhiwei Shi, and Huagang Li. "Surface defect gap solitons in optical lattices with nonlocal nonlinearity." International Journal of Modern Physics B 28, no. 31 (December 8, 2014): 1450219. http://dx.doi.org/10.1142/s0217979214502191.

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Анотація:

We show that stable surface fundamental defect solitons can exist in different gaps of an optical lattice with focusing nonlocal Kerr nonlinearity. For positive defect, solitons stably exist in the semi-infinite gap. For negative defect, solitons are stable in the semi-infinite gap and the first gap. Increasing the negative defect depth, the existent regions of defect solitons in the semi-infinite gap and in the first gap will be changed. The degree of the nonlocality will affect the profiles of these solitons.

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16

Jisha, Chandroth P., Alessandro Alberucci та Gaetano Assanto. "𝒫𝒯-symmetric nonlocal gap solitons in optical lattices". Journal of Nonlinear Optical Physics & Materials 23, № 04 (грудень 2014): 1450041. http://dx.doi.org/10.1142/s0218863514500416.

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The existence and stability of 𝒫𝒯-symmetric gap solitons in a periodic structure with defocusing nonlocal nonlinearity are studied. It is found that solitons are in general unstable, their instability rate depending on the magnitude of the imaginary potential. For low values of the imaginary potential solitons survive over distances many times the Rayleigh distance, whereas for high values of the imaginary potential solitons develop an oscillatory instability, eventually leading to a transverse drift towards the gain region.

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17

Wagenknecht, T., and A. R. Champneys. "When gap solitons become embedded solitons: a generic unfolding." Physica D: Nonlinear Phenomena 177, no. 1-4 (March 2003): 50–70. http://dx.doi.org/10.1016/s0167-2789(02)00773-x.

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18

Meng, Yunji, Renxia Ning, Kun Ma, Zheng Jiao, Haijiang Lv, and Youwen Liu. "Defect solitons supported by nonlinear fractional Schrödinger equation with a defective lattice." Journal of Nonlinear Optical Physics & Materials 28, no. 02 (June 2019): 1950021. http://dx.doi.org/10.1142/s0218863519500218.

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Анотація:

We investigate numerically the existence and stability of defect solitons in nonlinear fractional Schrödinger equation. For positive defects, defect solitons are only existent in the semi-infinite gap and are stable in their whole existence domain irrespective of Lévy index. For moderate deep defects, defect solitons are existent in both the semi-infinite gap and first gap, and their instability domains occur in the low-power region of the semi-infinite gap. While for deep enough defects, stable defect solitons can be found in the second gap. Increasing the strength of defect (or Lévy index) will narrow (or broaden) the existence and stability domains.

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19

Nireekshan Reddy, K., and S. Dutta Gupta. "Gap solitons with null-scattering." Optics Letters 39, no. 8 (April 8, 2014): 2254. http://dx.doi.org/10.1364/ol.39.002254.

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20

Kivshar, Yuri S., and Nikos Flytzanis. "Gap solitons in diatomic lattices." Physical Review A 46, no. 12 (December 1, 1992): 7972–78. http://dx.doi.org/10.1103/physreva.46.7972.

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21

Martijn de Sterke, C. "Nonlinear lattices and gap solitons." Physical Review E 48, no. 5 (November 1, 1993): 4136–37. http://dx.doi.org/10.1103/physreve.48.4136.

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22

Garanovich, Ivan, Andrey A. Sukhorukov, Yuri S. Kivshar, and Mario Molina. "Surface multi-gap vector solitons." Optics Express 14, no. 11 (2006): 4780. http://dx.doi.org/10.1364/oe.14.004780.

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23

Kartashov, Yaroslav V., Fangwei Ye, and Lluis Torner. "Vector mixed-gap surface solitons." Optics Express 14, no. 11 (2006): 4808. http://dx.doi.org/10.1364/oe.14.004808.

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24

Konotop, V. V., and G. P. Tsironis. "Dynamics of coupled gap solitons." Physical Review E 53, no. 5 (May 1, 1996): 5393–98. http://dx.doi.org/10.1103/physreve.53.5393.

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25

Malomed, Boris A., V. A. Nascimento, and Sadhan K. Adhikari. "Gap solitons in fermion superfluids." Mathematics and Computers in Simulation 80, no. 4 (December 2009): 648–59. http://dx.doi.org/10.1016/j.matcom.2009.08.017.

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26

Pezer, Robert, Hrvoje Buljan, Jason W. Fleischer, Guy Bartal, Oren Cohen, and Mordechai Segev. "Gap random-phase lattice solitons." Optics Express 13, no. 13 (2005): 5013. http://dx.doi.org/10.1364/opex.13.005013.

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27

Gaizauskas, E., A. Savickas, and K. Staliunas. "Radiation from band-gap solitons." Optics Communications 285, no. 8 (April 2012): 2166–70. http://dx.doi.org/10.1016/j.optcom.2011.12.088.

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28

Roeksabutr, Athikom, Thawatchai Mayteevarunyoo, and Boris A. Malomed. "Symbiotic two-component gap solitons." Optics Express 20, no. 22 (October 12, 2012): 24559. http://dx.doi.org/10.1364/oe.20.024559.

