Instability Gain Research Articles

Role of Higher-Order Scattering Coefficient and Residual Nonlinearities on Instability Criteria in Three-Body Bose-Einstein Condensates

We examine the instability characteristics in a three-body condensate and the effect of higher-order nonlinear effects caused by shape-dependent imprisonment and higher-order scattering coefficients such as S-wave scattering length and effective range for collisions. Using the linear stability technique, we study the spreading relations and gain profile of the adapted Gross Pitaevski equation with higher-order scattering coefficients and enduring nonlinearity. The role of higher-order interactions S-wave scattering length, residual nonlinearity, and effective range for collisions over the modulational instability in immiscible and miscible three-body Bose-Einstein condensates has been discussed in detail. MI can be excited in miscible condensates and changed in immiscible condensates because of residual nonlinearity, without taking into account higher-order nonlinearity and three-body condensates. However, the results of this work demonstrate that the influence of higher-order residual nonlinearity can cause the MI to change in both immiscible and immiscible condensates. The discovered MI spectrum reveals a new soliton production regime in three-body condensates. The results exhibit that higher-order scattering coefficient and remaining nonlinearity interplay can successfully switch the instability gain profile in miscible and immiscible condensates. This makes it possible to regulate the dynamics by varying the MI in a ternary combination of Bose-Einstein condensates.

Exploration on modulation instability in 𝒫𝒯-symmetric non-Kerr Bragg grating structures

In this paper, we study Modulation Instability (MI) and its correlated gain spectrum with Parity-Time ([Formula: see text])-symmetry. The cubic-quintic nonlinearities in the Bragg grating structure produce ultrashort pulses. The MI evaluation started with a linear stability approach, and we investigated the effects of various system functions regarding the instability gain spectra at the top and bottom sides of the Photonic BandGap (PBG), in addition to the anomalous and normal dispersion domains. The interaction of cubic and quintic (focusing and de-focusing) nonlinearity is highlighted, resulting in a new type of MI band. Due to the consequences of quintic nonlinearity, an additional MI band appears for the three dynamics associated with the gain/loss function for the edges of the bottom PBG. After enforcing the [Formula: see text]-symmetry for the anomalous dispersion system, the dent transformed into a split under the influence of the power in the de-focusing quintic effect. Overall, MI gain and bandwidths across the entire MI gain spectrum are usually increasing. As an outcome, we are confident that these studies will aid in the generation of gap solitons in [Formula: see text]-symmetry regimes.

Analytical formulas of coherent-synchrotron-radiation induced microbunching gain and emittance growth in an arbitrary achromatic four-bend chicane

The coherent synchrotron radiations (CSR) emitted by a high-brightness electron beam during transport in a bending magnet is a double-edged sword in electron accelerators. While CSR contributes to a stronger radiation field than the incoherent radiation, it simultaneously leads to degradation of the electron beam quality. Specifically, CSR effects manifest in increases of the beam energy spread and the projected emittance, and amplification of the microbunching instability. A dedicated design of the multi-bend transport lines to mitigate CSR effects has recently become a crucial consideration in modern high-brightness electron accelerators. This paper presents analytical formulas for the CSR-induced microbunching instability gain and for the induced emittance growth in an arbitrary achromatic four-bend chicane with inclusion of both the steady-state and transient CSR effects. For the microbunching instability, an iterative method is employed to solve the integral equation for the bunching factor, providing satisfactory gain formulas. Regarding the CSR-induced emittance growth, based on the linear transfer matrices and incorporating the expressions of the CSR-induced energy spread, analytical formulas are derived for the projected emittance growth in an arbitrary four-bend transport section. The analytical formulas are compared and show good agreement with semi-analytical Vlasov calculations and particle tracking simulations. As an application, the obtained analytical formulas are applied to evaluate the CSR effects in the design of a general achromatic four-bend bunch compressor chicane, providing a quick estimate on the microbunching gain and the induced emittance growth. From the widely adopted symmetric C-shape chicane to a non-symmetric S-shape chicane, a design recently proposed by the co-authors, our analytical formulas offer insight into the evolution of the microbunching gain and the emittance growth with the variations of design parameters. In comparison to the time-consuming, full numerical particle tracking simulations currently employed for CSR effect analyses, the analytical formulas presented in this paper significantly reduce the evaluation time, enabling systematic study of parametric dependencies and comprehensive optimization with inclusion of CSR effects within specified design parameter ranges.

