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Article ; Online: Basic fractional nonlinear-wave models and solitons.

Malomed, Boris A

2024 Volume 34, Issue 2

Abstract: This review article provides a concise summary of one- and two-dimensional models for the propagation of linear and nonlinear waves in fractional media. The basic models, which originate from Laskin's fractional quantum mechanics and more experimentally ... ...

Abstract	This review article provides a concise summary of one- and two-dimensional models for the propagation of linear and nonlinear waves in fractional media. The basic models, which originate from Laskin's fractional quantum mechanics and more experimentally relevant setups emulating fractional diffraction in optics, are based on the Riesz definition of fractional derivatives, which are characterized by the respective Lévy indices. Basic species of one-dimensional solitons, produced by the fractional models which include cubic or quadratic nonlinear terms, are outlined too. In particular, it is demonstrated that the variational approximation is relevant in many cases. A summary of the recently demonstrated experimental realization of the fractional group-velocity dispersion in fiber lasers is also presented.
Language	English
Publishing date	2024-02-11
Publishing country	United States
Document type	Journal Article
ZDB-ID	1472677-4
ISSN	1089-7682 ; 1054-1500
ISSN (online)	1089-7682
ISSN	1054-1500
DOI	10.1063/5.0190039
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Article ; Online: Discrete and Semi-Discrete Multidimensional Solitons and Vortices: Established Results and Novel Findings.

Malomed, Boris A

Entropy (Basel, Switzerland)

2024 Volume 26, Issue 2

Abstract: This article presents a concise survey of basic discrete and semi-discrete nonlinear models, which produce two- and three-dimensional (2D and 3D) solitons, and a summary of the main theoretical and experimental results obtained for such solitons. The ... ...

Abstract	This article presents a concise survey of basic discrete and semi-discrete nonlinear models, which produce two- and three-dimensional (2D and 3D) solitons, and a summary of the main theoretical and experimental results obtained for such solitons. The models are based on the discrete nonlinear Schrödinger (DNLS) equations and their generalizations, such as a system of discrete Gross-Pitaevskii (GP) equations with the Lee-Huang-Yang corrections, the 2D Salerno model (SM), DNLS equations with long-range dipole-dipole and quadrupole-quadrupole interactions, a system of coupled discrete equations for the second-harmonic generation with the quadratic (χ(2)) nonlinearity, a 2D DNLS equation with a superlattice modulation opening mini-gaps, a discretized NLS equation with rotation, a DNLS coupler and its PT-symmetric version, a system of DNLS equations for the spin-orbit-coupled (SOC) binary Bose-Einstein condensate, and others. The article presents a review of the basic species of multidimensional discrete modes, including fundamental (zero-vorticity) and vortex solitons, their bound states, gap solitons populating mini-gaps, symmetric and asymmetric solitons in the conservative and PT-symmetric couplers, cuspons in the 2D SM, discrete SOC solitons of the semi-vortex and mixed-mode types, 3D discrete skyrmions, and some others.
Language	English
Publishing date	2024-02-02
Publishing country	Switzerland
Document type	Journal Article ; Review
ZDB-ID	2014734-X
ISSN	1099-4300 ; 1099-4300
ISSN (online)	1099-4300
ISSN	1099-4300
DOI	10.3390/e26020137
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Article ; Online: Symmetry-breaking transitions in quiescent and moving solitons in fractional couplers.

Strunin, Dmitry V / Malomed, Boris A

Physical review. E

2023 Volume 107, Issue 6-1, Page(s) 64203

Abstract: We consider phase transitions, in the form of spontaneous symmetry breaking (SSB) bifurcations of solitons, in dual-core couplers with fractional diffraction and cubic self-focusing acting in each core, characterized by Lévy index α. The system ... ...

