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X-ray spectral features and classification of selected QSOs 选定qso的x射线光谱特征和分类
IF 0.5 Q3 PHYSICS, MULTIDISCIPLINARY Pub Date : 2021-10-14 DOI: 10.30970/jps.25.4901
L. Zadorozhna, A. Tugay, Nadiia Pulatova, Oleh Maluy
We present the results of a systematic analysis of the XMM-Newton spectra of nearby optically bright QSOs. The objects have been selected from X-ray Galaxy Catalog Xgal20. It is a catalog of 1172 manually identi(cid:28)ed and classi(cid:28)ed galaxies, obtained as a cross-correlation between the 4XMM-DR9 catalog and the Hyper-Linked Extragalactic Databases and Archives (HyperLeda) with an X-ray (cid:29)ux greater than F ≥ 10 − 13 erg / ( cm 2 · s ) . The goal of this work is to characterize the X-ray spectral properties of selected QSOs in the 0.1 (cid:21) 10 keV energy band. The majority of the sources (6 out of 11) are classi(cid:28)ed as radio-quiet QSOs. We studied optical spectra, hardness ratios and performed X-ray spectral (cid:28)ts for the 10 brighter sources. In most cases, the power law model with absorption is good enough to simulate observed continua. However, the details of the spectrum in some sources signi(cid:28)cantly complicate the model for (cid:28)tting. The majority of sources have steep spectra Γ > 2 . 1 . Extremely steep photon index ( ∼ 2 . 4 − 2 . 5 ) in our sample occurs for three radio-loud type I quasars. We detected Fe K α line for two radio-loud type II quasars. We (cid:28)nd no strong evidence for spectral hardening above 2 keV either for quasars, of type I, or for the obscured type II. For each quasar its type was established both based on the features and details of observed X-ray spectrum and previous data.
我们提出了一个系统分析的结果,xmm -牛顿光谱附近的光学明亮的qso。这些天体选自x射线星系目录Xgal20。它是一份包含1172个人工识别(cid:28)星系和分类(cid:28)星系的星表,通过4XMM-DR9星表和超链接星系外数据库与档案(HyperLeda)之间的相互关联获得,x射线(cid:29)ux大于F≥10−13 erg / (cm2·s)。本工作的目的是表征所选qso在0.1 (cid:21) 10 keV波段的x射线光谱特性。大多数源(11个中的6个)被归类为(cid:28)无线电静默qso。我们研究了10个较亮光源的光谱、硬度比和x射线光谱(cid:28)ts。在大多数情况下,带吸收的幂律模型足以模拟观测到的连续体。然而,某些源(cid:28)中的光谱细节可能会使(cid:28)的模型变得复杂。大多数源具有陡峭的光谱Γ > 2。1 . 极陡的光子指数(~ 2)。4−2。5)在我们的样本中出现在三个射电声I型类星体中。我们探测到了两个射电声II型类星体的Fe K α谱线。我们(cid:28)没有强有力的证据表明类星体的光谱硬化在2 keV以上,无论是类星体的I型,还是被遮蔽的II型。每个类星体的类型都是根据观测到的x射线光谱的特征和细节以及以前的数据来确定的。
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引用次数: 1
Generation of magnetic fields by thermomagnetic effects in a nonuniformly rotating layer of an electrically conductive fluid 在导电流体的非均匀旋转层中由热磁效应产生的磁场
IF 0.5 Q3 PHYSICS, MULTIDISCIPLINARY Pub Date : 2021-04-21 DOI: 10.30970/JPS.25.2401
M. Kopp, K. Kulik, A. Tur, V. Yanovsky
In this paper, the generation of magnetic fields in a nonuniformly rotating layer of finite thickness of an electrically conducting fluid by thermomagnetic (TM) instability. This instability arises due to the temperature gradient $nabla T_0$ and thermoelectromotive coefficient gradient $nablaalpha $. The influence of the generation of a toroidal magnetic field by TM instability on convective instability in a nonuniformly rotating layer of an electrically conductive fluid in the presence of a vertical constant magnetic field ${bf{B}}_0 | {rm OZ}$ is established. As a result of applying the method of perturbation theory for the small parameter $ epsilon = sqrt {(textrm {Ra}-textrm {Ra}_c) / textrm {Ra}_c} $ of supercriticality of the stationary Rayleigh number $textrm {Ra}_c$ a nonlinear equation of the Ginzburg-Landau type was obtained. This equation describes the evolution of the finite amplitude of perturbations. Numerical solutions of this equation made it possible to determine the heat transfer in the fluid layer with and without TM effects. It is shown that the amplitude of the stationary toroidal magnetic field noticeably increases with allowance for TM effects.