Mitigation of the microbunching instability through transverse Landau damping

The microbunching instability has been a long-standing issue for high-brightness free-electron lasers (FELs) and is a significant showstopper to achieve full longitudinal coherence in the x-ray regime. This paper reports the first experimental demonstration of microbunching instability mitigation through transverse Landau damping, based on linear optics control in a dispersive region. Analytical predictions for the microbunching content are supported by numerical calculations of the instability gain. The effect is confirmed through the experimental characterization of the spectral brightness of the FERMI FEL under different transverse optics configurations of the transfer line between the linear accelerator and the FEL. Published by the American Physical Society 2024

Dynamic interplay: unveiling inelastic breather collisions and modulation instability enhancement in a periodically gained inhomogeneous fiber optic communication system across temporal frequencies

Examining the impact of inhomogeneity on the propagation of femtosecond ultrafast optical pulses in fiber, we delve into the realm of the modified Hirota nonlinear Schrödinger equation (NLS) with inhomogeneity of variable coefficients (MIH-vc). Employing the Hirota bilinear method, we derive two soliton solutions for the modified Hirota NLS equation and analyze the effect of variable coefficients. The dynamical properties of these soliton solutions come to light as we meticulously analyze the corresponding plots. In our exploration, a noteworthy revelation unfolds as we witness the inelastic collision between two breathers, unleashing profound changes in the trajectory of femtosecond pulses. Furthermore, we showcase a detailed modulation instability analysis, unraveling the gain spectrum for our theoretical model. Through graphical illustrations, we elucidate how inhomogeneous functions intricately shape the modulation instability (MI) gain spectrum. A groundbreaking observation surfaces as, for the first time, we discern the periodic gain enhancement in relation to Group Velocity Dispersion along the fiber and its dynamic interactions.

Novel exact solutions to the perturbed Gerdjikov–Ivanov equation

This paper introduces the Nucci reduction method, a novel and efficient approach for deriving exact solutions to the perturbed Gerdjikov–Ivanov equation, offering a significant advancement in the field. The suggested technique involves transforming the equation into real and imaginary components prior to application. We successfully obtained four distinct exact and explicit solutions, along with the corresponding first integrals. Explanations and presentations of solutions are given in a logical manner. We derive an analytical expression for the instability gain and examine its key features using linear stability analysis. Finally, we compare the correctness of the analytical and numerical solutions. We demonstrate the robustness and stability of solitary waves through numerical simulations.

Some optical solitons and modulation instability analysis of (3 + 1)-dimensional nonlinear Schrödinger and coupled nonlinear Helmholtz equations

In this study, we acquired some optical solitons of (3 + 1) dimensional nonlinear Schrödinger equation (3DNLSE) and coupled nonlinear Helmholtz equations (CNLHE) by using generalized G′G\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\left(\\frac{{G}^{\\prime}}{G}\\right)$$\\end{document}-expansion method (GEM). We are able to derive exponential, trigonometric, and hyperbolic solutions. We notice that Mathematica 11.2 offer the equations for these answers. Aside from that, we display some of the solution’s graphic performance. Recently, accurate traveling-wave solutions for nonlinear partial differential equations (NLPDEs) have been acquired using this technique. Through linear stability analysis, we derive an analytical expression for the instability gain and analyze its main characteristics. Finally, we assess the robustness and stability of the solitary waves through numerical simulations and compare the accuracy of the analytical and numerical results. The obtained ultra-short optical solitons can be widely used as a guide for practical applications in telecommunications domain.

Propagation of solitary wave solutions to (4+1)-dimensional Davey–Stewartson–Kadomtsev–Petviashvili equation arise in mathematical physics and stability analysis

This innovative study simulates the (4+1)-dimensional Davey–Stewartson–Kadomtsev–Petviashvili (DSKP) equation, which has anomalous applications in the field of mathematical physics. The current research has two basic pillars. Firstly, numerous novel soliton solutions are synthesised in distinct formats, such as dark, bright, periodic, combo, W-shape, mixed trigonometric, exponential, and rational, based on the modified sardar sub-equation (MSSE) method and the improved F-expansion method. Secondly, the stability analysis of the selected model is manifested to study modulation instability (MI) gain. Furthermore, for the physical demonstration of the acquired solutions in 3D and 2D, contour and density plots are depicted. The discovered results have a distinctive feature that has not been developed before and indicate a good balance between the nonlinear physical components. Also, the resulting structure of the acquired results can enrich the nonlinear dynamical behaviours of the given system and may be useful in many domains, such as mathematical physics and fluid dynamics, as well as demonstrate that the approaches used are effective and worthy of validation.

