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Article ; Online: Topological solitonic macromolecules

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

Nature Communications, Vol 14, Iss 1, Pp 1-

2023 Volume 12

Abstract: 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	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.
Keywords	Science ; Q
Subject code	539
Language	English
Publishing date	2023-07-01T00:00:00Z
Publisher	Nature Portfolio
Document type	Article ; Online
Database	BASE - Bielefeld Academic Search Engine (life sciences selection)

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Article ; Online: Interplay between Binary and Three-Body Interactions and Enhancement of Stability in Trapless Dipolar Bose–Einstein Condensates

Sabari Subramaniyan / Kishor Kumar Ramavarmaraja / Radha Ramaswamy / Boris A. Malomed

Applied Sciences, Vol 12, Iss 1135, p

2022 Volume 1135

Abstract: We investigate the nonlocal Gross–Pitaevskii (GP) equation with long-range dipole-dipole and contact interactions (including binary and three-body collisions). We address the impact of the three-body interaction on stabilizing trapless dipolar Bose– ... ...

Abstract	We investigate the nonlocal Gross–Pitaevskii (GP) equation with long-range dipole-dipole and contact interactions (including binary and three-body collisions). We address the impact of the three-body interaction on stabilizing trapless dipolar Bose–Einstein condensates (BECs). It is found that the dipolar BECs exhibit stability not only for the usual combination of attractive binary and repulsive three-body interactions, but also for the case when these terms have opposite signs. The trapless stability of the dipolar BECs may be further enhanced by time-periodic modulation of the three-body interaction imposed by means of Feshbach resonance. The results are produced analytically using the variational approach and confirmed by numerical simulations.
Keywords	Bose–Einstein condensates ; Gross–Pitaevskii equation ; dipole-dipole interaction ; variational method ; Runge–Kutta method ; Crank–Nicolson method ; Technology ; T ; Engineering (General). Civil engineering (General) ; TA1-2040 ; Biology (General) ; QH301-705.5 ; Physics ; QC1-999 ; Chemistry ; QD1-999
Subject code	531
Language	English
Publishing date	2022-01-01T00:00:00Z
Publisher	MDPI AG
Document type	Article ; Online
Database	BASE - Bielefeld Academic Search Engine (life sciences selection)

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Article ; Online: Editorial

Boris A. Malomed

Applied Sciences, Vol 7, Iss 9, p

Guided-Wave Optics

2017 Volume 962

Abstract: Guided waves represent a vast class of phenomena in which the propagation of collective excitations in various media is steered in required directions by fixed (or, sometimes, reconfigurable) conduits [.] ...

Abstract	Guided waves represent a vast class of phenomena in which the propagation of collective excitations in various media is steered in required directions by fixed (or, sometimes, reconfigurable) conduits [.]
Keywords	n/a ; Technology ; T ; Engineering (General). Civil engineering (General) ; TA1-2040 ; Biology (General) ; QH301-705.5 ; Physics ; QC1-999 ; Chemistry ; QD1-999
Language	English
Publishing date	2017-09-01T00:00:00Z
Publisher	MDPI AG
Document type	Article ; Online
Database	BASE - Bielefeld Academic Search Engine (life sciences selection)

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Article ; Online: Robust $${\bf{P}}{\bf{T}}$$ PT symmetry of two-dimensional fundamental and vortex solitons supported by spatially modulated nonlinearity

Eitam Luz / Vitaly Lutsky / Er’el Granot / Boris A. Malomed

Scientific Reports, Vol 9, Iss 1, Pp 1-

2019 Volume 19

Abstract: Abstract The real spectrum of bound states produced by $${\bf{P}}{\bf{T}}$$ PT -symmetric Hamiltonians usually suffers breakup at a critical value of the strength of gain-loss terms, i.e., imaginary part of the complex potential. The breakup essentially ... ...

