Stability Zone Research Articles

Influence of disk aberrations on high-power thin-disk laser cavities.

We present a systematic study on the influence of thin-disk aberrations on the performance of thin-disk laser oscillators. To evaluate these effects, we have developed a spatially resolved numerical model supporting arbitrary phase profiles on the intracavity components that estimates the intracavity beam shape and the output power of thin-disk laser oscillators. By combining this model with the experimentally determined phase profile of the thin-disk (measured with interferometry), we can predict the operation mode of high-power thin-disk lasers, including mode degradation, higher-order mode coupling, and stability zone shrinking, all of which are in good agreement with experiment. Our results show that one of the main mechanisms limiting the performance is the small deviation of the disk's phase profile from perfect radial symmetry. This result is an important step to scaling modelocked thin-disk oscillators to the kW-level and will be important in the design of future active multi-pass cavity arrangements.

Monitoring Offshore CO2 Sequestration Using Marine CSEM Methods; Constraints Inferred from Field- and Laboratory-Based Gas Hydrate Studies

Offshore geological sequestration of CO2 offers a viable approach for reducing greenhouse gas emissions into the atmosphere. Strategies include injection of CO2 into the deep-ocean or ocean-floor sediments, whereby depending on pressure–temperature conditions, CO2 can be trapped physically, gravitationally, or converted to CO2 hydrate. Energy-driven research continues to also advance CO2-for-CH4 replacement strategies in the gas hydrate stability zone (GHSZ), producing methane for natural gas needs while sequestering CO2. In all cases, safe storage of CO2 requires reliable monitoring of the targeted CO2 injection sites and the integrity of the repository over time, including possible leakage. Electromagnetic technologies used for oil and gas exploration, sensitive to electrical conductivity, have long been considered an optimal monitoring method, as CO2, similar to hydrocarbons, typically exhibits lower conductivity than the surrounding medium. We apply 3D controlled-source electromagnetic (CSEM) forward modeling code to simulate an evolving CO2 reservoir in deep-ocean sediments, demonstrating sufficient sensitivity and resolution of CSEM data to detect reservoir changes even before sophisticated inversion of data. Laboratory measurements place further constraints on evaluating certain systems within the GHSZ; notably, CO2 hydrate is measurably weaker than methane hydrate, and >1 order of magnitude more conductive, properties that may affect site selection, stability, and modeling considerations.

The Mesoarchean plutonic complex from the Carajás province, Amazonian craton: Petrogenesis, zircon U[sbnd]Pb SHRIMP geochronology and tectonic implications

This study investigates the origin of the different Mesoarchean granitoids of the Ourilândia plutonic complex from the Carajás province (northern Brazil), as well as their geodynamic significance. This complex integrates interdigitated plutons of 2.88 Ga biotite granite (BG) and sanukitoid (SNK), with subordinate high-K calc-alkaline (HKCA) granodiorite-granite and tonalite-trondhjemite-granodiorite (TTG). (i) The BG is represented by equigranular monzogranite, which can be formed by 18% melting from TGG-type trondhjemite. (ii) The SNKs are composed of granodiorites (equigranular, heterogranular and porphyritic), with subordinate tonalite, quartz monzodiorite and quartz diorite, all with mafic microgranular enclaves. The different SNK-type granitoids and quartz monzodiorite were generated by 18–33% melting from mantle previously enriched by 20–40% TTG-type melt in the garnet stability zone. On the other hand, quartz diorite and mafic enclaves formed from fluid-metasomatized mantle at lower depths. (iii) The HKCA granodiorite-granite group (also called high-Ti SNK) is composed of porphyritic granodiorite and heterogranular monzogranite. The granodiorite can be formed by 30% melting from mantle enriched by 40% TTG-type melt under oxidizing conditions, with the participation of a component enriched in HFSEs. The heterogranular monzogranite is a hybridization product between 60% metasomatized mantle-derived magmas (high-Ti granodiorite) and 40% crust-derived magmas (equigranular monzogranite). (iv) The TTG-type tonalitic xenolith and porphyritic trondhjemite were formed by partial melting of hydrous metabasalts; however, the trondhjemite petrogenesis involves hybridization with enriched mantle-derived magmas. The BG and SNK provided coeval crystallization ages of 2881 ± 10 Ma and 2886 ± 14 Ma, respectively. In addition, in the BG, three more crystal populations were identified with ages of 3040 ± 40 Ma, 2976 ± 09 Ma and 2934 ± 21 Ma. The first two are interpreted as xenocrystals, and the latter is interpreted as inherited crystals. ∼2.88 Ga represents the main period of crustal growth in the Ourilândia do Norte area, with emplacement of juvenile magmas and crustal reworking. The studied rocks were formed in a post-subduction collision setting with coeval mantle and crust-derived magma generation over a short time span (∼2.88 Ga), where shear zones conditioned the ascent and emplacement of the Ourilândia magmas.