Spatiotemporal dynamics of modulation instability in Kerr nonlinear media with pure-quartic dispersion

We present the analytical and numerical analysis on spatiotemporal dynamics of modulation instability (MI) in Kerr nonlinear media with pure-quartic dispersion. We apply a linear stability method to arrive at a universal expression for pure-quartic instability gain, which can simultaneously describe the temporal, spatial, and spatiotemporal cases. The results show that the condition of such three fundamental instability occurrence in pure-quartic dispersion media (PDM) is the same as that in conventional quadratic dispersion media (QDM). Another interesting observation is that the maximum gain is also the same in both cases. For temporal instability, there exists a critical power below which the instability bandwidth becomes wider than the corresponding case in QDM or otherwise. For spatiotemporal instability, the instability region depending on critical frequencies is found to show some remarkable difference when compared with the latter case. The analytical prediction resulting from linear stability analysis is confirmed by the numerical method.

Transmission across a ribbon containing a square [formula omitted] impurity

We study the spectrum and transmission coefficient of plane waves propagating along square ribbons of varying widths, containing a square-shaped, PT-symmetric impurity region. We start with a zero-width ribbon (1D chain) and place a PT symmetric dimer. The spectrum is computed numerically and the instability gain is computed as a function of the gain/loss dimer strength. The transmission coefficient is obtained in closed form and examined as a function of wavevector and the gain/loss parameter. Next, we study a ribbon in a narrow ladder configuration containing a square PT impurity. As before, we compute the instability gain numerically and the transmission coefficient in closed form for the two possible input modes. Finally, we repeat the calculations for a wider ladder ribbon containing a Lieb-like impurity in a PT configuration. For all cases and transmission channels, we obtain transmission divergences in wavevector-gain/loss parameter space, whose number increases with the width of the ribbon.

Impact of viscothermal loss on modulation instability and rogue waves in left-handed nonlinear diffractive acoustic transmission line metamaterials

In this study, the transmission line approach is used to describe the studied acoustic metamaterial model. Through Kirchoff’s pressure and volume-velocity laws and using multiple scales method, nonlinear coupled Schrödinger equations are obtained. Then, the amplitude disturbance method is applied to these equations to obtain and plot the modulational instability gain curves. Analytically, the impact of viscothermal loss on the modulational instability gain is studied. The similarity technique is used to derive integrable Manakov’s equations. First and second-order rational rogue wavelike solutions of coupled nonlinear Schrödinger are deduced. The results indicate that the modulational instability gain and Rogue wave intensities depend on the viscothermal parameter. This parameter can be considered in the design of nonlinear acoustic metamaterials to minimize the damage caused by the dynamics of freak waves.

Solitonic rogue waves induced by the modulation instability in a split-ring-resonator-based left-handed coplanar waveguide

Modulation instability and nonlinear excitation modes in lower and upper frequency bands are investigated in the nonlinear left-handed coplanar waveguide, where nonlinear capacitance (voltage-dependent) is used. The multi-scale method is employed to derive a system of two coupled nonlinear Schödinger equations governing the evolution of the kink and bright solitons of these modes. A modulation instability is investigated to show the effects of the left-handed and right-handed influences on the modulation instability gain and the intensity of the plane wave. In the lower and upper frequency modes, the breathing structures have strong values for the left-handed component. At the end, the numerical simulation of the continuous wave is used to show the development of the modulated waves and localized objects. Another relevant localized structure has been obtained to display the second-order breathers and Akhmediev breathers of types A and B under the variation of the perturbed wave number. Both linear inductances and perturbed wave numbers are tools for controlling the amplitude of the localized structures, and modulation instability is sensitive to these parameters.