Abstract	Abstract The real spectrum of bound states produced by $${\bf{P}}{\bf{T}}$$ PT -symmetric Hamiltonians usually suffers breakup at a critical value of the strength of gain-loss terms, i.e., imaginary part of the complex potential. The breakup essentially impedes the use of $${\bf{P}}{\bf{T}}$$ PT -symmetric systems for various applications. On the other hand, it is known that the $${\bf{P}}{\bf{T}}$$ PT symmetry can be made unbreakable in a one-dimensional (1D) model with self-defocusing nonlinearity whose strength grows fast enough from the center to periphery. The model is nonlinearizable, i.e., it does not have a linear spectrum, while the (unbreakable) $${\bf{P}}{\bf{T}}$$ PT symmetry in it is defined by spectra of continuous families of nonlinear self-trapped states (solitons). Here we report results for a 2D nonlinearizable model whose $${\bf{P}}{\bf{T}}$$ PT symmetry remains unbroken for arbitrarily large values of the gain-loss coefficient. Further, we introduce an extended 2D model with the imaginary part of potential ~xy in the Cartesian coordinates. The latter model is not a $${\bf{P}}{\bf{T}}$$ PT -symmetric one, but it also supports continuous families of self-trapped states, thus suggesting an extension of the concept of the $${\bf{P}}{\bf{T}}$$ PT symmetry. For both models, universal analytical forms are found for nonlinearizable tails of the 2D modes, and full exact solutions are produced for particular solitons, including ones with the unbreakable $${\bf{P}}{\bf{T}}$$ PT symmetry, while generic soliton families are found in a numerical form. The $${\bf{P}}{\bf{T}}$$ PT -symmetric system gives rise to generic families of stable single- and double-peak 2D solitons (including higher-order radial states of the single-peak solitons), as well as families of stable vortex solitons with m = 1, 2, and 3. In the model with imaginary potential ~xy, families of single- and multi-peak solitons and vortices are stable if the imaginary potential is subject to spatial confinement. In an elliptically deformed version of the latter model, an exact solution is found for vortex solitons with m = 1.
Keywords	Medicine ; R ; Science ; Q
Subject code	539
Language	English
Publishing date	2019-03-01T00:00:00Z
Publisher	Nature Publishing Group
Document type	Article ; Online
Database	BASE - Bielefeld Academic Search Engine (life sciences selection)

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Article ; Online: Three-dimensional solitons in Rydberg-dressed cold atomic gases with spin–orbit coupling

Yuan Zhao / Heng-Jie Hu / Qian-Qian Zhou / Zhang-Cai Qiu / Li Xue / Si-Liu Xu / Qin Zhou / Boris A. Malomed

Scientific Reports, Vol 13, Iss 1, Pp 1-

2023 Volume 9

Abstract: Abstract We present numerical results for three-dimensional (3D) solitons with symmetries of the semi-vortex (SV) and mixed-mode (MM) types, which can be created in spinor Bose–Einstein condensates of Rydberg atoms under the action of the spin–orbit ... ...

Abstract	Abstract We present numerical results for three-dimensional (3D) solitons with symmetries of the semi-vortex (SV) and mixed-mode (MM) types, which can be created in spinor Bose–Einstein condensates of Rydberg atoms under the action of the spin–orbit coupling (SOC). By means of systematic numerical computations, we demonstrate that the interplay of SOC and long-range spherically symmetric Rydberg interactions stabilize the 3D solitons, improving their resistance to collapse. We find how the stability range depends on the strengths of the SOC and Rydberg interactions and the soft-core atomic radius.
Keywords	Medicine ; R ; Science ; Q
Language	English
Publishing date	2023-10-01T00:00:00Z
Publisher	Nature Portfolio
Document type	Article ; Online
Database	BASE - Bielefeld Academic Search Engine (life sciences selection)

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Article ; Online: Localized solutions of Lugiato-Lefever equations with focused pump

Wesley B. Cardoso / Luca Salasnich / Boris A. Malomed

Scientific Reports, Vol 7, Iss 1, Pp 1-

2017 Volume 11

Abstract: Abstract Lugiato-Lefever (LL) equations in one and two dimensions (1D and 2D) accurately describe the dynamics of optical fields in pumped lossy cavities with the intrinsic Kerr nonlinearity. The external pump is usually assumed to be uniform, but it can ...