Energy-ecological assessment of the boiler equipment modernized with the jet-niche technology

The results devoted to the issues of energy-ecological assessment of industrial boiler equipment with jet-niche combustion technology are given in the paper. The basic principles underlying this technology include: rational distribution of fuel in the oxidant stream; stable adjustable structure of fuel, oxidant and combustion products; self-regulation of the fuel mixture composition in the zone of the torch stabilization when the unit load changes. As of today, a large number of industrial gas-burning equipment has been modernized by jet-niche technology, including: boilers, furnaces, dryers, metallurgical facilities, etc. The results of industrial implementation of the technology allowed to accumulate a significant amount of technical information and gave the possibility of preliminary environmental assessment during the modernization of gas combustion equipment. As practice shows, at the present stage the main direction of the technology improvement is to enhance its environmental performance. The influence of the main regime and technical parameters of fire equipment on its emission indicators is established in the paper. Possibilities for reducing nitrogen oxides by primary technological methods, the simplest and most effective of which is the introduction of recirculation gases into the furnace space, have been identified. According to the results of the analysis of emission indicators of the modernized fire equipment with a capacity of 0.5–60 MW, data to estimate the emission indicators of low and medium power boilers depending on the main influencing factors, namely, unit size, excess air ratio and boiler load were obtained. The influence of the introduction of recirculation gases into the furnace space on the level of nitrogen oxides concentration is also taken into account. The efficiency of application of the recirculation gases introduction scheme into the primary air flow in comparison with combustion technologies based on vortex burners is shown. According to the results of the industrial experiment, the energy efficiency of the proposed measures was established on the example of the dependences of efficiency on the load of boilers PTVM-50 and KVGM-20.

Neural net detection of seismic features related to gas hydrates and free gas accumulations on the northern U.S. Atlantic margin

Bottom-simulating reflections (BSRs) that sometimes mark the base of the gas hydrate stability zone in marine sediments are often identified based on the reverse polarity reflections that cut across stratigraphic layering in seismic amplitude data. On the northern U.S. Atlantic margin (USAM) between Cape Hatteras and Hudson Canyon, legacy seismic data have revealed pronounced BSRs south of the deepwater extension of Hudson Canyon and more subtle ones from offshore Delaware south to Cape Hatteras, where the reflections sometimes follow stratigraphic layering. Using high-resolution seismic data acquired during the 2018 Mid-Atlantic Resource Imaging Experiment and a supervised neural net, we identify seismic features associated with gas hydrates and/or the top of gas between Hudson Canyon and Cape Hatteras. Using seismic attributes especially sensitive to the presence of gas, we train a neural network algorithm on seismic data from an area with strong BSRs and then apply the model to the rest of the data set. The results indicate that gas hydrate and/or shallow free gas are significantly more widespread on the northern part of the USAM than previously known. Seismic indicators of gas extend landward from the 2000 m isobath to the upper continental slope in sectors with (offshore Virginia) and, to a lesser extent, without (offshore New Jersey) pervasive upper slope methane seeps. Higher sand content and intermediate sediment thickness, factors related to the container size and gas charge in a petroleum systems framework, are associated with more robust gas indicators.

Gas Sources, Migration, and Accumulation Systems: The Shallow Subsurface and Near-Seafloor Gas Hydrate Deposits