本文研究了热磁不稳定性在有限厚度的导电流体非均匀旋转层中产生磁场的问题。这种不稳定性是由温度梯度$nabla T_0$和热电动势系数梯度$nablaalpha $引起的。建立了在垂直恒定磁场${bf{B}}_0 | {rm OZ}$存在下,TM不稳定性产生的环向磁场对导电流体非均匀旋转层对流不稳定性的影响。将微扰理论方法应用于稳态瑞利数$textrm {Ra}_c$超临界小参数$ epsilon = sqrt {(textrm {Ra}-textrm {Ra}_c) / textrm {Ra}_c} $,得到了金兹堡-朗道型非线性方程。这个方程描述了有限振幅扰动的演化。该方程的数值解可以确定有和没有TM效应时流体层内的换热情况。结果表明,考虑TM效应后,静止环向磁场的振幅显著增大。
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引用次数: 1
Acoustic waves in a turbulent giant molecular cloud taking into account the correlations of gravitational field 考虑引力场相关性的湍流巨分子云中的声波
IF 0.5 Q3 PHYSICS, MULTIDISCIPLINARY Pub Date : 2021-02-28 DOI: 10.30970/JPS.25.1903
Îëåñÿ Ãîí÷àðà, ïðîñï. Ãàãàðiíà
A hydrodynamic model for the description of small acoustic oscillations in a turbulent giant molecular cloud is constructed by averaging the Euler equation over Reynolds, taking into account the turbulence of a self-consistent gravitational (cid:28)eld that has zero (cid:28)rst moment and nonzero second moment in equilibrium. It is shown that, in addition to the Reynolds turbulent stress tensor, the momentum (cid:29)ow tensor includes the second correlation moment of the gravitational (cid:28)eld strength, both potential and vortex, for which the time equation is obtained from the Einstein equations in non-relativistic approximation. After linearization, this equation is ∂ t (cid:104) g i g k (cid:105) = ( ∂ k v i + ∂ i v k − 2 ∂ l v l δ ik ) (cid:10) g 2 (cid:11) 0 / 6 , where ∂ t ant ∂ i are the time and spatial derivatives, v i is the mass velocity component, (cid:10) g 2 (cid:11) 0 is the square of a self-consistent gravitational (cid:28)eld strength equilibrium value. Two transverse and longitudinal branches of acoustic oscillations in a homogeneous isotropic cloud are obtained. Zeroing of the transverse oscillations velocity gives a limiting condition for the stability of the giant molecular cloud (cid:10) v 2 (cid:11) 0 − (cid:10) g 2 (cid:11) 0 / (8 πGρ 0 ) ≥ 0 , where (cid:10) v 2 (cid:11) 0 is the mean square turbulent velocity, G is the gravitational constant, ρ 0 is the equilibrium density value. Thus, the doubled energy density of the turbulent motion must be greater than the gravitational (cid:28)eld energy density. It is shown that the thermal motion does not a(cid:27)ect the stability of the system. For the spherical shape of the cloud, the radius of the giant molecular cloud is obtained, which is consistent with observational data.
