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Tabi CB, Tagwo H, Kofané TC. Modulational instability in nonlinear saturable media with competing nonlocal nonlinearity. Phys Rev E 2022; 106:054201. [PMID: 36559471 DOI: 10.1103/physreve.106.054201] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/01/2022] [Accepted: 10/10/2022] [Indexed: 11/06/2022]
Abstract
The modulational instability (MI) phenomenon is addressed in a nonlocal medium under controllable saturation. The linear stability analysis of a plane-wave solution is used to derive an expression for the growth rate of MI that is exploited to parametrically discuss the possibility for the plane wave to disintegrate into nonlinear localized light patterns. The influence of the nonlocal parameter, the saturation coefficient, and the saturation index are mainly explored in the context of a Gaussian nonlocal response. It is pointed out that the instability spectrum, which tends to be quenched by the high nonlocality parameter, gets amplified under the right choices of the saturation parameters, especially the saturation index. Via direct numerical simulations, confirmations of analytical predictions are given, where competing nonlocal and saturable nonlinearities enable the emergence of trains of patterns as manifestations of MI. The comprehensive parametric analysis carried out throughout the numerical experiment reveals the robustness of the obtained rogue waves of A- and B-type Akhmediev breathers, as the nonlinear signature of MI, providing the saturation index as a suitable tool to manipulate nonlinear waves in nonlocal media.
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Affiliation(s)
- Conrad Bertrand Tabi
- Department of Physics and Astronomy, Botswana International University of Science and Technology, Private Mail Bag 16 Palapye, Botswana
| | - Hippolyte Tagwo
- Laboratory of Mechanics, Department of Physics, Faculty of Science, University of Yaoundé I, P.O. Box 812, Yaoundé, Cameroon
| | - Timoléon Crépin Kofané
- Department of Physics and Astronomy, Botswana International University of Science and Technology, Private Mail Bag 16 Palapye, Botswana.,Laboratory of Mechanics, Department of Physics, Faculty of Science, University of Yaoundé I, P.O. Box 812, Yaoundé, Cameroon.,Centre d'Excellence Africain en Technologies de l'Information et de la Communication, University of Yaoundé I, Cameroon
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Qin YH, Zhao LC, Yang ZQ, Ling L. Multivalley dark solitons in multicomponent Bose-Einstein condensates with repulsive interactions. Phys Rev E 2021; 104:014201. [PMID: 34412198 DOI: 10.1103/physreve.104.014201] [Citation(s) in RCA: 6] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/12/2021] [Accepted: 06/09/2021] [Indexed: 06/13/2023]
Abstract
We obtain multivalley dark soliton solutions with asymmetric or symmetric profiles in multicomponent repulsive Bose-Einstein condensates by developing the Darboux transformation method. We demonstrate that the width-dependent parameters of solitons significantly affect the velocity ranges and phase jump regions of multivalley dark solitons, in sharp contrast to scalar dark solitons. For double-valley dark solitons, we find that the phase jump is in the range [0,2π], which is quite different from that of the usual single-valley dark soliton. Based on our results, we argue that the phase jump of an n-valley dark soliton could be in the range [0,nπ], supported by our analysis extending up to five-component condensates. The interaction between a double-valley dark soliton and a single-valley dark soliton is further investigated, and we reveal a striking collision process in which the double-valley dark soliton is transformed into a breather after colliding with the single-valley dark soliton. Our analyses suggest that this breather transition exists widely in the collision processes involving multivalley dark solitons. The possibilities for observing these multivalley dark solitons in related Bose-Einstein condensates experiments are discussed.
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Affiliation(s)
- Yan-Hong Qin
- School of Physics, Northwest University, Xi'an 710127, China
- Shaanxi Key Laboratory for Theoretical Physics Frontiers, Xi'an 710127, China
| | - Li-Chen Zhao
- School of Physics, Northwest University, Xi'an 710127, China
- NSFC-SPTP Peng Huanwu Center for Fundamental Theory, Xi'an 710127, China
- Shaanxi Key Laboratory for Theoretical Physics Frontiers, Xi'an 710127, China
| | - Zeng-Qiang Yang
- Department of Physics, School of Arts and Sciences, Shaanxi University of Science and Technology, Xi'an 710021, China
| | - Liming Ling
- School of Mathematics, South China University of Technology, Guangzhou 510640, China
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Zhao LC, Qin YH, Lee C, Liu J. Classification of dark solitons via topological vector potentials. Phys Rev E 2021; 103:L040204. [PMID: 34005860 DOI: 10.1103/physreve.103.l040204] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/29/2020] [Accepted: 04/07/2021] [Indexed: 11/07/2022]
Abstract
Dark solitons are some of the most interesting nonlinear excitations and are considered to be the one-dimensional topological analogs of vortices. However, in contrast to their two-dimensional vortex counterparts, the topological characteristics of a dark soliton are far from fully understood because the topological charge defined according to the phase jump cannot reflect its essential property. Here, similar to the complex extension used in the exploration of the partition-function zeros to depict thermodynamic states, we extend the complex coordinate space to explore the density zeros of dark solitons. Surprisingly we find that these zeros constitute some pointlike magnetic fields, each of which has a quantized magnetic flux of elementary π. The corresponding vector potential fields demonstrate the topology of the Wess-Zumino term and can depict the essential characteristics of dark solitons. Then we classify the dark solitons according to the Euler characteristic of the topological manifold of the vector potential fields. Our study not only reveals the topological features of dark solitons but can also be applied to explore and identify new dark solitons with high topological complexity.