Compared with the deeply buried marine gas hydrate deposits, gas hydrates in the shallow subsurface, close to and at the seafloor, have attracted more attention owing to their concentrated distribution, high saturation, and easy access. They accumulate at relatively shallow depths <100–120 m and occur as gas hydrate-bearing mounds (also known as hydrate outcrops, pingoes) at the seafloor derived from the growth of hydrates in the shallow subsurface or as pure hydrate chunks formed by gas leakage. This paper reviews and summarizes such gas hydrate systems globally from the perspective of gas sources, migration pathways, and accumulation processes. Here, we divided them into four categories: fault-chimney-controlled, diapir-fault-controlled, fault-controlled, and submarine mud volcano-controlled deposits. Gas chimneys originate immediately above the restricted regions, mostly affected by faults where high gas concentrations trigger elevated pore fluid pressures. Diapirism derives a dendritic network of growth faults facilitating focused gas discharge and hydrate formation near the seafloor. Furthermore, pre-existing faults or fractures created by overpressured gas from greater depths in accretionary tectonics at convergent margins act as preferential pathways channeling free gas upwards to the seafloor. Gas flux rates decrease from the submarine mud volcano center to its margins, creating a concentric pattern of distributing temperature, gas concentrations, and hydrate contents in shallow sediments around the mud volcano. Hydrate-bound hydrocarbons are commonly of thermogenic origin and correspond to high-background geothermal conditions, whereas microbial gas is dominant in a few cases. The presence of heavier hydrocarbons mitigates the inhibition of hydrate formation by salt or heat. Fluid migration and pathways could be compared to the “blood” and “bones” in an organic system, respectively. The root of a pathway serves as the “heart” that gathers and provides considerable free gas concentrations in a restricted area, thereby triggering pore fluid pressures as one important drive force for focused fluid flow in impermeable sediments (the organic system). Besides the suitable temperature and pressure conditions, a prerequisite for the formation and stability of hydrate deposits in the shallow subsurface and at the seafloor is the sufficient supply of gas-rich fluids through the hydrate stability zone. Thus, the proportion of gas migrating from deep sources is significantly larger than that trapped in hydrates. As such, such marine hydrate deposits seem more like temporary carbon storage rather than the main culprit for climate warming at least in a short period.

Seismic evidence of gas hydrate and seafloor fluid escape on the upper Amazon deep-sea fan, Brazilian equatorial margin

The Amazon fan contains a gas hydrate province known from a bottom-simulating reflection (BSR) that lies within an upper slope compressional belt. In this study, the extent and character of the BSR and its relation to thrust-fold structures is examined using a grid of 2D and 3D seismic data. We show the BSR to comprise a series of elongate patches up to 16 km wide that are present along 300 km of the slope in water depths of 750-2250 m and extend over a total area of 6800 km2. The elongate BSR patches show a strong spatial correspondence with the arcuate crests of thrust-fold anticlines. In profile, the BSR patches exhibit convex forms and/or locally irregular relief that rises toward the seafloor. In plan, 3D seismic horizon maps reveal columnar BSR elevations up to 1 km wide, which rise beneath seafloor mounds and depressions, up to 0.5 km wide and 30 m in relief, interpreted as small mud volcanoes and possible pockmarks. The elongate BSR patches are interpreted to record the structurally-controlled rise of warm, gas-rich fluids into the crests of thrust-folds and their leakage into the gas hydrate stability zone, and in places to seafloor, through a near-surface system of faults, hydrofractures and vents.

Control System Development and Implementation of a CNC Laser Engraver for Environmental Use with Remote Imaging.

This article is aimed at studying the features of the control systems development for a small-sized Computer Numerical Control (CNC) portative laser engraver. The CNC is implemented in mobile maintenance and repair platforms for remote sensing of the environment where the wild environment may not allow us to access the animals and places. The proposed work in this paper is based on recent research, which shows that applying the automated CNC speeds up the processes of repair, modernizes the equipment size, and significantly reduces the economic costs; accordingly, the authors developed a block diagram of a portable CNC laser engraver. The choice of the hardware was also made, taking into account the possibility of quick replacement in the field, which reduces the repair time and the cost of the developed layout. A control system based on the selected modules was synthesized, and a stability check was carried out using MatLab tools. To check the correctness of the developed control system, the authors developed and assembled an experimental layout to illustrate the results of engraving on such a layout. Finally, the stability and sensitivity of the proposed system have been obtained and proved that the system works in a comfortable zone of stability. The obtained results show that the proposed CNC laser engraver has achieved the expected improvements (high speed, small size, short production and repairing time, minimum human influence factor, and achieving a better outcome).

Noise-induced formation of heterogeneous patterns in the Turing stability zones of diffusion systems

We study a phenomenon of stochastic generation of waveform patterns for reaction-diffusion systems in the Turing stability zone where the homogeneous equilibrium is a single attractor. In this analysis, we use a distributed variant of the Selkov glycolytic model with diffusion and random forcing. It is shown that in the Turing stability zone, random disturbances can induce a diversity of metastable spatial patterns with different waveforms. We carry out the parametric analysis of statistical characteristics of evolution of these patterns, and reveal the dominant patterns in the stochastic flow of mixed spatial structures.