考虑具有零(cid:28)静止矩和非零平衡第二矩的自一致引力场(cid:28)的湍流,通过对Reynolds上的欧拉方程进行平均,建立了描述湍流巨大分子云中小声波振荡的流体动力学模型。结果表明,除了雷诺湍流应力张量外,动量(cid:29)ow张量还包含引力场强(cid:28)的第二次相关矩,即势和涡,其时间方程由非相对论近似的爱因斯坦方程得到。线性化后,该方程为∂t (cid:104) g i g k (cid:105) =(∂k vi +∂iv k−2∂l v l δ ik) (cid:10) g 2 (cid:11) 0 / 6,其中∂t ant∂i是时间和空间导数,vi是质量速度分量,(cid:10) g 2 (cid:11) 0是自洽引力(cid:28)场强平衡值的平方。得到了均匀各向同性云中声振荡的两个横向和纵向分支。横向振荡速度归零给出了巨大分子云(cid:10) v2 (cid:11) 0 - (cid:10) g2 (cid:11) 0 / (8 πGρ 0)≥0的稳定性的极限条件,其中(cid:10) v2 (cid:11) 0为湍流速度的均方,g为引力常数,ρ 0为平衡密度值。因此,紊流运动的倍能量密度必须大于重力场(cid:28)的能量密度。结果表明,热运动不影响系统的稳定性。对于云的球形,得到了巨分子云的半径,与观测数据一致。
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引用次数: 1
Bound-state solutions of the modified Klein–Gordon and Schrödinger equations for arbitrary l-state with the modified Morse potential in the symmetries of noncommutative quantum mechanics 非对易量子力学对称性中任意l态修正Morse势的修正Klein-Gordon方程和Schrödinger方程的束缚态解
IF 0.5 Q3 PHYSICS, MULTIDISCIPLINARY Pub Date : 2021-02-23 DOI: 10.30970/JPS.25.1002
A. Maireche
In this work, approximate analytical solutions of both modi(cid:28)ed Klein(cid:21)Gordon equation and Schr(cid:4)odinger equation in noncommutative relativistic and nonrelativistic three-dimensional real space have been explored by using the Pekeris approximation scheme to deal with the centrifugal term, Bopp’s shift method and standard perturbation theory. We present the bound-state energy equation with a newly proposed potential called the modi(cid:28)ed Morse potential under the condition of equal scalar and vector potentials. The potential is a superposition of the Morse potential and some exponential radial terms. The aim of combining these potentials is to have an extensive application. We show that the new energy depends on the global parameters ( Θ c and σ c ) characterizing the noncommutativity space-space and the potential parameter ( D e , r e , α ) in addition to the Gamma function and the discreet atomic quantum numbers ( j, l, s, m ) . The present results are applied in calculating both the energy spectrum for a few heterogeneous (LiH, HCl, NO) and homogeneous (H 2 , I 2 , O 2 ) diatomic molecules. We have also discussed some special cases of physical importance.
本文利用处理离心项的Pekeris近似格式、Bopp位移法和标准摄动理论,探讨了非对易相对论和非相对论三维实空间中modi(cid:28)ed Klein(cid:21)Gordon方程和Schr(cid:4)odinger方程的近似解析解。在标量势和矢量势相等的条件下,我们用一个新提出的称为modcid:28的摩尔斯势给出了束缚态能量方程。势是摩尔斯势和一些指数径向项的叠加。结合这些潜力的目的是为了得到广泛的应用。我们证明了新能量取决于表征非交换性空间-空间的全局参数(Θ c和σ c)和势参数(D e, re, α),以及伽马函数和离散原子量子数(j, l, s, m)。本文的结果应用于计算一些非均相(LiH, HCl, NO)和均相(h2, i2, o2)双原子分子的能谱。我们还讨论了一些具有物理重要性的特殊情况。
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引用次数: 22
Particle in a uniform field in a noncommutative space with preserved time reversal and rotational symmetries 非交换空间中具有时间反转和旋转对称性的均匀场中的粒子
IF 0.5 Q3 PHYSICS, MULTIDISCIPLINARY Pub Date : 2021-02-19 DOI: 10.30970/JPS.25.2002
Kh. P. Gnatenko, Kh. I. Stakhur, A. V. Kryzhova
Quantized space described by time reversal invariant and rotationally invariant noncommutative algebra of canonical type is studied. A particle in uniform field is considered. We find exactly the energy of a particle in uniform field in the quantized space and its wavefunctions. It is shown that the motion of the particle in the field direction in time reversal invariant and rotationally invariant noncommutative space is the same as in the ordinary space (space with the ordinary commutation relations for operators of coordinates and operators of momenta). Noncommutativity of coordinates has influence only on the motion of the particle in the directions perpendicular to the field direction. Namely, space quantization has effect on the mass of the particle.