Abstract	We consider phase transitions, in the form of spontaneous symmetry breaking (SSB) bifurcations of solitons, in dual-core couplers with fractional diffraction and cubic self-focusing acting in each core, characterized by Lévy index α. The system represents linearly coupled optical waveguides with the fractional paraxial diffraction or group-velocity dispersion (the latter system was used in a recent experiment [Nat. Commun. 14, 222 (2023)10.1038/s41467-023-35892-8], which demonstrated the first observation of the wave propagation in an effectively fractional setup). By dint of numerical computations and variational approximation, we identify the SSB in the fractional coupler as the bifurcation of the subcritical type (i.e., the symmetry-breaking phase transition of the first kind), whose subcriticality becomes stronger with the increase of fractionality 2-α, in comparison with very weak subcriticality in the case of the nonfractional diffraction, α=2. In the Cauchy limit of α→1, it carries over into the extreme subcritical bifurcation, manifesting backward-going branches of asymmetric solitons which never turn forward. The analysis of the SSB bifurcation is extended for moving (tilted) solitons, which is a nontrivial problem because the fractional diffraction does not admit Galilean invariance. Collisions between moving solitons are studied too, featuring a two-soliton symmetry-breaking effect and merger of the solitons.
Language	English
Publishing date	2023-07-18
Publishing country	United States
Document type	Journal Article
ZDB-ID	2844562-4
ISSN	2470-0053 ; 2470-0045
ISSN (online)	2470-0053
ISSN	2470-0045
DOI	10.1103/PhysRevE.107.064203
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Article ; Online: Rogue waves and instability arising from long-wave-short-wave resonance beyond the integrable regime.

Sun, Wen-Rong / Malomed, Boris A / Li, Jin-Hua

Physical review. E

2024 Volume 109, Issue 2-1, Page(s) 24209

Abstract: We consider instability and localized patterns arising from the long-wave-short-wave resonance in the nonintegrable regime numerically. We study the stability and instability of elliptic-function periodic waves with respect to subharmonic perturbations, ... ...

Abstract	We consider instability and localized patterns arising from the long-wave-short-wave resonance in the nonintegrable regime numerically. We study the stability and instability of elliptic-function periodic waves with respect to subharmonic perturbations, whose period is a multiple of the period of the elliptic waves. We thus find the modulational instability (MI) of the corresponding dnoidal waves. Upon varying parameters of dnoidal waves, spectrally unstable ones can be transformed into stable states via the Hamiltonian Hopf bifurcation. For snoidal waves, we find a transition of the dominant instability scenario between the MI and the instability with a bubblelike spectrum. For cnoidal waves, we produce three variants of the MI. Evolution of the unstable states is also considered, leading to formation of rogue waves on top of the elliptic-wave and continuous-wave backgrounds.
Language	English
Publishing date	2024-03-15
Publishing country	United States
Document type	Journal Article
ZDB-ID	2844562-4
ISSN	2470-0053 ; 2470-0045
ISSN (online)	2470-0053
ISSN	2470-0045
DOI	10.1103/PhysRevE.109.024209
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Article ; Online: Bimetal Thin Film, Semiconductors, and 2D Nanomaterials in SPR Biosensors: An Approach to Enhanced Urine Glucose Sensing.

Kumar, Shatrughna / Yadav, Archana / Malomed, Boris A

IEEE transactions on nanobioscience

2024 Volume 23, Issue 2, Page(s) 336–343

Abstract: This work introduces a systematic approach for the development of Kretschmann configuration-based biosensors designed for non-invasive urine glucose detection. The methodology encompasses the utilization of various semiconductors, including Silicon (Si), ...

Abstract	This work introduces a systematic approach for the development of Kretschmann configuration-based biosensors designed for non-invasive urine glucose detection. The methodology encompasses the utilization of various semiconductors, including Silicon (Si), Germanium (Ge), Gallium Nitride (GaN), Aluminum Nitride (AlN), and Indium Nitride (InN), in combination with a bimetallic layer (comprising Au and Ag films of equal thickness) to enhance the biosensor sensitivity. Additionally, 2D nanomaterials, such as Black Phosphorus and Graphene, are integrated into the semiconductor layers to enhance performance further. These configurations are meticulously optimized through the application of the transfer matrix method (TMM), and the sensing parameters are assessed using the angular modulation method. Among the semiconductors, AlN and GaN exhibit superior results. On these substrates, Graphene and Black phosphorous (BP) layers are applied, resulting in four final structures (thicknesses in nm): BK7/Au(26)/Ag(26)/Si(6)/BP(0.53)/Biosample, BK7/Au(26)/Ag(26)/AlN(14)/BP(0.53)/Biosample, BK7/Au(26)/Ag(26)/GaN(12)/BP(0.53)/Biosample, and BK7/Au(26)/Ag(26)/GaN(12)/Graphene(0.34)/Biosample. These biosensors achieve Sensitivity(° /RIU) and Figure of Merit (FoM) (1/RIU) of 380, 360, 440, 400, and 58.5, 90, 90.65, and 82.4, respectively. Subsequently, these high-performing sensors undergo testing with actual urine glucose samples. Among them, two biosensors, BK7/Au(26)/Ag(26)/AlN(14)/BP (0.53)/Biosample and BK7/Au(26)/Ag(26)/GaN(14)/Graphene(0.34)/Biosample, exhibit outstanding performance, with sensitivities (° /RIU) and FoM (1/RIU) of 394.44 & 294.44, and 112.6 & 92.01 respectively. A comparison is also made with relevant previously published work, revealing improved performance in glucose detection.
MeSH term(s)	Graphite ; Surface Plasmon Resonance ; Glucose ; Nanostructures ; Semiconductors ; Silicon ; Aluminum Compounds
Chemical Substances	Graphite (7782-42-5) ; aluminum nitride (7K47D7P3M0) ; Glucose (IY9XDZ35W2) ; Silicon (Z4152N8IUI) ; Aluminum Compounds
Language	English
Publishing date	2024-03-28
Publishing country	United States
Document type	Journal Article
ISSN	1558-2639
ISSN (online)	1558-2639
DOI	10.1109/TNB.2024.3354571
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Article ; Online: Trapping wave fields in an expulsive potential by means of linear coupling.