Effects of coupling coefficient dispersion on the Fermi-Pasta-Ulam-Tsingou recurrence in two-core optical fibers

In a two-core optical fiber (TCF), the linear coupling coefficient between the two cores in general varies with the optical wavelength, a phenomenon known as coupling coefficient dispersion (CCD). Here we study the effects of CCD on the Fermi-Pasta-Ulam-Tsingou recurrence (FPUT) phenomena in a TCF. Modulation instability tends to be a precursor in the formation of breathers. The subsequent decay of breathers and re-emergence of modulation instability lead to FPUT type periodic patterns. For the symmetric or antisymmetric continuous-wave (CW) state of a TCF, CCD does not affect the modulation instability gain spectra. However, if asymmetric perturbations are applied to a symmetric CW state, CCD can drastically modify FPUT. In the anomalous dispersion regime, without CCD, only FPUT dynamics without energy transfer between the two cores occurs. With CCD effects, FPUT dynamics with strong energy transfer between the two cores can arise. As CCD increases, FPUT dynamics without energy transfer never vanishes, but the corresponding number of FPUT cycles can be drastically reduced to only one. In the normal dispersion regime, no FPUT dynamics with energy transfer between the two cores occurs. The major CCD effect is to significantly decrease the FPUT cycles, and only one FPUT cycle can be observed at relatively large magnitude of CCD values. As the magnitude of CCD increases further, more FPUT cycles arise again. Moreover, larger CCD will lead to higher (lower) propagation speed of the wave patterns in the anomalous (normal) dispersion regime respectively. To enhance theoretical insight, we perform a Floquet analysis for the linearized stability equations with periodic coefficients based on the FPUT dynamics in the normal dispersion regime. The monodromy matrix and eigenvalues can be computed explicitly. Larger eigenvalues correlate with stronger instability and more rapid disintegration of the periodic patterns, agreeing well with the trends of the numerical simulations.

High-repetition-rate pulse generation via self-sustaining cross-gain modulation in a semiconductor-based laser.

We present a simple and efficient method for generating regular pulse trains with GHz pulse repetition rates in lasers based on semiconductor optical amplifiers (SOAs). This method enables pulse formation without active modulation or saturable absorption of the generated radiation. The method relies upon the self-sustaining cross-gain modulation which is achieved by adding the negative optical feedback (NOF) to a ring laser configuration. The resulting modulation of laser gain is shown to be restricted to the frequencies which match both the spacing of longitudinal laser modes and the highest peaks in the NOF-induced instability gain spectrum. This enables the reproducible stationary pulse generation at the strictly defined repetition rates. The feasibility of the method was confirmed by the stable generation of sub-nanosecond pulses at repetition rates up to 1.79 GHz in a SOA-based laser with a simple fiber cavity.

Tunable modulation instability spectra in negative index materials

This paper investigates the formation of tunable modulation instability windows in metamaterials. We consider the influence of third-order dispersion, fourth-order dispersion, cubic nonlinearity, quintic nonlinearity, detuning parameter, self-steepening and higher-order nonlinear dispersions on the gain spectrum in addition to the basic requirement to observe modulation instability such as group velocity dispersion and self-phase modulation. As the metamaterials provide engineering freedom, all the material parameters are tunable, which leads to tunable modulation instability gain spectrum formation. This tunable gain spectrum provides additional ways to form solitons and ultrashort pulses with desired parameters.

Analysis of lump solutions and modulation instability to fractional complex Ginzburg–Landau equation arise in optical fibers

In this paper, the fractional complex Ginzburg–Landau equation (CGLE) with Kerr law in nonlinear optics, which simulates soliton propagation in various waveguides in the presence of a detuning component which comes from the nonlinear Schrödinger equation (NLSE) with the inclusion of the growth and damping terms, is examined. The Hirota bilinear method is exercised to retrieve lump solitons such as the 1-kink wave solution, 2-kink wave solution, double exponential wave solution, and homoclinic breather wave solution to the model. We also scrutinize some M-shaped solutions in the forms of M-shaped rational solutions and the M-shaped interaction with rogue and kink waves. In addition, the instability modulation and gain spectra of the CGLE are examined. The originality of the study lies in the secured outcomes, which were never before produced and effectively balance the nonlinear physical aspects. To illustrate the dynamic of these waves, some of the solutions are sketched in three-dimensional, two-dimensional, contour, and density plots. The produced results are encouraging which can be used to describe the phenomena occurring in nonlinear optical or plasma physics. The computed solutions demonstrate that the suggested approaches are skillful, categorical, consistent, and effective in identifying exact solutions to a variety of complicated nonlinear problems that have recently arisen in nonlinear optics, applied sciences, and engineering.