研究了正则型时反转不变和旋转不变非交换代数描述的量子化空间。考虑均匀场中的粒子。我们精确地求出了量子化空间中均匀场中粒子的能量及其波函数。证明了粒子在时间反转不变和旋转不变非对易空间中的场方向运动与在普通空间(坐标算子和动量算子具有普通对易关系的空间)中的运动相同。坐标的非交换性只影响粒子在垂直于场方向的方向上的运动。即空间量子化对粒子的质量有影响。
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引用次数: 0
Nonlinear wave dynamics of a disperse granular layer stimulated by an inwards moving piston 由向内运动活塞刺激的分散颗粒层的非线性波动动力学
IF 0.5 Q3 PHYSICS, MULTIDISCIPLINARY Pub Date : 2021-02-16 DOI: 10.30970/JPS.25.1401
S. Mykulyak, S. Skurativskyi
Three-dimensional simulations of wave propagation in a granular medium layer containing particles with polydisperse size distribution are performed using the discrete element method (DEM). The wave is generated by a piston subjected to an impulse load. It is shown that in the free surface layer, rotation wave structures are formed. Their location, time of occurrence and duration are determi-ned using correlation analysis. These wave structures are revealed when the friction between the grains (particles) is incorporated and, moreover, the gravitation (cid:28)eld resulting in the non-uniform distribution of the inter-particle force (cid:28)eld is taken into account. The absence of the rotation wave formation is also shown when the inhomogeneity caused by the gravitational (cid:28)eld is destroyed by vertical loading.
采用离散元法(DEM)对含多分散粒径颗粒的颗粒介质层中的波传播进行了三维模拟。这种波是由活塞受到脉冲载荷而产生的。结果表明,在自由面层中,形成了旋转波结构。利用相关分析确定其位置、发生时间和持续时间。当考虑颗粒(颗粒)之间的摩擦和重力场(cid:28)导致颗粒间力场(cid:28)分布不均匀时,这些波的结构就会显现出来。当重力场(cid:28)引起的不均匀性被垂直加载破坏时,旋转波的形成也不存在。
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引用次数: 1
Increasing the efficiency of modeling the energy characteristics of nanoclusters 提高纳米团簇能量特性建模的效率
IF 0.5 Q3 PHYSICS, MULTIDISCIPLINARY Pub Date : 2021-02-05 DOI: 10.30970/JPS.25.1001
O. Vasylenko, V. Reva, V. Pogosov
Context. The paper presents a computational scheme and a number of techniques for increasing the e(cid:30)ciency of mathematical modeling of the energy characteristics of metal clusters with vacancies. The object of the research is the process of calculating wave functions and (cid:28)nding eigenvalues using the Numerov and the shooting methods. local density approximation for calculating the energy characteristics of nanoclusters. At the simulation stage, the one-electron wave function was calculated by (cid:16)stitching(cid:17) it from two parts at an empirically selected point with normalization before and after the procedure. A number of techniques have been developed to improve the quality of the simulation: calculating the optimal step, limiting changes in the electrostatic pro(cid:28)le, managing the resulting data arrays, etc. For calculations on a supercomputer, the distribution between the (cid:29)ows was carried out. Results. At the modeling stage, economic models of the metal sphere with a vacancy in the center were developed. For the simulation stage, a method of stable two-sided calculation of the wave function using the shooting and the Numerov methods with the optimal step has been developed. The full computational scheme for the simulation is implemented in C ++ for calculation on a PC and on a supercomputer. The simulation results were compared with the ab-initio calculation data and experimental data for Cs, Rb, K, Na, Li, Mg, and Al clusters with and without vacancies (calculation error < 15%). Conclusions. The developed computational scheme and modeling technique allow increasing the simulation e(cid:30)ciency and obtaining adequate energy characteristics of metal spherical nanoclusters with and without vacancies. Further research might focus on the modi(cid:28)cation of models and simulation techniques for the study of layered nanoscale systems.