Hacker, Nir / Malomed, Boris A

Physical review. E

2022 Volume 105, Issue 3-1, Page(s) 34213

Abstract: We demonstrate the existence of confined states in one- and two-dimensional (1D and 2D) systems of two linearly coupled components, with the confining harmonic-oscillator (HO) potential acting upon one component and an expulsive anti-HO potential acting ... ...

Abstract	We demonstrate the existence of confined states in one- and two-dimensional (1D and 2D) systems of two linearly coupled components, with the confining harmonic-oscillator (HO) potential acting upon one component and an expulsive anti-HO potential acting upon the other. The systems can be implemented in optical and BEC dual-core waveguides. In the 1D linear system, codimension-one solutions are found in an exact form for the ground state (GS) and dipole mode (the first excited state). Generic solutions are produced by means of the variational approximation and are found in a numerical form. Exact codimension-one solutions and generic numerical ones are also obtained for the GS and vortex states in the 2D system (the exact solutions are found for all values of the vorticity). Both the trapped and antitrapped components of the bound states may be dominant ones, in terms of the norm. The localized modes may be categorized as bound states in continuum, as they coexist with delocalized ones. The 1D states, as well as the GS in 2D, are weakly affected and remain stable if the self-attractive or repulsive nonlinearity is added to the system. The self-attraction makes the vortex states unstable against splitting, while they remain stable under the action of the self-repulsion.
Language	English
Publishing date	2022-04-10
Publishing country	United States
Document type	Journal Article
ZDB-ID	2844562-4
ISSN	2470-0053 ; 2470-0045
ISSN (online)	2470-0053
ISSN	2470-0045
DOI	10.1103/PhysRevE.105.034213
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Article ; Online: Formation of Rogue Waves and Modulational Instability with Zero-Wavenumber Gain in Multicomponent Systems with Coherent Coupling.

Liu, Lei / Sun, Wen-Rong / Malomed, Boris A

Physical review letters

2023 Volume 131, Issue 9, Page(s) 93801

Abstract: It is known that rogue waves (RWs) are generated by the modulational instability (MI) of the baseband type. Starting with the Bers-Kaup-Reiman system for three-wave resonant interactions, we identify a specific RW-building mechanism based on MI which ... ...

Abstract	It is known that rogue waves (RWs) are generated by the modulational instability (MI) of the baseband type. Starting with the Bers-Kaup-Reiman system for three-wave resonant interactions, we identify a specific RW-building mechanism based on MI which includes zero wavenumber in the gain band. An essential finding is that this mechanism works solely under a linear relation between the MI gain and a vanishingly small wavenumber of the modulational perturbation. The same mechanism leads to the creation of RWs by MI in other multicomponent systems-in particular, in the massive Thirring model.
Language	English
Publishing date	2023-09-18
Publishing country	United States
Document type	Journal Article
ZDB-ID	208853-8
ISSN	1079-7114 ; 0031-9007
ISSN (online)	1079-7114
ISSN	0031-9007
DOI	10.1103/PhysRevLett.131.093801
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Article ; Online: One-dimensional Townes solitons in dual-core systems with localized coupling.