Abstract	Abstract Lugiato-Lefever (LL) equations in one and two dimensions (1D and 2D) accurately describe the dynamics of optical fields in pumped lossy cavities with the intrinsic Kerr nonlinearity. The external pump is usually assumed to be uniform, but it can be made tightly focused too–in particular, for building small pixels. We obtain solutions of the LL equations, with both the focusing and defocusing intrinsic nonlinearity, for 1D and 2D confined modes supported by the localized pump. In the 1D setting, we first develop a simple perturbation theory, based in the sech ansatz, in the case of weak pump and loss. Then, a family of exact analytical solutions for spatially confined modes is produced for the pump focused in the form of a delta-function, with a nonlinear loss (two-photon absorption) added to the LL model. Numerical findings demonstrate that these exact solutions are stable, both dynamically and structurally (the latter means that stable numerical solutions close to the exact ones are found when a specific condition, necessary for the existence of the analytical solution, does not hold). In 2D, vast families of stable confined modes are produced by means of a variational approximation and full numerical simulations.
Keywords	Medicine ; R ; Science ; Q
Subject code	518
Language	English
Publishing date	2017-12-01T00:00:00Z
Publisher	Nature Publishing Group
Document type	Article ; Online
Database	BASE - Bielefeld Academic Search Engine (life sciences selection)

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Article ; Online: Spin–orbit coupling and nonlinear modes of the polariton condensate in a harmonic trap

Hidetsugu Sakaguchi / Boris A Malomed / Dmitry V Skryabin

New Journal of Physics, Vol 19, Iss 8, p

2017 Volume 085003

Abstract: We consider a model of the exciton-polariton condensate based on a system of two Gross–Pitaevskii equations coupled by the second-order differential operator, which represents the spin–orbit coupling in the system. Also included are the linear gain, ... ...

Abstract	We consider a model of the exciton-polariton condensate based on a system of two Gross–Pitaevskii equations coupled by the second-order differential operator, which represents the spin–orbit coupling in the system. Also included are the linear gain, effective diffusion, nonlinear loss, and the standard harmonic-oscillator trapping potential, as well as the Zeeman splitting. By means of combined analytical and numerical methods, we identify stable two-dimensional modes supported by the nonlinear system. In the absence of the Zeeman splitting, these are mixed modes, which combine zero and nonzero vorticities in each of the two spinor components, and vortex–antivortex complexes. We have also found a range of parameters where the mixed-mode and vortex–antivortex states coexist and are stable. Sufficiently strong Zeeman splitting creates stable semi-vortex states, with vorticities 0 in one component and 2 in the other.
Keywords	polaritons ; condensates ; vortices ; Science ; Q ; Physics ; QC1-999
Subject code	535
Language	English
Publishing date	2017-01-01T00:00:00Z
Publisher	IOP Publishing
Document type	Article ; Online
Database	BASE - Bielefeld Academic Search Engine (life sciences selection)

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Article ; Online: Modulational Instability in Linearly Coupled Asymmetric Dual-Core Fibers

Arjunan Govindarajan / Boris A. Malomed / Arumugam Mahalingam / Ambikapathy Uthayakumar

Applied Sciences, Vol 7, Iss 7, p

2017 Volume 645

Abstract: We investigate modulational instability (MI) in asymmetric dual-core nonlinear directional couplers incorporating the effects of the differences in effective mode areas and group velocity dispersions, as well as phase- and group-velocity mismatches. ... ...

Abstract	We investigate modulational instability (MI) in asymmetric dual-core nonlinear directional couplers incorporating the effects of the differences in effective mode areas and group velocity dispersions, as well as phase- and group-velocity mismatches. Using coupled-mode equations for this system, we identify MI conditions from the linearization with respect to small perturbations. First, we compare the MI spectra of the asymmetric system and its symmetric counterpart in the case of the anomalous group-velocity dispersion (GVD). In particular, it is demonstrated that the increase of the inter-core linear-coupling coefficient leads to a reduction of the MI gain spectrum in the asymmetric coupler. The analysis is extended for the asymmetric system in the normal-GVD regime, where the coupling induces and controls the MI, as well as for the system with opposite GVD signs in the two cores. Following the analytical consideration of the MI, numerical simulations are carried out to explore nonlinear development of the MI, revealing the generation of periodic chains of localized peaks with growing amplitudes, which may transform into arrays of solitons.
Keywords	modulational instability ; asymmetric nonlinear fiber couplers ; linear stability approach ; coupled nonlinear Schrödinger equations ; Technology ; T ; Engineering (General). Civil engineering (General) ; TA1-2040 ; Biology (General) ; QH301-705.5 ; Physics ; QC1-999 ; Chemistry ; QD1-999
Subject code	535
Language	English
Publishing date	2017-06-01T00:00:00Z
Publisher	MDPI AG
Document type	Article ; Online
Database	BASE - Bielefeld Academic Search Engine (life sciences selection)

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Article ; Online: Families of stable solitons and excitations in the PT-symmetric nonlinear Schrödinger equations with position-dependent effective masses

Yong Chen / Zhenya Yan / Dumitru Mihalache / Boris A. Malomed

Scientific Reports, Vol 7, Iss 1, Pp 1-

2017 Volume 21

Abstract: Abstract Since the parity-time-( $$\pmb{\mathscr{P}}\pmb{\mathscr{T}}$$ P T -) symmetric quantum mechanics was put forward, fundamental properties of some linear and nonlinear models with $$\pmb{\mathscr{P}}\pmb{\mathscr{T}}$$ P T -symmetric potentials ... ...