上下文。本文提出了一种计算方案和一些技术,以提高具有空位的金属团簇能量特性数学建模的效率。研究对象是用数值法和射击法计算波函数和(cid:28)特征值的过程。计算纳米团簇能量特性的局部密度近似。在模拟阶段,通过(cid:16)将(cid:17)在经验选择的点上从两个部分拼接(cid:17)并在程序前后进行归一化计算单电子波函数。为了提高模拟质量,已经开发了许多技术:计算最佳步长,限制静电pro(cid:28)le的变化,管理结果数据阵列等。为了在超级计算机上进行计算,进行了(cid:29)ows之间的分布。结果。在建模阶段,建立了中心有空位的金属球的经济模型。在模拟阶段,提出了一种采用最优步进的射击法和Numerov法稳定计算波函数的方法。仿真的完整计算方案是用c++语言实现的,可以在PC机和超级计算机上进行计算。将模拟结果与Cs、Rb、K、Na、Li、Mg和Al簇有无空位的ab-initio计算数据和实验数据进行了比较(计算误差< 15%)。结论。所开发的计算方案和建模技术可以提高模拟效率,并获得具有和不具有空位的金属球形纳米团簇的足够的能量特性。进一步的研究可以集中在层状纳米级体系的模型和模拟技术的修正上。
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引用次数: 0
Approximate evaluation of the duration of the orbital motion of artificial Earth satellites taking into account light pressure 考虑光压力的人造地球卫星轨道运动持续时间的近似计算
IF 0.5 Q3 PHYSICS, MULTIDISCIPLINARY Pub Date : 2021-01-29 DOI: 10.30970/JPS.25.1901
M. M. Koval'chuk, Y. Vovchyk, O. Baran, A. Bilinsky, I. P. Laushnyk, M. Stodilka, M. Hirnyak
A comprehensive research was conducted to establish the in(cid:29)uence of solar pressure on the existence of arti(cid:28)cial Earth satellites in their orbit. Six low-orbit satellites and one satellite with a high-elliptical orbit moving in orbit during 2001(cid:21)2020 were selected for the study. We used the USSTRATCOM database of the satellites’ orbital elements (http://www.space-track.org/), additional data were taken from CalSky (https://www.calsky.com) and TLEtools (https://tletools.readthedocs.io). Taking into account light pressure, we re(cid:28)ned the calculation of the duration of a satellite’s orbital motion, which we had performed earlier [M. M. Koval’chuk, Bull. Natl. Univ. Kyiv. Astron. 55, 39 (2017)], and clari(cid:28)ed the moment of its destruction. Using the proposed method allowed us to reduce the di(cid:27)erence between the calculated and the real lifetime of satellites: for low-orbit satellites, the di(cid:27)erence between the calculated and the real time of their existence in orbit does not exceed ± 1 day, for a satellite with a highly elliptical orbit it is +2 days. Such accuracy is su(cid:30)cient to produce proper forecasts. Thus, consideration of light pressure gives a small correction in the calculations in the case of low-orbit satellites, but this correction can be signi(cid:28)cant for low-mass and large-surface objects moving in medium and high (geostationary) orbits [Ch. Lucking, C. Colombo, C. R. McInnes, Acta Astronaut. 77, 197 (2012)].Keywords:
为了确定太阳压力对人造地球卫星在轨存在的影响,进行了全面的研究。选取2001(cid:21)2020年在轨运行的6颗低轨道卫星和1颗高椭圆轨道卫星作为研究对象。我们使用了USSTRATCOM卫星轨道要素数据库(http://www.space-track.org/),其他数据来自CalSky (https://www.calsky.com)和TLEtools (https://tletools.readthedocs.io)。考虑到光的压力,我们(cid:28)需要计算卫星轨道运动的持续时间,我们之前已经做过了。科瓦尔丘克先生,布尔。国家的。大学,基辅。天文学,55,39(2017)],而克拉丽(cid:28)则记录了它毁灭的时刻。采用该方法可以减小卫星计算寿命与实际寿命之间的差值(cid:27):对于低轨道卫星,其计算寿命与实际在轨生存时间的差值不超过±1天,对于高椭圆轨道卫星,其差值为+2天。这样的精确度对于做出正确的预测是非常重要的。因此,在低轨道卫星的情况下,考虑光压的计算误差很小,但对于在中、高(地球静止)轨道上运行的低质量和大表面物体,这种误差可能很大(cid:28) [Ch. Lucking, C. Colombo, C. R. McInnes,《宇航员学报》,77,197(2012)]。关键词:
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引用次数: 0
Groups of meteorites and meteorite-dropping fireballs in asteroidal orbits 成群的陨石和陨石坠落的火球在小行星轨道上
IF 0.5 Q3 PHYSICS, MULTIDISCIPLINARY Pub Date : 2021-01-01 DOI: 10.30970/jps.25.4902
Y. Gorbanev, N. Konovalova, N. K. Davruqov
This paper presents the results of a study of the existence of nine near-Earth meteorite-producing groups in asteroidal orbits, containing sporadic (cid:28)reballs from the IAU MDC-2007 database, sporadic meteors from the SonotaCo database, meteorites (cid:22) namely, L 5 , L 6 and H 4 − H 6 ordinary chondrites and an ureilite, for which atmospheric and orbital parameters are known from instrumental observations. Orbits of the selected members of meteorite-producing groups were classi(cid:28)ed as asteroid orbits according to the Tisserand parameter T j > 3 . 1 . Dynamic links between the members of the identi(cid:28)ed meteorite-producing groups and instrumentally observed known meteorites which were taken as a reference for the search of potential group members were tested using orbital similarity criteria, in particular the Drummond criterion (cid:22) D D and the Southworth and Hawkins criterion (cid:22) D SH . As a result, several meteorite-dropping sporadic (cid:28)reballs and small meteors, whose orbits are similar to the asteroid orbits of nine known meteorites, were detected and reckoned as possible members of groups.
