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Dai Z, Yang Z, Ling X, Zhang S, Pang Z, Li X, Wang Y. Tripole-mode and quadrupole-mode solitons in (1 + 1)-dimensional nonlinear media with a spatial exponential-decay nonlocality. Sci Rep 2017; 7:122. [PMID: 28273924 PMCID: PMC5427903 DOI: 10.1038/s41598-017-00197-6] [Citation(s) in RCA: 35] [Impact Index Per Article: 5.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/04/2016] [Accepted: 02/14/2017] [Indexed: 11/18/2022] Open
Abstract
The approximate analytical expressions of tripole-mode and quadrupole-mode solitons in (1 + 1)-dimensional nematic liquid crystals are obtained by applying the variational approach. It is found that the soliton powers for the two types of solitons are not equal with the same parameters, which is much different from their counterparts in the Snyder-Mitchell model (an ideal and typical strongly nolocal nonlinear model). The numerical simulations show that for the strongly nonlocal case, by expanding the response function to the second order, the approximate soliton solutions are in good agreement with the numerical results. Furthermore, by expanding the respond function to the higher orders, the accuracy and the validity range of the approximate soliton solutions increase. If the response function is expanded to the tenth order, the approximate solutions are still valid for the general nonlocal case.
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Affiliation(s)
- Zhiping Dai
- College of Physics and Electronic Engineering, Hengyang Normal University, Hengyang, 421002, China
| | - Zhenjun Yang
- College of Physics and Information Engineering, Hebei Advanced Thin Films Laboratory, Hebei Normal University, Shijiazhuang, 050024, China.
| | - Xiaohui Ling
- College of Physics and Electronic Engineering, Hengyang Normal University, Hengyang, 421002, China
| | - Shumin Zhang
- College of Physics and Information Engineering, Hebei Advanced Thin Films Laboratory, Hebei Normal University, Shijiazhuang, 050024, China
| | - Zhaoguang Pang
- College of Physics and Information Engineering, Hebei Advanced Thin Films Laboratory, Hebei Normal University, Shijiazhuang, 050024, China
| | - Xingliang Li
- College of Physics and Information Engineering, Hebei Advanced Thin Films Laboratory, Hebei Normal University, Shijiazhuang, 050024, China
| | - Youwen Wang
- College of Physics and Electronic Engineering, Hengyang Normal University, Hengyang, 421002, China
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Kartashov YV, Vysloukh VA, Torner L. Asymmetric soliton mobility in competing linear-nonlinear parity-time-symmetric lattices. OPTICS LETTERS 2016; 41:4348-4351. [PMID: 27628394 DOI: 10.1364/ol.41.004348] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/06/2023]
Abstract
We address the transverse mobility of spatial solitons in competing parity-time-symmetric linear and nonlinear lattices. The competition between out-of-phase linear and nonlinear lattices results in a drastic mobility enhancement within a range of soliton energies. We show that within such a range, the addition of even a small imaginary part in the linear potential makes soliton mobility strongly asymmetric. For a given initial phase tilt, the velocity of soliton motion grows with an increase of the balanced gain/losses. In this regime of enhanced mobility, tilted solitons can efficiently drag other solitons that were initially at rest to form moving soliton pairs.
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3
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Solitons in PT-symmetric periodic systems with the logarithmically saturable nonlinearity. Sci Rep 2016; 6:32990. [PMID: 27596716 PMCID: PMC5011714 DOI: 10.1038/srep32990] [Citation(s) in RCA: 32] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/24/2016] [Accepted: 08/15/2016] [Indexed: 11/10/2022] Open
Abstract
We report on the formation and stability of induced solitons in parity-time (PT) symmetric periodic systems with the logarithmically saturable nonlinearity. Both on-site and off-site lattice solitons exist for the self-focusing nonlinearity. The most intriguing result is that the above solitons can also be realized inside the several higher-order bands of the band structure, due to the change of nonlinear type with the soliton power. Stability analysis shows that on-site solitons are linearly stably, and off-site solitons are unstable in their existence domain.
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4
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Small-Amplitude Nonlinear Modes under the Combined Effect of the Parabolic Potential, Nonlocality and PT Symmetry. Symmetry (Basel) 2016. [DOI: 10.3390/sym8080072] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/16/2022] Open
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5
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Zhan K, Hou C. Lattice surface solitons in diffusive nonlinear media driven by the quadratic electro-optic effect. OPTICS EXPRESS 2014; 22:11646-11653. [PMID: 24921286 DOI: 10.1364/oe.22.011646] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/03/2023]
Abstract
We study theoretically surface lattice solitons driven by quadratic electro-optic effect at the interface between an optical lattice and diffusive nonlinear media with self-focusing and self-defocusing saturable nonlinearity. Surface solitons originating from self-focusing nonlinearity can be formed in the semi-infinite gap, and are stable in whole domain of their existence. In the case of self-defocusing nonlinearity, both surface gap and twisted solitons are predicted in first gap. We discover that surface gap solitons can propagate stably in whole existence domain except for an extremely narrow region close to the Bloch band, and twisted solitons are linearly unstable in the entire existence domain.
