Soliton Width Research Articles

Thouless pumping and trapping of two-component gap solitons

We study Thouless pumping and arresting of gap solitons in a two-component Bose gas loaded into an optical superlattice. We show that, depending on the atomic interactions and chemical potentials, the two solitons can be simultaneously pumped or trapped, but we also identify regimes where one soliton is pumped and the other arrested. These behaviors can be understood by considering an effective model of the system based on a variational approach, which reveals that the soliton width is a suitable qualifier for the observed behaviors: solitons with a larger width get transported, while solitons with a smaller width get trapped. Since these widths can be controlled by tuning interactions, it should be possible to observe all behaviors experimentally. Published by the American Physical Society 2024

Pattern transformation and control of generalized multi-peak breathing solitons induced by transverse cross modulation

Based on the nonlocal nonlinear Schrödinger equation, the pattern transformation and control of transverse cross-modulated sine-Gaussian (TCMSG) breathing solitons during transmission are studied. Several expressions have been derived, including the transmission, soliton width, phase wavefront curvature, and so on. The study demonstrates that the coefficient of transverse cross modulation term controls the pattern transformation of the TCMSG breathing solitons. TCMSG breathing solitons can form generalized spatial solitons and breathers during transmission. The variation of the soliton width extrema and their change rates with the transverse cross modulation term coefficient is investigated. The influence of the initial incident power and the transverse cross modulation term coefficient on the soliton width change rate and phase wavefront curvature extrema is studied.

Impact of out-of-plane deformation on atomic reconstruction in twisted van der Waals bilayers

The effects of out-of-plane deformation on atomic relaxation in twisted van der Waals bilayers are investigated by comprehensive multiscale modeling and simulations. The model integrates the DFT-informed generalized stacking-fault energy for interlayer interaction between layers and the Föppl–von Kármán plate theory for elastic energy in each layer with minimization of the total free energy for atomic relaxation governed by a gradient flow method. Our simulation results elucidate twist-angle dependent moiré pattern, strain field, tortional displacement field and stacking domain structures, in good agreement with recent experimental observations. In particular, we derive the strain soliton solution at a small twist angle and the soliton free elastic solution at a large twist angle for the reconstructed van der Waals bilayer with out-of-plane deformation. These results show that out-of-plane deformation not only modifies the strain soliton width but also induces substantial alterations in the strain field, local rotation, and stacking structures. Our findings reveal the non-neglectable role played by out-of-plane deformation in the atomic relaxation of twisted van der Waals bilayers, particularly at smaller twist angles. The intricate interplay between in-plane atomic relaxation and out-of-plane deformation provides opportunities for strain engineering in twisted van der Waals bilayers.

Photovoltaic spatial gap solitons in biased photorefractive optical lattices

We investigate the existence and characteristics of spatially confined optical gap solitons within an optical lattice embedded in a biased bulk photovoltaic photorefractive crystal. The Floquet-Bloch theory is used to analyze the uniform lattice and derive the optical lattice band structure. In the photonic band gaps, which are typically opaque to light transmission, the photorefractive nonlinearity permits the formation of solitons. The paraxial Helmholtz equation is set up and solved thereby discovering single hump and double hump soliton states in both band gaps. Interestingly, we have not found any multi peak solitons to exist in this particular case. We examine the characteristics of these gap solitons, finding that the soliton width (an indicator of nonlinearity) and intensity depend on their location within the band gap. We find that the magnitude of the external electric field profoundly affects the gap soliton characteristics. Additionally, the Vakhitov-Kolokolov (VK) criterion, perturbation analysis and numerical techniques are used to analyze the stability of the various types of the spatial gap solitons in both the band gaps.