Effect of spin on the instability of THz plasma waves in field-effect transistors under non-ideal boundary conditions

Terahertz (THz) radiation can be generated due to the instability of THz plasma waves in field-effect transistors (FETs). In this work, we discuss the instability of THz plasma waves in the channel of FETs with spin and quantum effects under non-ideal boundary conditions. We obtain a linear dispersion relation by using the hydrodynamic equation, Maxwell equation and spin equation. The influence of source capacitance, drain capacitance, spin effects, quantum effects and channel width on the instability of THz plasma waves under the non-ideal boundary conditions is investigated in great detail. The results of numerical simulation show that the THz plasma wave is unstable when the drain capacitance is smaller than the source capacitance; the oscillation frequency with asymmetric boundary conditions is smaller than that under non-ideal boundary conditions; the instability gain of THz plasma waves becomes lower under non-ideal boundary conditions. This finding provides a new idea for finding efficient THz radiation sources and opens up a new mechanism for the development of THz technology.

Modulated wave patterns brought by higher-order dispersion and cubic–quintic nonlinearity in monoatomic chains with anharmonic potential

This work investigates the modulation instability and wave patterns in the extended nonlinear Schrödinger equation with higher-order dispersion and cubic–quintic nonlinearity. We use the one-dimensional monoatomic chain with anharmonic potential to derive the discrete model. From the multiple scale method combined with a quasidiscreteness approximation, we derive the cubic–quintic nonlinear schrödinger equation, and thereafter an expression of the modulation instability gain is obtained by using a linearized expression. One notices that the modulation instability growth is sensitive to the higher-order dispersion and nonlinearities terms. A split-step Fourier method is used to assess the analytical predictions. A long evolution of the continuous wave is shown to lead to the formation of the bright soliton, and Akhemediev breathers also emerge to manifest the modulation instability. We have also demonstrated that the excitation wave number generates the train of waves to confirm the fact that the continuous wave can grow exponentially with any value of the latter. We mention equally that the model of the extended cubic–quintic nonlinearity with complex envelope has opened new features of the modulated wave patterns in monoatomic chains.

Translation of obstructive sleep apnea pathophysiology and phenotypes to personalized treatment: a narrative review.

Obstructive Sleep Apnea (OSA) arises due to periodic blockage of the upper airway (UA) during sleep, as negative pressure generated during inspiration overcomes the force exerted by the UA dilator muscles to maintain patency. This imbalance is primarily seen in individuals with a narrowed UA, attributable to factors such as inherent craniofacial anatomy, neck fat accumulation, and rostral fluid shifts in the supine posture. Sleep-induced attenuation of UA dilating muscle responsiveness, respiratory instability, and high loop gain further exacerbate UA obstruction. The widespread comorbidity profile of OSA, encompassing cardiovascular, metabolic, and neuropsychiatric domains, suggests complex bidirectional relationships with conditions like heart failure, stroke, and metabolic syndrome. Recent advances have delineated distinct OSA phenotypes beyond mere obstruction frequency, showing links with specific symptomatic manifestations. It is vital to bridge the gap between measurable patient characteristics, phenotypes, and underlying pathophysiological traits to enhance our understanding of OSA and its interplay with related outcomes. This knowledge could stimulate the development of tailored therapies targeting specific phenotypic and pathophysiological endotypes. This review aims to elucidate the multifaceted pathophysiology of OSA, focusing on the relationships between UA anatomy, functional traits, clinical manifestations, and comorbidities. The ultimate objective is to pave the way for a more personalized treatment paradigm in OSA, offering alternatives to continuous positive airway pressure therapy for selected patients and thereby optimizing treatment efficacy and adherence. There is an urgent need for personalized treatment strategies in the ever-evolving field of sleep medicine, as we progress from a 'one-size-fits-all' to a 'tailored-therapy' approach.

Effects of the higher-order dispersion on solitary waves and modulation instability in a monomode fiber

In this paper, we investigate the modulation instability and the dynamics of solitary waves in a higher-order nonlinear Schrödinger equation. We use a powerful and robust method known as the modified sub-equation method to secure the solitary waves and other numerous solutions to this nonlinear model. Several constraint conditions that guarantee the existence of these solutions are highlighted. Utilizing a linearizing technique, we establish the modulation instability gain. The influence of the higher nonlinear component on the modulation instability is also discussed. Furthermore, we perform the numerical simulations of this model by using the split-step Fourier method. Finally, several solutions are shown in two and three dimensions to better explain the behavior of the considered model. The two-dimensional plots depict Peregrine soliton under the influence of the nonlinear dispersion term. These graphs are useful for understanding the dynamic properties of the obtained results.