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6
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Yin C, He Y, Li H, Xie J. Solitons in parity-time symmetric potentials with spatially modulated nonlocal nonlinearity. OPTICS EXPRESS 2012; 20:19355-19362. [PMID: 23038578 DOI: 10.1364/oe.20.019355] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/01/2023]
Abstract
We study the solitons in parity-time symmetric potential in the medium with spatially modulated nonlocal nonlinearity. It is found that the coefficient of the spatially modulated nonlinearity and the degree of the uniform nonlocality can profoundly affect the stability of solitons. There exist stable solitons in low-power region, and unstable solitons in high-power region. In the unstable cases, the solitons exhibit jump from the original site to the next one, and they can continue the motion into the other lattices. The region of the stable soliton can be expanded by increasing the coefficient of the modulated nonlocality. Finally, critical amplitude of the imaginary part of the linear PT lattices is obtained, above which solitons are unstable and decay immediately.
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Affiliation(s)
- Chengping Yin
- Laboratory of Quantum Information Technology, School of Physics and Telecommunication Engineering, South China Normal University, Guangzhou 510006, China.
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Prilepsky JE, Derevyanko SA, Gredeskul SA. Controlling soliton refraction in optical lattices. PHYSICAL REVIEW LETTERS 2011; 107:083901. [PMID: 21929169 DOI: 10.1103/physrevlett.107.083901] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/26/2011] [Indexed: 05/31/2023]
Abstract
We show in the framework of the 1D nonlinear Schrödinger equation that the value of the refraction angle of a fundamental soliton beam passing through an optical lattice can be controlled by adjusting either the shape of an individual waveguide or the relative positions of the waveguides. In the case of the shallow refractive index modulation, we develop a general approach for the calculation of the refraction angle change. The shape of a single waveguide crucially affects the refraction direction due to the appearance of a structural form factor in the expression for the density of emitted waves. For a lattice of scatterers, wave-soliton interference inside the lattice leads to the appearance of an additional geometric form factor. As a result, the soliton refraction is more pronounced for the disordered lattices than for the periodic ones.
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Affiliation(s)
- Jaroslaw E Prilepsky
- Nonlinearity and Complexity Research Group, Aston University, B4 7ET Birmingham, United Kingdom.
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8
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Bugaychuk S, Conte R. Ginzburg-Landau equation for dynamical four-wave mixing in gain nonlinear media with relaxation. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2009; 80:066603. [PMID: 20365290 DOI: 10.1103/physreve.80.066603] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/01/2009] [Indexed: 05/29/2023]
Abstract
We consider the dynamical degenerate four-wave mixing (FWM) model in a cubic nonlinear medium including both the time relaxation of the induced nonlinearity and the nonlocal coupling. The initial ten-dimensional FWM system can be rewritten as a three-variable intrinsic system (namely, the intensity pattern, the amplitude of the nonlinearity, and the total net gain) which is very close to the pumped Maxwell-Bloch system. In the case of a purely nonlocal response the initial system reduces to a real damped sine-Gordon (SG) equation. We obtain a solution of this equation in the form of a sech function with a time-dependent coefficient. By applying the reductive perturbation method to this damped SG equation, we obtain exactly the cubic complex Ginzburg Landau equation (CGL3) but with a time dependence in the loss or gain coefficient. The CGL3 describes the properties of the spatially localized interference pattern formed by the FWM.
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Affiliation(s)
- Svitlana Bugaychuk
- Institute of Physics, National Academy of Sciences, 46 Prospect Nauki, Kiev, Ukraine.
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Ye F, Dong L, Hu B. Localization of light in a parabolically bending waveguide array in thermal nonlinear media. OPTICS LETTERS 2009; 34:584-586. [PMID: 19252559 DOI: 10.1364/ol.34.000584] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/27/2023]
Abstract
A parabolically longitudinally bending waveguide array imprinted into thermal nonlinear media is found to support the localized stationary solitons. The localization results from the suppression of a curvature effect by the nonlinearity with an infinite-range nonlocality. The localization criterion is given analytically. Solitons propagate stably along a curved trajectory without bending loss, and their locations are significantly influenced by the waveguide curvature. These solitons represent the first example of stationary localized solitons encountered in curved waveguides.