Generalized cosine-Gaussian breathing solitons with transverse cross modulation in nonlocal nonlinear media

Based on the nonlocal nonlinear Schrödinger equation, the propagation characteristics of transverse cross-modulated cosine-Gaussian (TCMCG) breathing solitons in strongly nonlocal media are studied. A series of mathematical expressions are provided to describe the propagation dynamics characteristics of the TCMCG breathing solitons, including the soliton width, soliton width change rate, soliton width extreme values, change rates of soliton width extreme values, phase wavefront curvature and phase wavefront curvature extreme values, etc. The research results indicate that by modulating TCMCG breathing solitons, generalized high-order spatial solitons can be formed with periodic changes in light intensity modes but unchanged in beam width. The cosine function parameter has a significant impact on the propagation dynamics characteristics, which appears in the initial expression and plays a cross modulation role in the transverse spatial light intensity. The effect of the initial incident power on soliton width extreme values and phase wavefront curvature extreme values is also discussed.

Modified Korteweg–de Vries solitons with quartic nonlinearity in a dusty plasma

The present multicomponent dusty plasma with ions, Cairns distributed electrons and immobile dusts has been investigated first time through modified Korteweg–de Vries (mKdV) equation of quartic nonlinearity derived by reductive perturbation technique. In this new investigation, it is found that the dust ion-acoustic (DIA) solitary waves have smaller amplitudes compared to the amplitudes of mKdV-DIA compressive solitons of our previous investigation []. Roles of non-thermal parameter (β), dust to ion density ratio (σ), number of dust charge (Z d ) and initial streaming speed of ion (u i0) in the growth of amplitudes and widths of this new mKdV-DIA solitons are investigated.

Riemann–Hilbert approach, dark solitons and double‐pole solutions for Lakshmanan–Porsezian–Daniel equation in an optical fiber, a ferromagnetic spin or a protein

AbstractInverse scattering transform for the defocusing Lakshmanan–Porsezian–Daniel equation with nonzero boundary condition is constructed via the Riemann–Hilbert approach. Since poles of the associated reflection coefficient are simple, ‐dark soliton solutions corresponding to simple poles are constructed. For ‐dark soliton solutions, results show that the soliton amplitude and width are not affected by the strength of the higher‐order linear and nonlinear effects , but soliton velocity has a linear correlation with ; the interactions between the two‐dark solitons and among the three‐dark solitons are elastic and experience phase and position shifts. Besides, asymptotic analysis of the double‐pole solutions for the focusing Lakshmanan–Porsezian–Daniel equation with nonzero boundary condition is presented. Different from ‐dark soliton solutions which locate in the straight lines and experience position shift after the interaction, the double‐pole solutions diverge from each other logarithmically and experience no position shift after the interaction.

Effect of the Soliton Width on Nonequilibrium Exchange Phases of Anyons.

Unlike bosons and fermions, quasiparticles in two-dimensional quantum systems, known as anyons, exhibit statistical exchange phases that range between 0 and π. In fractional quantum Hall states, these anyons, possessing a fraction of the electron charge, traverse along chiral edge channels. This movement facilitates the creation of anyon colliders, where coupling different edge channels through a quantum point contact enables the observation of two-particle interference effects. Such configurations are instrumental in deducing the anyonic exchange phase via current cross-correlations. Prior theoretical models represented dilute anyon beams as discrete steps in the boson fields. However, our study reveals that incorporating the finite width of the soliton shape is crucial for accurately interpreting recent experiments, especially for collider experiments involving anyons with exchange phases θ>π/2, where prior theories fall short.

Twisted partially coherent solitons in strongly nonlocal nonlinear media

The analytical propagation formulae of twisted partially coherent beams in strongly nonlocal nonlinear media (SNNM) are derived. It is shown that a twisted partially coherent soliton (TPCS) can be formed in SNNM when the critical power arrives. The analytical expressions of the characteristic parameters of TPCSs are also derived, e.g., the critical power, soliton width, soliton coherence width, and soliton twist parameter. It is found that the characteristics of TPCSs can be manipulated by the twist parameter. In particular, a TPCS may convert to a soliton without twist when the critical coherence width arrives.