Investigating geological storage of carbon dioxide in a gas hydrate reservoir of the Shenhu area, South China Sea

Deep-water shallow-buried sand layers above the base of methane hydrate stability zone (BMHSZ) have been recognized as favorable reservoirs for gas hydrate accumulation. Carbon dioxide (CO2) injection into the sand layers provides significant advantages over onshore geological storage options because of CO2 hydrate formation and high CO2 density under conditions of pressure and temperature. However, reservoir characterization and geological conditions for storing CO2 in gas-charged sand layers below the BMHSZ have not been well studied.We investigate deep-water shallow-buried strata in the Shenhu area by analyzing and interpreting 3D seismic and well logs data. We present the W07–W23 gas hydrate reservoir that consists of two Lower Pleistocene sand zones: gas hydrate and free gas accumulation within levee facies in the upper zone and free gas accumulation within channel facies in the lower zone. Analysis of well data shows a 51 m thick total gas section interbedded with gas hydrate and inferred gas hydrate saturation as high as 20% of sediment pore space. Average porosity in the reservoir is estimated from log data at approximately 50%. Permeability in the hydrate-free sediments, as inferred from empirical equations retrieved from the offset wells, ranges 3–5 mD. We estimate that a total of 13–40 × 109 m3 of gas could be contained within the two zones and they may store roughly 5.7–11.4 × 107 ton of CO2. These results provide an improved understanding of gas hydrate reservoirs for occurrence of gas hydrate, free gas accumulations and CO2 storage capability below the traditional BMHSZ.

On the solutions and stability for an auto-parametric dynamical system

The main goal of this study is to look at the motion of a damped two degrees-of-freedom (DOF) auto-parametric dynamical system. Lagrange’s equations are used to derive the governing equations of motion (EOM). Up to a good desired order, the approximate solutions are achieved utilizing the method of multiple scales (MMS). Two cases of resonance, namely; internal and primary external one are examined simultaneously to explore the solvability conditions of the motion and the corresponding modulation equations (ME). These equations are reduced to two algebraic equations, through the elimination of the modified phases, in terms of the detuning parameters and the amplitudes. The kind of stable or unstable fixed point is estimated. In certain plots, the time histories graphs of the achieved solutions, as well as the adjusted phases and amplitudes are used to depict the motion of the system at any instant. The conditions of Routh–Hurwitz are used to study the various stability zones and their analysis. The achieved outcomes are considered to be novel and original, in which the used strategy is applied on a particular dynamical system. The significance of the studied system can be observed in its applications in a number of disciplines, such as swaying structures and rotor dynamics.

The dynamical motion of a rolling cylinder and its stability analysis: analytical and numerical investigation

The present paper addresses the dynamical motion of two degrees-of-freedom (DOF) auto-parametric system consisting of a connected rolling cylinder with a damped spring. This motion has been considered under the action of an excitation force. Lagrange's equations from second kind are utilized to obtain the governing system of motion. The uniform approximate solutions of this system are acquired up to higher order of approximation using the technique of multiple scales in view of the abolition of emerging secular terms. All resonance cases are characterized, and the primary and internal resonances are examined simultaneously to set up the corresponding modulation equations and the solvability conditions. The time histories of the amplitudes, modified phases, and the obtained solutions are graphed to illustrate the system's motion at any given time. The nonlinear stability approach of Routh–Hurwitz is used to examine the stability of the system, and the different zones of stability and instability are drawn and discussed. The characteristics of the nonlinear amplitude for the modulation equations are investigated and described, as well as their stabilities. The gained results can be considered novel and original, where the methodology was applied to a specific dynamical system.

Saturation sensitivity and influencing factors of marine DC resistivity inversion to submarine gas hydrate

The submarine gas hydrate usually exists in the sediment on the continental slope. The bottom simulating reflector on the reflected seismic was identified as the bottom of the hydrate stability zone. However, many BSRs may not find the hydrate’s effective storage and its underlying free gas in many places. It is essential to identify the saturation of the hydrate. The resistivity can be used to evaluate the hydrate’s porosity and saturation. The hydrate boasts a high resistance to the surrounding sediments. The sensitivity of the marine Direct Current resistivity method (DCR) to the high resistance of the sediment can be used to evaluate the saturation of the hydrate. We have assessed the sensitivity of various DCR array arrangements, towed depths, hydrate thicknesses, and saturation. These influencing factors for improving recognition ability were also systematically analyzed. We have compared the inversion results of various DCR array arrangements, as well as different depths, thicknesses, and hydrate saturation, and calculated the saturation. We suggest using the corrected saturation equation to analyze the DCR results, which can improve the ability of hydrate identification. Evaluating these parameters will help develop or select DCR instruments for detecting the submarine gas hydrate.