Kumar, Shatrughna / Li, Pengfei / Malomed, Boris A

Physical review. E

2023 Volume 108, Issue 2-1, Page(s) 24202

Abstract: The recent creation of Townes solitons (TSs) in binary Bose-Einstein condensates and experimental demonstration of spontaneous symmetry breaking (SSB) in solitons propagating in dual-core optical fibers has drawn renewed interest in the TS and SSB ... ...

Abstract	The recent creation of Townes solitons (TSs) in binary Bose-Einstein condensates and experimental demonstration of spontaneous symmetry breaking (SSB) in solitons propagating in dual-core optical fibers has drawn renewed interest in the TS and SSB phenomenology in these and other settings. In particular, stabilization of TSs, which are always unstable in free space, is a relevant problem with various ramifications. We introduce a system which admits exact solutions for both TSs and SSB of solitons. It is based on a dual-core waveguide with quintic self-focusing and fused (localized) coupling between the cores. The respective system of coupled nonlinear Schrödinger equations gives rise to exact solutions for full families of symmetric and asymmetric solitons, which are produced by the supercritical SSB bifurcation (i.e., the symmetry-breaking phase transition of the second kind). Stability boundaries of asymmetric solitons are identified by dint of numerical methods. Unstable solitons spontaneously transform into robust moderately asymmetric breathers or strongly asymmetric states with small intrinsic oscillations. The setup can be used in the design of photonic devices operating in coupling and switching regimes.
Language	English
Publishing date	2023-09-18
Publishing country	United States
Document type	Journal Article
ZDB-ID	2844562-4
ISSN	2470-0053 ; 2470-0045
ISSN (online)	2470-0053
ISSN	2470-0045
DOI	10.1103/PhysRevE.108.024202
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Article ; Online: Stable higher-charge vortex solitons in the cubic-quintic medium with a ring potential.

Dong, Liangwei / Fan, Mingjing / Malomed, Boris A

Optics letters

2023 Volume 48, Issue 18, Page(s) 4817–4820

Abstract: We put forward a model for trapping stable optical vortex solitons (VSs) with high topological charges m. The cubic-quintic nonlinear medium with an imprinted ring-shaped modulation of the refractive index is shown to support two branches of VSs, which ... ...

Abstract	We put forward a model for trapping stable optical vortex solitons (VSs) with high topological charges m. The cubic-quintic nonlinear medium with an imprinted ring-shaped modulation of the refractive index is shown to support two branches of VSs, which are controlled by the radius, width, and depth of the modulation profile. While the lower-branch VSs are unstable in their nearly whole existence domain, the upper branch is completely stable. Vortex solitons with m ≤ 12 obey the anti-Vakhitov-Kolokolov stability criterion. The results suggest possibilities for the creation of stable narrow optical VSs with a low power, carrying higher vorticities.
Language	English
Publishing date	2023-09-14
Publishing country	United States
Document type	Journal Article
ISSN	1539-4794
ISSN (online)	1539-4794
DOI	10.1364/OL.500054
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Article ; Online: Topological solitonic macromolecules.

Zhao, Hanqing / Malomed, Boris A / Smalyukh, Ivan I

Nature communications

2023 Volume 14, Issue 1, Page(s) 4581

Abstract: Being ubiquitous, solitons have particle-like properties, exhibiting behaviour often associated with atoms. Bound solitons emulate dynamics of molecules, though solitonic analogues of polymeric materials have not been considered yet. Here we ... ...

Abstract	Being ubiquitous, solitons have particle-like properties, exhibiting behaviour often associated with atoms. Bound solitons emulate dynamics of molecules, though solitonic analogues of polymeric materials have not been considered yet. Here we experimentally create and model soliton polymers, which we call "polyskyrmionomers", built of atom-like individual solitons characterized by the topological invariant representing the skyrmion number. With the help of nonlinear optical imaging and numerical modelling based on minimizing the free energy, we reveal how topological point defects bind the solitonic quasi-atoms into polyskyrmionomers, featuring linear, branched, and other macromolecule-resembling architectures, as well as allowing for encoding data by spatial distributions of the skyrmion number. Application of oscillating electric fields activates diverse modes of locomotion and internal vibrations of these self-assembled soliton structures, which depend on symmetry of the solitonic macromolecules. Our findings suggest new designs of soliton meta matter, with a potential for the use in fundamental research and technology.
Language	English
Publishing date	2023-07-29
Publishing country	England
Document type	Journal Article
ZDB-ID	2553671-0
ISSN	2041-1723 ; 2041-1723
ISSN (online)	2041-1723
ISSN	2041-1723
DOI	10.1038/s41467-023-40335-5
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