Dark solitons in liquid crystals with competing re-orientational and thermal nonlocal nonlinearities

The properties of dark solitons in liquid crystals with competing nonlinearities are investigated by the model proposed by Jung. Under the condition of the rectangular response function, the relationship between the width of the dark soliton and the parameters of the medium is obtained by the variational method. It is found that the width of the dark solitons first decreases and then increases with the increment of the orientational nonlocality, the width of the soliton increases monotonously with the increase of the thermal nonlocality, and the width of the soliton decreases monotonously with the increase of the thermal nonlinearity coefficient. It is also found that the width of dark solitons is more sensitive to the orientational nonlocality than the other parameters. In addition, the width of the soliton increases monotonously with the grayness of the solitons. The analytical results are consistent with the numerical simulations that are obtained by the split-step Fourier algorithm.

Shortcuts to adiabatic soliton compression in active nonlinear Kerr media.

We implement variational shortcuts to adiabaticity for optical pulse compression in an active nonlinear Kerr medium with distributed amplification and spatially varying dispersion and nonlinearity. Starting with the hyperbolic secant ansatz, we employ a variational approximation to systematically derive dynamical equations, establishing analytical relationships linking the amplitude, width, and chirp of the pulse. Through the inverse engineering approach, we manipulate the distributed gain/loss, nonlinearity and dispersion profiles to efficiently compress the optical pulse over a reduced distance with high fidelity. In addition, we explore the dynamical stability of the system to illustrate the advantage of our protocol over conventional adiabatic approaches. Finally, we analyze the impact of tailored higher-order dispersion on soliton self-compression and derive physical constraints on the final soliton width for the complementary case of soliton expansion. The broader implications of our findings extend beyond optical systems, encompassing areas such as cold-atom and magnetic systems highlighting the versatility and relevance of our approach in various physical contexts.

Intensity variability in stationary solutions of the Fractional Nonlinear Schrödinger Equation

Solitons that propagate in optical fiber with indexes of refraction, dispersion, and diffraction are balanced, making pulses or electromagnetic waves propagate without any distortion. This is closely related to use of nonlinear refractive index in fiber optics. If an optical fiber only uses a nonlinear refractive index, then the partial signal can be lost over time. This study aims to analyze the variability of stationary solutions in multi-solitons formed using Fractional Nonlinear Schrödinger (FNLS). The parameter p indicates energy level of the solution to FNLS equation which has a positive integer value. This study focuses on 3 variations of p values, namely p = 0 which indicates the ground state, p = 1 which indicates the first excited state, and p = 2 which indicates the second excited state. During the first to second excited state, multi soliton peaks are formed with the same amplitude symmetrically. The amplitude experienced by the middle soliton in second excited state is lower which indicates the input signal obtained from the FNLS solution in the ground state in the form of triple-soliton. The polarization mode cause the soliton pulse width to shrink and the consequent amplitude in the first excited state to increase.

Nonlinear dynamics of large-amplitude, small-scale Alfvén waves

We study large-amplitude, very oblique Alfvén waves at low β, with small gradient length scales, comparable to the ion inertial scale di. Such waves have large density fluctuations and slight dispersion from finite-frequency and finite-ion sound radius effects. We derive a weakly nonlinear evolution equation governing the behavior of the waves in one dimension and categorize the different solitons appearing in different regimes: the regular solitons involve full rotations of the transverse magnetic field similar to modified Korteweg–de Vries (mKdV) solitons (our nonlinear equation reduces to the mKdV equation in the long-wavelength limit). However, for sufficiently small soliton widths, some become singular, small-amplitude solitons with density discontinuities and, are, thus expected to become strongly dissipative in a real plasma. These solutions may be useful in explaining some aspects of the sharp, ion-scale magnetic field rotations (switchbacks) observed in the near-Sun solar wind by Parker Solar Probe.