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29

Kartashov, Yaroslav V., Boris A. Malomed, Victor A. Vysloukh, and Lluis Torner. "Gap solitons on a ring." Optics Letters 33, no. 24 (December 5, 2008): 2949. http://dx.doi.org/10.1364/ol.33.002949.

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30

Kivshar, Yuri S. "Gap solitons due to cascading." Physical Review E 51, no. 2 (February 1, 1995): 1613–15. http://dx.doi.org/10.1103/physreve.51.1613.

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31

Sukhorukov, Andrey A., Dragomir N. Neshev, Alexander Dreischuh, Wieslaw Krolikowski, Jeremy Bolger, Benjamin J. Eggleton, Lam Bui, Arnan Mitchell, and Yuri S. Kivshar. "Observation of polychromatic gap solitons." Optics Express 16, no. 9 (April 14, 2008): 5991. http://dx.doi.org/10.1364/oe.16.005991.

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32

Mayteevarunyoo, Thawatchai, and Boris A. Malomed. "Gap solitons in grating superstructures." Optics Express 16, no. 11 (May 14, 2008): 7767. http://dx.doi.org/10.1364/oe.16.007767.

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33

Akter, Afroja, Md Jahedul Islam, and Javid Atai. "Quiescent Gap Solitons in Coupled Nonuniform Bragg Gratings with Cubic-Quintic Nonlinearity." Applied Sciences 11, no. 11 (May 25, 2021): 4833. http://dx.doi.org/10.3390/app11114833.

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Анотація:

We study the stability characteristics of zero-velocity gap solitons in dual-core Bragg gratings with cubic-quintic nonlinearity and dispersive reflectivity. The model supports two disjointed families of gap solitons (Type 1 and Type 2). Additionally, asymmetric and symmetric solitons exist in both Type 1 and Type 2 families. A comprehensive numerical stability analysis is performed to analyze the stability of solitons. It is found that dispersive reflectivity improves the stability of both types of solitons. Nontrivial stability boundaries have been identified within the bandgap for each family of solitons. The effects and interplay of dispersive reflectivity and the coupling coefficient on the stability regions are also analyzed.

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34

Komissarova, M. V., T. M. Lysak, I. G. Zakharova, and A. A. Kalinovich. "Parametric gap solitons in PT-symmetric optical structures." Journal of Physics: Conference Series 2249, no. 1 (April 1, 2022): 012008. http://dx.doi.org/10.1088/1742-6596/2249/1/012008.

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Abstract It is well known that quadratic nonlinearity and feedback through Bragg periodicity are the basis for parametric gap solitons. The major part of the relevant investigations refers to passive systems. At the same time, optical systems supplemented with active elements can demonstrate unusual properties. Asymmetry intrinsic to structures with parity-time (PT) symmetry is a bright confirmation of this statement. The interplay of nonlinearity, Bragg reflection and gain/loss profile can lead to the complicated pattern of wave interactions and novel results. In this study we address the properties of two-color solitons in complex PT symmetric periodic structures with quadratic nonlinearity. We focus on the case of single Bragg resonance. We reveal the region of parameters where stable parametric solitons may exist. We demonstrate that characteristics of forming solitons depend on the order of alteration of amplifying and absorbing layers.

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35

Park, Jae Whan, Euihwan Do, Jin Sung Shin, Sun Kyu Song, Oleksandr Stetsovych, Pavel Jelinek, and Han Woong Yeom. "Creation and annihilation of mobile fractional solitons in atomic chains." Nature Nanotechnology 17, no. 3 (December 22, 2021): 244–49. http://dx.doi.org/10.1038/s41565-021-01042-8.

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AbstractLocalized modes in one-dimensional (1D) topological systems, such as Majonara modes in topological superconductors, are promising candidates for robust information processing. While theory predicts mobile integer and fractional topological solitons in 1D topological insulators, experiments so far have unveiled immobile, integer solitons only. Here we observe fractionalized phase defects moving along trimer silicon atomic chains formed along step edges of a vicinal silicon surface. By means of tunnelling microscopy, we identify local defects with phase shifts of 2π/3 and 4π/3 with their electronic states within the band gap and with their motions activated above 100 K. Theoretical calculations reveal the topological soliton origin of the phase defects with fractional charges of ±2e/3 and ±4e/3. Additionally, we create and annihilate individual solitons at desired locations by current pulses from the probe tip. Mobile and manipulable topological solitons may serve as robust, topologically protected information carriers in future information technology.

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36

Jones, Hugh, and Mykola Kulishov. "Solitons in a PT -symmetric grating-assisted co-directional coupler." Journal of Physics: Conference Series 2038, no. 1 (October 1, 2021): 012015. http://dx.doi.org/10.1088/1742-6596/2038/1/012015.