Wall stabilization of the rigid ballooning m = 1 mode in a long-thin mirror trap

The prospect of stabilization of the m = 1 ‘rigid’ ballooning mode in an open axially symmetric long-thin trap with the help of a conducting lateral wall surrounding a column of isotropic plasma is studied. It was found that for effective wall stabilization, the beta parameter β must exceed some critical value β crit. The dependence of β crit on the mirror ratio, radial pressure profile, axial profile of the vacuum magnetic field, and the width of vacuum gap between plasma and lateral wall was studied. Minimal critical beta at the level of 70% is achieved at zero vacuum gap, although stability zone at β → 1 exists even at extremely wide vacuum gap. It is shown that when a conducting lateral wall is combined with conducting end plates simulating attachment of the end MHD stabilizers to the central cell of an open trap, there are two critical beta values and two stability zones that can merge, making stable the entire range of allowable beta values 0 < β < 1.

The stability of 3-DOF triple-rigid-body pendulum system near resonances

In this article, the motion of three degree-of-freedom (DOF) dynamical system consisting of a triple rigid body pendulum (TRBP) in the presence of three harmonically external moments is studied. In view of the generalized coordinates of the system, Lagrange's equations are used to obtain the governing system of equations of motion (EOM). The analytic approximate solutions are gained up to the third approximation utilizing the approach of multiple scales (AMS) as novel solutions. The solvability conditions are determined in accordance with the elimination of secular terms. Therefore, the arising various resonances cases have been categorized and the equations of modulation have been achieved. The temporal histories of the obtained approximate solutions, as well as the resonance curves, are visually displayed to reveal the positive effects of the various parameters on the dynamical motion. The numerical results of the governing system are achieved using the fourth-order Runge–Kutta method. The visually depicted comparison of asymptotic and numerical solutions demonstrates high accuracy of the employed perturbation approach. The criteria of Routh–Hurwitz are used to investigate the stability and instability zones, which are then analyzed in terms of steady-state solutions. The strength of this work stems from its uses in engineering vibrational control applications which carry the investigated system a huge amount of importance.

Human Settlement Resilience Zoning and Optimizing Strategies for River-Network Cities under Flood Risk Management Objectives: Taking Yueyang City as an Example

The dense river network and large population in the southern region of China are vulnerable to flooding stress, which challenges the construction of human settlements. This paper analyzes the causes of flood risk and the dilemma of human settlement improvement in river-network cities, introduces the principle of resilience to human settlements, and conducts a quantitative study on the resilience of human settlements in river-network cities with the goal of flood risk management. Taking Yueyang city, a river-network city in the Yangtze River Basin, as the empirical research object, we conduct a flood resilience zoning of the human settlements based on the flood risk assessment model and use the GIS spatial overlay method to correct the resilience of the current human living space against the territorial spatial planning of Yueyang city. Ultimately, we propose a strategy for optimizing human settlements under flood risk management. The results show that (1) the highest-risk and high-risk areas of Yueyang city were mainly located in Dongting Lake and its interconnected water system, the southwest local area and the southeastern fringe, while the low-risk and lowest-risk areas were mainly located in the northeast local area and the northwestern fringe, with low flood stress risk. (2) The spatial system of human settlement resilience was constructed based on the flood risk assessment level. Among them, the human settlement flood resilience zoning of Yueyang city was divided into five categories from low to high: human settlement control zone, restriction zone, buffer zone, construction zone and expansion zone; the flood resilience zoning of Yueyang city’s current living space was divided into three categories from low to high: structure adjustment zone, flood restriction zone and development stability zone. (3) The specific control implementation and execution of the human settlements in Yueyang city mainly focus on the interrelationship between the risk of flooding in the watershed and the development of human activities through zoning regulation and collaborative management to optimize the human settlements. The study results can provide positive intervention and guidance for constructing urban and rural territorial spatial prevention planning and improving human living quality in river-network cities in China.