Superposition of modulated nonlinear waves in inhomogeneous systems with negative coherent coupling

The superimposed wave solutions of the variable coefficient nonlinear Schrödinger equations with negative coherent coupling are derived under a more relaxed constraint condition than those in previous literatures. For the benefit of the more relaxed constraint, the dispersion, nonlinearity, and gain/loss can be designed freely, and the obtained solutions can describe the nonlinear waves in general inhomogeneous optical fiber systems. The obtained solutions with two free phase parameters can be deemed to be the superposition of the typical simple modulated solutions, and the arbitrary of the optical parameters and the free phase parameters be expected to give the rise of abundant forms of modulation functions, that leads to the diverse characteristics of superimposed waves. Take the kink dispersion fiber systems with constant gain/loss and trigonometric gain/loss as examples, rich dynamics of the superimposed waves are displayed. By changing the gain/loss, the physical features of superimposed waves, such as the amplitudes of solitons and Kuznetsov-Ma breathers, the widths of solitons, the distances between Kuznetsov-Ma breathers, and the backgrounds of Akhmediev breathers and rogue waves can be controlled. The interaction of solitons or Kuznetsov-Ma breathers, and the number of the rogue waves or Akhmediev breathers can also be manipulated by selecting appropriate value of gain/loss. The results presented here may be useful to explore the diverse dynamics of superimposed waves and prove significance for the control of nonlinear waves in weakly birefringent fibers.

Dispersive optical solitons with DWDM topology and multiplicative white noise

The primary objective of this research is to investigate and analyze the intricate dynamics exhibited by dispersive optical soliton solutions within dispersion-flattened fibers while considering the impact of white noise. By examining this phenomenon, the study aims to gain a comprehensive understanding of the behavior and characteristics of these solitons, which are essential in the field of optical communication. A wide range of soliton solutions is obtained by the extended auxiliary equation procedure and the unified Riccati equation scheme, which are two powerful methods employed in the field of nonlinear dynamics and soliton theory to obtain a diverse array of soliton solutions. These techniques enable researchers to explore and analyze a wide range of complex nonlinear phenomena in various physical systems. This wide range of soliton solutions contributes to a deeper understanding of nonlinear phenomena and provides valuable insights into the fundamental properties and applications of solitons in different areas of science and engineering, including optics, fluid dynamics, plasma physics, and condensed matter physics. White noise only affects the phase part of the solitons and does not spread to other components. Such conclusions are applicable only under the specific transformation and the special simplification employed in deriving the solutions in the paper. The existence of white noise does not change the soliton amplitudes, widths, or velocities in any component. This paper is the first to report an essential observation concerning dispersion-flattened fibers, which has never been reported before.

Behavior of ion acoustic solitons in a two-electron temperature plasma of a multi-pole line cusp plasma device (MPD)

This article presents the experimental observations and characterization of ion acoustic solitons (IASs) in a unique multi-pole line cusp plasma device (MPD), in which the magnitude of the pole-cusp magnetic field can be varied. In addition, by varying the magnitude of the pole-cusp magnetic field, the proportion of the two-electron-temperature components in the filament-produced plasmas of the MPD can be varied. The solitons are experimentally characterized by measuring their amplitude-width relation and Mach numbers. The nature of the solitons is further established by making two counter-propagating solitons interact with each other. Later, the effect of the two-temperature electron population on soliton amplitude and width is studied by varying the magnitude of the pole cusp-magnetic field. It has been observed that different proportions of two-electron-temperature significantly influence the propagation of IASs. The amplitude of the solitons has been found to be inversely proportional to the effective electron temperature (Teff).

Quantum decay of an optical soliton

Optical solitons are known to be classically stable objects which are robust to perturbations. In this work, we show that due to quantum mechanical effects, an optical soliton that is initially in a classical soliton coherent state will shed photons into the continuum and hence decay. The standard formulation of the quantized soliton uses the linearized version of the quantum nonlinear Schrodinger equation in the background of the classical soliton, and the quantized soliton remains stable in this approximation. We show that if higher-order interaction terms are taken into account, the soliton is no longer stable, and its photon number decreases quadratically as a function of the number of soliton cycles. We compute the power spectrum for the continuum radiation and find a narrow band that is localized about the initial soliton momentum with a cut-off that is inversely proportional to the initial soliton width.