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Affiliation(s)
- Fangwei Ye
- Department of Physics, Centre for Nonlinear Studies and The Beijing-Hong Kong-Singapore Joint Centre for Nonlinear and Complex Systems (Hong Kong), Hong Kong Baptist University, Kowloon Tong, China.
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Rasmussen PD, Bennet FH, Neshev DN, Sukhorukov AA, Rosberg CR, Krolikowski W, Bang O, Kivshar YS. Observation of two-dimensional nonlocal gap solitons. OPTICS LETTERS 2009; 34:295-297. [PMID: 19183636 DOI: 10.1364/ol.34.000295] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/27/2023]
Abstract
We demonstrate, both theoretically and experimentally, the existence of nonlocal gap solitons in two-dimensional periodic photonic structures with defocusing thermal nonlinearity. We employ liquid-infiltrated photonic crystal fibers and show how the system geometry can modify the effective response of a nonlocal medium and the properties of two-dimensional gap solitons.
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Affiliation(s)
- Per Dalgaard Rasmussen
- Nonlinear Physics Centre, Research School of Physical Sciences and Engineering, Australian National University, Canberra, ACT, Australia
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Kominis Y, Hizanidis K. Power dependent soliton location and stability in complex photonic structures. OPTICS EXPRESS 2008; 16:12124-12138. [PMID: 18679488 DOI: 10.1364/oe.16.012124] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/26/2023]
Abstract
The presence of spatial inhomogeneity in a nonlinear medium results in the breaking of the translational invariance of the underlying propagation equation. As a result traveling wave soliton solutions do not exist in general for such systems, while stationary solitons are located in fixed positions with respect to the inhomogeneous spatial structure. In simple photonic structures with monochromatic modulation of the linear refractive index, soliton position and stability do not depend on the characteristics of the soliton such as power, width and propagation constant. In this work, we show that for more complex photonic structures where either one of the refractive indices (linear or nonlinear) is modulated by more than one wavenumbers, or both of them are modulated, soliton position and stability depends strongly on its characteristics. The latter results in additional functionality related to soliton discrimination in such structures. The respective power (or width/propagation constant) dependent bifurcations are studied in terms of a Melnikov-type theory. The latter is used for the determination of the specific positions, with respect to the spatial structure, where solitons can be located. A wide variety of cases are studied, including solitons in periodic and quasiperiodic lattices where both the linear and the nonlinear refractive index are spatially modulated. The investigation of a wide variety of inhomogeneities provides physical insight for the design of a spatial structure and the control of the position and stability of a localized wave.
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Affiliation(s)
- Y Kominis
- School of Electrical and Computer Engineering, National Technical University of Athens, Zographou GR-15773, Athens, Greece.
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12
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Sivan Y, Fibich G, Ilan B. Drift instability and tunneling of lattice solitons. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2008; 77:045601. [PMID: 18517683 DOI: 10.1103/physreve.77.045601] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/12/2007] [Indexed: 05/26/2023]
Abstract
We derive an analytic formula for the lateral dynamics of solitons in a general inhomogeneous nonlinear media, and show that it can be valid over tens of diffraction lengths. In particular, we show that solitons centered at a lattice maximum can be "mathematically unstable" but "physically stable." We also derive an analytic upper bound for the critical velocity for tunneling, which is valid even when the standard Peierls-Nabarro potential approach fails.
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Affiliation(s)
- Y Sivan
- Department of Physics and Astronomy, Tel Aviv University, Tel Aviv, Israel
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Pardo R, Pérez-García VM. Dissipative solitons that cannot be trapped. PHYSICAL REVIEW LETTERS 2006; 97:254101. [PMID: 17280357 DOI: 10.1103/physrevlett.97.254101] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/20/2006] [Indexed: 05/13/2023]
Abstract
We show that dissipative solitons in systems with high-order nonlinear dissipation cannot survive in the presence of trapping potentials of the rigid wall or asymptotically increasing type. Solitons in such systems can survive in the presence of a weak potential but only with energies out of the interval of existence of linear quantum mechanical stationary states.
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Affiliation(s)
- Rosa Pardo
- Departamento de Matemática Aplicada, Facultad de Ciencias Químicas, Universidad Complutense, Avda. Complutense s/n, 28040 Madrid, Spain.