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Abstract We explore a co-directional coupling arrangement between two waveguides mediated by a PT-symmetric sinusoidal grating characterized by an index-modulation parameter κ and a gain/loss parameter g. We show that the device supports soliton-like solutions for both the PT -conserving regime g < κ and the PT -broken regime g > κ. In the first case the coupler exhibits a gap in wave-number k and the solitons can be regarded as an extension of a previous solution found for pure index modulation. In the second case the coupler exhibits a gap in frequency ω and the solutions are entirely new.

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37

Yang, S. R. Eric. "Soliton Fractional Charges in Graphene Nanoribbon and Polyacetylene: Similarities and Differences." Nanomaterials 9, no. 6 (June 14, 2019): 885. http://dx.doi.org/10.3390/nano9060885.

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Анотація:

An introductory overview of current research developments regarding solitons and fractional boundary charges in graphene nanoribbons is presented. Graphene nanoribbons and polyacetylene have chiral symmetry and share numerous similar properties, e.g., the bulk-edge correspondence between the Zak phase and the existence of edge states, along with the presence of chiral boundary states, which are important for charge fractionalization. In polyacetylene, a fermion mass potential in the Dirac equation produces an excitation gap, and a twist in this scalar potential produces a zero-energy chiral soliton. Similarly, in a gapful armchair graphene nanoribbon, a distortion in the chiral gauge field can produce soliton states. In polyacetylene, a soliton is bound to a domain wall connecting two different dimerized phases. In graphene nanoribbons, a domain-wall soliton connects two topological zigzag edges with different chiralities. However, such a soliton does not display spin-charge separation. The existence of a soliton in finite-length polyacetylene can induce formation of fractional charges on the opposite ends. In contrast, for gapful graphene nanoribbons, the antiferromagnetic coupling between the opposite zigzag edges induces integer boundary charges. The presence of disorder in graphene nanoribbons partly mitigates antiferromagnetic coupling effect. Hence, the average edge charge of gap states with energies within a small interval is e / 2 , with significant charge fluctuations. However, midgap states exhibit a well-defined charge fractionalization between the opposite zigzag edges in the weak-disorder regime. Numerous occupied soliton states in a disorder-free and doped zigzag graphene nanoribbon form a solitonic phase.

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38

Wang, Qing, Dumitru Mihalache, Milivoj R. Belić, Lingling Zhang, Lin Ke, and Liangwei Zeng. "Controllable propagation paths of gap solitons." Optics Letters 47, no. 5 (February 16, 2022): 1041. http://dx.doi.org/10.1364/ol.453604.

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39

Mills, D. L., and S. E. Trullinger. "Gap solitons in nonlinear periodic structures." Physical Review B 36, no. 2 (July 15, 1987): 947–52. http://dx.doi.org/10.1103/physrevb.36.947.

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40

Mok, Joe T., C. Martijn de Sterke, Ian C. M. Littler, and Benjamin J. Eggleton. "Dispersionless slow light using gap solitons." Nature Physics 2, no. 11 (October 22, 2006): 775–80. http://dx.doi.org/10.1038/nphys438.

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41

Conti, Claudio, Gaetano Assanto, and Stefano Trillo. "Parametric gap solitons in quadratic media." Optics Express 3, no. 11 (November 23, 1998): 389. http://dx.doi.org/10.1364/oe.3.000389.

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42

Bilbault, J. M., and M. Remoissenet. "Gap solitons in nonlinear electrical superlattices." Journal of Applied Physics 70, no. 8 (October 15, 1991): 4544–50. http://dx.doi.org/10.1063/1.349090.

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43

Alfimov, G., and V. V. Konotop. "On the existence of gap solitons." Physica D: Nonlinear Phenomena 146, no. 1-4 (November 2000): 307–27. http://dx.doi.org/10.1016/s0167-2789(00)00138-x.

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44

Flytzanis, Nikos, and Boris A. Malomed. "Gap solitons in gapless coupled chains." Physics Letters A 227, no. 5-6 (March 1997): 335–39. http://dx.doi.org/10.1016/s0375-9601(97)00065-0.

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45

Schöllmann, J. "On the stability of gap solitons." Physica A: Statistical Mechanics and its Applications 288, no. 1-4 (December 2000): 218–24. http://dx.doi.org/10.1016/s0378-4371(00)00423-4.

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46

Iizuka, Takeshi. "Gap Solitons in Nonlinear Polyatomic Chains." Journal of the Physical Society of Japan 71, no. 5 (May 15, 2002): 1284–95. http://dx.doi.org/10.1143/jpsj.71.1284.

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47

Mayteevarunyoo, Thawatchai, Boris A. Malomed, and Athikom Reoksabutr. "Bragg management for spatial gap solitons." Journal of the Optical Society of America B 27, no. 10 (September 9, 2010): 1957. http://dx.doi.org/10.1364/josab.27.001957.

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48

Li, Haozhao. "Gap theorems for Kähler-Ricci solitons." Archiv der Mathematik 91, no. 2 (August 2008): 187–92. http://dx.doi.org/10.1007/s00013-008-2628-6.

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Tadano, Homare. "Gap theorems for Ricci-harmonic solitons." Annals of Global Analysis and Geometry 49, no. 2 (December 18, 2015): 165–75. http://dx.doi.org/10.1007/s10455-015-9485-x.

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