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Affiliation(s)
- L-C Zhao
- School of Physics, Northwest University, Xi'an 710127, China.,Shaanxi Key Laboratory for Theoretical Physics Frontiers, Xi'an 710127, China
| | - Y-H Qin
- School of Physics, Northwest University, Xi'an 710127, China
| | - C Lee
- Guangdong Provincial Key Laboratory of Quantum Metrology and Sensing & School of Physics and Astronomy, Sun Yat-Sen University (Zhuhai Campus), Zhuhai 519082, China.,State Key Laboratory of Optoelectronic Materials and Technologies, Sun Yat-Sen University (Guangzhou Campus), Guangzhou 510275, China
| | - J Liu
- Graduate School, China Academy of Engineering Physics, Beijing 100193, China.,CAPT, HEDPS, and IFSA Collaborative Innovation Center of the Ministry of Education, Peking University, Beijing 100871, China
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Ziółkowski A, Weinert-Raczka E. Dark screening solitons in multiple quantum well planar waveguide. ACTA ACUST UNITED AC 2007. [DOI: 10.1088/1464-4258/9/7/021] [Citation(s) in RCA: 13] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/12/2022]
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Kivshar YS, Afanasjev VV. Drift instability of dark solitons in saturable media. OPTICS LETTERS 1996; 21:1135-1137. [PMID: 19876277 DOI: 10.1364/ol.21.001135] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/28/2023]
Abstract
It is shown that dark solitons display an inherent instability for a strong saturation of the nonlinear refractive index provided that the background intensity exceeds a certain critical value. Such an instability manifests itself as a drift of a black soliton that transform into a gray soliton and radiation.
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Pelinovsky DE, Kivshar YS, Afanasjev VV. Instability-induced dynamics of dark solitons. PHYSICAL REVIEW. E, STATISTICAL PHYSICS, PLASMAS, FLUIDS, AND RELATED INTERDISCIPLINARY TOPICS 1996; 54:2015-2032. [PMID: 9965285 DOI: 10.1103/physreve.54.2015] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
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Taya M, Bashaw MC, Fejer MM, Segev M, Valley GC. Observation of dark photovoltaic spatial solitons. PHYSICAL REVIEW. A, ATOMIC, MOLECULAR, AND OPTICAL PHYSICS 1995; 52:3095-3100. [PMID: 9912595 DOI: 10.1103/physreva.52.3095] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
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Abstract
Optical dark solitons described by the generalized nonlinear Schrödinger equation are discussed, and the criterion of soliton instability is presented. This analytical criterion is confirmed numerically for an exactly solvable model of nonlinear saturation.
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Abstract
We present what is to our knowledge the first general theory for describing interacting well-separated gray spatial solitons, propagating in an arbitrary self-defocusing nonlinearity. It reveals why two dark solitons will in general repel, becoming less dark as they propagate. The results are illustrated with analytic expressions for the Kerr and the saturating nonlinearities.
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Kivshar YS, Yang X. Perturbation-induced dynamics of dark solitons. PHYSICAL REVIEW. E, STATISTICAL PHYSICS, PLASMAS, FLUIDS, AND RELATED INTERDISCIPLINARY TOPICS 1994; 49:1657-1670. [PMID: 9961379 DOI: 10.1103/physreve.49.1657] [Citation(s) in RCA: 31] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
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Królikowski W, Akhmediev N, Luther-Davies B. Darker-than-black solitons: Dark solitons with total phase shift greater than pi. PHYSICAL REVIEW. E, STATISTICAL PHYSICS, PLASMAS, FLUIDS, AND RELATED INTERDISCIPLINARY TOPICS 1993; 48:3980-3987. [PMID: 9961056 DOI: 10.1103/physreve.48.3980] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
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