本文介绍了在小行星轨道上存在的9个近地陨石产生群的研究结果,其中包括来自IAU MDC-2007数据库的零星(cid:28)回球,来自SonotaCo数据库的零星流星,陨石(cid:22),即l5, l6和h4 - h6普通球粒陨石和一颗球粒陨石,其大气和轨道参数已通过仪器观测得到。根据Tisserand参数tjb>3,选定的产生陨石群成员的轨道被归类为小行星轨道。1 . 已确定的(cid:28)ed陨石产生群的成员与仪器观测到的已知陨石之间的动态联系,作为搜索潜在群体成员的参考,使用轨道相似标准进行测试,特别是Drummond标准(cid:22) D D和Southworth and Hawkins标准(cid:22) D SH。结果,发现了几颗零星的(cid:28)回球和小流星,它们的轨道与九颗已知陨石的小行星轨道相似,并认为它们可能是群的成员。
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引用次数: 1
Optical soliton perturbation and polarization with quadratic--cubic nonlinearity by sine-Gordon equation approach 二次-三次非线性光孤子摄动与偏振
IF 0.5 Q3 PHYSICS, MULTIDISCIPLINARY Pub Date : 2021-01-01 DOI: 10.30970/JPS.25.2001
Y. Yıldırım, E. Topkara, A. Biswas, H. Triki, M. Ekici, P. Guggilla, S. Khan, M. Belić
This paper recovers a full spectrum of optical solitons that are generated by the combined e(cid:27)ects of dispersion and nonlinearity of the pulse propagation. The quadratic(cid:21)cubic form of the nonlinear refractive index is incorporated in the governing nonlinear Schr(cid:4)odinger equation, which governs the dynamics of the soliton transmission across trans-continental and transoceanic distances. The model is considered with a nonlinear chromatic dispersion that is required to sustain for smooth transmission of soliton pulses in optical (cid:28)bers, couplers, PCF, magneto-optic waveguides, crystals, metamaterials, metasurfaces, birefringent (cid:28)bers, DWDM systems and other form of waveguides. Solitons in birefringent (cid:28)bers as well as solitons in polarization preserving (cid:28)bers are considered. The governing model is treated with Hamiltonian type perturbation terms. The perturbation terms are with full intensity. The model is studied for the intensity count m = 1 . The adopted integration algorithm is the sine-Gordon equation method that reveals single form soliton solutions as well as dual-form soliton solutions. These solitons are dark soliton, singular soliton, bright soliton and combo singular soliton. Also, dark soliton represents a kink/anti-kink solitary wave or a shock wave in (cid:29)uid dynamics. The respective constraint conditions are also in place to guarantee the existence of such solitons.
本文恢复了由脉冲传播的色散和非线性共同作用的e(cid:27)个分量所产生的全谱光孤子。非线性折射率的二次(cid:21)三次形式被纳入控制非线性Schr(cid:4)odinger方程,该方程控制孤子跨大陆和跨海洋传输的动力学。该模型考虑了在光学(cid:28)波导、耦合器、PCF、磁光波导、晶体、超材料、超表面、双折射(cid:28)波导、DWDM系统和其他形式的波导中维持孤子脉冲平滑传输所需的非线性色散。考虑了双折射(cid:28)光阑中的孤子和保偏振(cid:28)光阑中的孤子。用哈密顿型摄动项处理控制模型。微扰项是满强度的。对强度计数m = 1时的模型进行了研究。所采用的积分算法是正弦戈登方程法,可以显示单形式孤子解和双形式孤子解。这些孤子是暗孤子,奇异孤子,亮孤子和组合奇异孤子。暗孤子在流体动力学中代表扭结/反扭结孤子波或激波。相应的约束条件也保证了这种孤子的存在。
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引用次数: 1
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