Abstract	Abstract Since the parity-time-( $$\pmb{\mathscr{P}}\pmb{\mathscr{T}}$$ P T -) symmetric quantum mechanics was put forward, fundamental properties of some linear and nonlinear models with $$\pmb{\mathscr{P}}\pmb{\mathscr{T}}$$ P T -symmetric potentials have been investigated. However, previous studies of $$\pmb{\mathscr{P}}\pmb{\mathscr{T}}$$ P T -symmetric waves were limited to constant diffraction coefficients in the ambient medium. Here we address effects of variable diffraction coefficient on the beam dynamics in nonlinear media with generalized $$\pmb{\mathscr{P}}\pmb{\mathscr{T}}$$ P T -symmetric Scarf-II potentials. The broken linear $$\pmb{\mathscr{P}}\pmb{\mathscr{T}}$$ P T symmetry phase may enjoy a restoration with the growing diffraction parameter. Continuous families of one- and two-dimensional solitons are found to be stable. Particularly, some stable solitons are analytically found. The existence range and propagation dynamics of the solitons are identified. Transformation of the solitons by means of adiabatically varying parameters, and collisions between solitons are studied too. We also explore the evolution of constant-intensity waves in a model combining the variable diffraction coefficient and complex potentials with globally balanced gain and loss, which are more general than $$\pmb{\mathscr{P}}\pmb{\mathscr{T}}$$ P T -symmetric ones, but feature similar properties. Our results may suggest new experiments for $$\pmb{\mathscr{P}}\pmb{\mathscr{T}}$$ P T -symmetric nonlinear waves in nonlinear nonuniform optical media.
Keywords	Medicine ; R ; Science ; Q
Subject code	535
Language	English
Publishing date	2017-04-01T00:00:00Z
Publisher	Nature Portfolio
Document type	Article ; Online
Database	BASE - Bielefeld Academic Search Engine (life sciences selection)

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Article ; Online: A PT -Symmetric Dual-Core System with the Sine-Gordon Nonlinearity and Derivative Coupling

Jesús Cuevas-Maraver / Boris A. Malomed / Panayotis G. Kevrekidis

Symmetry, Vol 8, Iss 6, p

2016 Volume 39

Abstract: As an extension of the class of nonlinear PT -symmetric models, we propose a system of sine-Gordon equations, with the PT symmetry represented by balanced gain and loss in them. The equations are coupled by sine-field terms and first-order derivatives. ... ...

Abstract	As an extension of the class of nonlinear PT -symmetric models, we propose a system of sine-Gordon equations, with the PT symmetry represented by balanced gain and loss in them. The equations are coupled by sine-field terms and first-order derivatives. The sinusoidal coupling stems from local interaction between adjacent particles in coupled Frenkel–Kontorova (FK) chains, while the cross-derivative coupling, which was not considered before, is induced by three-particle interactions, provided that the particles in the parallel FK chains move in different directions. Nonlinear modes are then studied in this system. In particular, kink-kink (KK) and kink-anti-kink (KA) complexes are explored by means of analytical and numerical methods. It is predicted analytically and confirmed numerically that the complexes are unstable for one sign of the sinusoidal coupling and stable for another. Stability regions are delineated in the underlying parameter space. Unstable complexes split into free kinks and anti-kinks that may propagate or become quiescent, depending on whether they are subject to gain or loss, respectively.
Keywords	kinks and anti-kinks ; soliton complexes ; Frenkel–Kontorova model ; cross-derivative coupling ; three-body interactions ; Physics ; QC1-999 ; Science ; Q
Subject code	539
Language	English
Publishing date	2016-05-01T00:00:00Z
Publisher	MDPI AG
Document type	Article ; Online
Database	BASE - Bielefeld Academic Search Engine (life sciences selection)

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