Temporal behavior of bright and dark spatial solitons in photorefractive crystals having both the linear and quadratic electro-optic effects based on low amplitude approximations

We investigate the formation or time evolution characteristics of bright and dark optical spatial solitons in novel photorefractive media with linear and quadratic electro-optic effects. This study was carried out at low amplitude. By the application of low amplitude approximation to the time-dependent wave (soliton) propagation equation, bright soliton solution (BSS) and dark soliton solution (DSS) were each obtained analytically, and both are exact solutions. The change in soliton width or the intensity full width at half maximum (FWHM) of two soliton types can also be calculated directly from the BSS and the DSS, providing a suitable description of the bright and dark solitons time evolution in novel photorefractive media. Only steady state solitons are formed in low amplitude, and the quasi-steady state soliton does not exist as reported at high saturation values. We compare analytical BSS with numerical calculation results of previous studies and find good agreement between analytics and numerics on the amplitude limit. In contrast to bright solitons, which can arise in the dominant linear or quadratic electro-optic effect, dark solitons in novel photorefractive media always exist under the dominant quadratic electro-optic effects only. We found that the time evolution of dark solitons from the DSS corresponds with time-independent optical spatial solitons studies in a similar media. Lastly, BSS and DSS found at low amplitude limits are fundamental soliton solutions or initial state soliton (at low peak intensity ratio regime) that can play an important role in further investigations of optical spatial solitons formation in novel photorefractive media.

Nonlinear Dynamics of Ion-Acoustic Waves in a Magnetized Plasma With Trapped Electrons

The dynamics of obliquely propagating ion-acoustic waves (IAWs) in a collisionless, magnetized plasma consisting of free and trapped electrons, having a vortex-like distribution and fluid ions immersed in an external static magnetic field, has been investigated. The reductive perturbation technique (RPT) has been used to derive a Schamel’s modified Laedke–Spatschek (S–LS) equation. Several nonlinear structures have been obtained, like solitary waves, periodic and quasi-periodic oscillations, as well as chaotic structures. The effects of the magnetic field strength, the wave propagation obliqueness, the Mach number, and the electrons trapping on these nonlinear structures have been explored. The increase in the magnetic field strength has been found to reduce the soliton width and enhance its amplitude, while the role of rising the trapping parameter is only to increase the solitary wave amplitude. For a relatively weak magnetic field, the increase in the Mach number may change the solitonic structure to a periodic oscillation and the latter to a quasi-periodic one, while the decrease in the propagation angle to the magnetic field direction may bring about the second transition (periodic <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\rightarrow$</tex-math> </inline-formula> quasi-periodic). Furthermore, depending on the plasma parameters, the intensification of the magnetic field can lead to the transition from a quasi-periodic to a chaotic behavior of the electrostatic wave.

Dissipative Kawahara ion-acoustic solitary and cnoidal waves in a degenerate magnetorotating plasma

The two-dimensional fluid quantum hydrodynamic (QHD) is adopted as the basis for a discussion of the effects of Landau quantization magnetic field, the Coriolis force, and collisional frequency on the (non)linear properties of the dissipative ion-acoustic waves (IAWs). By employing the reductive perturbation technique (RPT), the damped Korteweg–de Vries (KdV) equation which contains the lowest perturbation order actions is derived. It was found that with an increase in amplitude, the soliton width and the velocity diverge from the prediction of the damped KdV equation as observed in some laboratory experiments, i.e. the damped KdV approximation becomes invalid to describe the system. Therefore, it is necessary to investigate the effect of higher-order which leads to the damped Kawahara equation. This equation is a completely non-integrable differential equation. Thus, a new approximate solution which is called a semi-analytical solution is derived in detail. The obtained results can help in understanding the features of quantum IAWs in dense and slowly rotating astrophysical plasmas and maybe understand the quantum Hall effect of novel materials like graphene and topological insulators.