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14
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Mihalache D, Mazilu D, Lederer F, Crasovan LC, Kartashov YV, Torner L, Malomed BA. Stable solitons of even and odd parities supported by competing nonlocal nonlinearities. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2006; 74:066614. [PMID: 17280169 DOI: 10.1103/physreve.74.066614] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/11/2006] [Indexed: 05/13/2023]
Abstract
We introduce a one-dimensional phenomenological model of a nonlocal medium featuring focusing cubic and defocusing quintic nonlocal optical nonlinearities. By means of numerical methods, we find families of solitons of two types, even-parity (fundamental) and dipole-mode (odd-parity) ones. Stability of the solitons is explored by means of computation of eigenvalues associated with modes of small perturbations, and tested in direct simulations. We find that the stability of the fundamental solitons strictly follows the Vakhitov-Kolokolov criterion, whereas the dipole solitons can be destabilized through a Hamiltonian-Hopf bifurcation. The solitons of both types may be stable in the nonlocal model with only quintic self-attractive nonlinearity, in contrast with the instability of all solitons in the local version of the quintic model.
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Affiliation(s)
- D Mihalache
- Horia Hulubei National Institute for Physics and Nuclear Engineering (IFIN-HH), 407 Atomistilor, Magurele-Bucharest, 077125, Romania
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Xu Z, Kartashov YV, Torner L. Gap solitons supported by optical lattices in photorefractive crystals with asymmetric nonlocality. OPTICS LETTERS 2006; 31:2027-9. [PMID: 16770421 DOI: 10.1364/ol.31.002027] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/10/2023]
Abstract
We address the impact of the asymmetric nonlocal diffusion nonlinearity of gap solitons supported by photorefractive crystals with an imprinted optical lattice. We reveal how the asymmetric nonlocal response alters the domains of existence and the stability of solitons originating from different gaps. We find that in such media gap solitons cease to exist above a threshold of the nonlocality degree. We discuss how the interplay between nonlocality and lattice strength modifies the gap soliton mobility.
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Affiliation(s)
- Zhiyong Xu
- ICFO-Institut de Ciencies Fotoniques and Universitat Politecnica de Catalunya, Mediterranean Technology Park, Castelldefels (Barcelona), Spain.
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Shen M, Wang Q, Shi J, Hou P, Kong Q. Partially coherent accessible solitons in strongly nonlocal media. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2006; 73:056602. [PMID: 16803052 DOI: 10.1103/physreve.73.056602] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/29/2005] [Indexed: 05/10/2023]
Abstract
We study the propagation of incoherent accessible solitons in strongly nonlocal media with arbitrary response function. Based on the linear propagation equation and the mutual coherence function approach, we obtain an exact analytical solution of such incoherent accessible solitons. The solitons radius is related to the total power as well as the coherence characteristics of the incoherent beam. We find that there is not a threshold for incoherent solitons exist in strongly nonlocal media because the model is linear. Evolution behaviors of the solitons width and the coherence radius are also described when the solitons undergo linear harmonic oscillation.
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Affiliation(s)
- Ming Shen
- Department of Physics, Shanghai University, PR China.
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Mihalache D, Mazilu D, Lederer F, Malomed BA, Kartashov YV, Crasovan LC, Torner L. Three-dimensional spatiotemporal optical solitons in nonlocal nonlinear media. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2006; 73:025601. [PMID: 16605390 DOI: 10.1103/physreve.73.025601] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/17/2005] [Indexed: 05/08/2023]
Abstract
We demonstrate the existence of stable three-dimensional spatiotemporal solitons (STSs) in media with a nonlocal cubic nonlinearity. Fundamental (nonspinning) STSs forming one-parameter families are stable if their propagation constant exceeds a certain critical value that is inversely proportional to the range of nonlocality of nonlinear response. All spinning three-dimensional STSs are found to be unstable.
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Affiliation(s)
- D Mihalache
- National Institute of Physics and Nuclear Engineering, Institute of Atomic Physics, Department of Theoretical Physics, P.O. Box MG-6, Bucharest, Romania
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Xu Z, Kartashov YV, Torner L. Upper threshold for stability of multipole-mode solitons in nonlocal nonlinear media. OPTICS LETTERS 2005; 30:3171-3. [PMID: 16342710 DOI: 10.1364/ol.30.003171] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/05/2023]
Abstract
We address the stability of multipole-mode solitons in nonlocal Kerr-type nonlinear media. Such solitons comprise several out-of-phase peaks packed together by the forces acting between them. We discover that dipole-, triple-, and quadrupole-mode solitons can be made stable, whereas all higher-order soliton bound states are unstable.
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Affiliation(s)
- Zhiyong Xu
- ICFO-Institut de Ciencies Fotoniques and Universitat Politecnica de Catalunya, Barcelona, Spain.
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