The Potential to Preserve Relic Hydrates below the Stability Zone in Low-Permeability Layers of the Berezovo Formation of the North of Western Siberia

The Potential to Preserve Relic Hydrates below the Stability Zone in Low-Permeability Layers of the Berezovo Formation of the North of Western Siberia

Effect of the ignition location on lean light-off limits for a gas turbine combustor

The ignition performance of the spray flame is an important safety parameter in a gas turbine combustor. Previous studies have shown that the spark axial location has a significant influence on the ignition performance and flame propagation process, and further research is required. The ignition performance and flame kernel propagation at different spark radial locations in a gas turbine model combustor are studied experimentally in this paper to summarize the influence of spark location on ignition performance from the perspective of kernel propagations, and to find the optimal ignition location. The flame propagation trajectory of each ignition location is obtained through high-speed imaging tests. Four conclusions are obtained as follows: 1) In a successful ignition event, flame kernels from different ignition positions will eventually propagate to the same position, which is defined as the flame holding position (FHP). After the flame residence stage, the kernel will begin to grow until the entire combustor is ignited. The FHP is with low axial velocity, small turbulent fluctuation and appropriate fuel concentration to effectively maintain the flame. 2) The ignition performance is the worst when the ignitor is near the wall, and is the best when the ignitor is near the FHP, that is, the inner boundary of the recirculation zone. 3) The ignition performance deteriorates if the flame has to cover greater distances before reaching the FHP where it can ignite the flame stabilization zone. A spark at the FHP can greatly reduce the propagation distance of the flame kernel, thereby avoiding the obstruction of the propagation process. 4) The propagation trajectory of the flame kernel is related to the ignition location and is mainly controlled by the non-reacting flow field and fuel concentration.

Zircon geochronological and geochemical insights into pluton building and volcanic-hypabyssal-plutonic connections: Oki-Dōzen, Sea of Japan—A complex intraplate alkaline volcano

Abstract The relationship between plutonic and volcanic components of magmatic plumbing systems continues to be a question of intense debate. The Oki-Dōzen Islands, Sea of Japan, preserve outcrops of temporally associated plutonic, hypabyssal, and volcanic rocks. Post-intrusion uplift juxtaposed Miocene syenites in inferred faulted contact with volcanic trachytes that are cut by rhyolite hypabyssal dikes. This provides a window deep into the timing and origins of magma storage architecture and dynamics. Zircon is ubiquitous in all samples; our aim is to determine what its age and composition can reveal about the plutonic-volcanic connection. Here we show magma source characteristics are recorded in zircon Hf isotopes; source composition and assimilation of heterogeneous hydrothermally altered crust in zircon O isotopes; and extensive fractional crystallization in zircon trace elements. Combined with new UTh-Pb SHRIMP zircon ages, 6.4–5.7 Ma, compositional data show pluton formation was by protracted amalgamation of discrete magma pulses. The rhyolite dike preserves an evolved fraction segregated from these discrete magmas. Synchronous with plutonism was a volcanic eruption of trachyte magma derived from the same source, which may have stalled at a relatively shallow depth prior to eruption. Stalling occurred at least above the amphibole stability zone because amphibole-compatible Sc and Ti were not depleted in the trachyte melt resulting in elevated values of these in volcanic compared to plutonic zircon. Identifying smaller episodic magma pulses in a larger magmatic complex places constraints on potential magma fluxes and eruptible volumes. High-flux, large volume, plume-related ocean island magmatic systems may have extensive vertically distributed multi-stage magmatic reservoirs and subduction-related systems transcrustal magma reservoirs. By contrast, Oki-Dōzen was a low-flux system with incremental pluton growth and small- to moderate-scale eruptions.

W-shaped profile and breather-like soliton of the fractional nonlinear Schrödinger equation describing the polarization mode in optical fibers

We use the fractional nonlinear Schrödinger equation (FNLSE) to describe the polarization mode in optical fiber with Self-Steepening, Self-Frequency Shift, and Cubic-quintic terms to analyze the effects of the fractional time parameter (FTP) on bright and dark solitons as well as breather-like solitons. We use the transformation hypothesis and auxiliary equations method to obtain three families of solutions such as combined bright soliton, dark solitons, and rational solitons. We have shown the effects of the fractional parameter (FP) on the W-shaped profile, bright and dark optical soliton solutions as well as the corresponding chirp component. It is observed that for small values of the FP, optical soliton shape is affected and the soliton is unstable. Moreover, one observes the effects of fraction time on Modulation Instability (MI) gain spectra and MI bands. For certain values of the FP, it is formed sides lobes and for specific small values of the FP, both stability zone increases and amplitude of the MI gain increase while the stability zones increase. To confirm the robustness of the analytical results, we have used a numerical investigation. One exhibits the formation of breathers-like soliton with stable amplitude for small values of the FTP. It results from this study that the FP is efficient and can be used as an energy source where soliton or breathers-like soliton are involved for communication in optical fibers.