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Comparison of laser ablation in the sub-picosecond and nanosecond regimes with MHz repetition rate at 515 nm and application to graphite 515 nm频率下亚皮秒和纳秒激光烧蚀的比较及其在石墨上的应用
IF 3 4区 材料科学 Q3 MATERIALS SCIENCE, MULTIDISCIPLINARY Pub Date : 2026-10-15 DOI: 10.1007/s00339-026-10325-7
V. Sanchez, C. E. Cifuentes Quintal, T. Doualle, Y. Pontillon, L. Gallais

Micro-machining with ultra-short (sub-ps) and short (ns) pulsed lasers is used to minimize thermal effects, as the heat-affected zone depends on pulse duration. The distinction between ’cold’ (ultra-short regime) and ’hot’ (short regime) ablation holds for single-shot processes, but for high-repetition-rates, it involves additional effects such as incubation, plasma shielding, and thermal accumulation, making the choice of optimal pulse duration more complex. This study compares laser cutting and engraving using sub-picosecond and nanosecond lasers at the same repetition rate of 0.5 MHz. Experiments on graphite determined ablation properties and optimal processing parameters. A thermal model was used to understand the heat accumulation resulting in incubation phenomenon and allows us to characterize the heat affected zone for a given process. Results highlight the influence of pulse duration and process parameters on efficiency and thermal effects, offering insight for high-repetition rates laser processing of sensitive materials.

使用超短(亚ps)和短(ns)脉冲激光进行微加工可以最大限度地减少热效应,因为热影响区取决于脉冲持续时间。“冷”(超短周期)和“热”(短周期)消融之间的区别适用于单次过程,但对于高重复率,它涉及到额外的影响,如孵育,等离子体屏蔽和热积累,使最佳脉冲持续时间的选择更加复杂。本研究比较了在相同的0.5 MHz重复频率下使用亚皮秒和纳秒激光切割和雕刻。通过实验确定了石墨的烧蚀性能和最佳工艺参数。一个热模型被用来理解导致孵化现象的热积累,并允许我们表征一个给定过程的热影响区。研究结果强调了脉冲持续时间和工艺参数对效率和热效应的影响,为高重复频率激光加工敏感材料提供了新的思路。
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引用次数: 0
Numerical design and 1D-CNN surrogate modeling of a tunable Graphene/Au/MXene/WS₂/Cu terahertz metasurface for high-sensitivity RI-based glucose sensing 可调石墨烯/Au/MXene/ ws2 /Cu太赫兹超表面的数值设计和1D-CNN替代模型,用于高灵敏度基于ri的葡萄糖传感
IF 3 4区 材料科学 Q3 MATERIALS SCIENCE, MULTIDISCIPLINARY Pub Date : 2026-10-15 DOI: 10.1007/s00339-026-10336-4
M. Chairman, S. Gopinath

Reliable, non-invasive glucose monitoring remains essential for improving diabetes management, motivating the development of highly sensitive terahertz (THz) biosensors. This study proposes a hybrid Graphene/Au/MXene/Cu metasurface biosensor on a SiO₂ substrate featuring a central copper rectangular resonator, MXene–WS₂-coated V-shaped resonators, concentric gold rings, and a graphene layer to enhance plasmonic field confinement. Full-wave COMSOL simulations and parametric optimization investigated graphene chemical potential (0.1–0.9 eV), incidence angle (0°–80°), and resonator dimensions across four structural configurations. The optimized design achieved a maximum local sensitivity of 1000 GHz/RIU over a glucose refractive index range of 1.335–1.338, with a figure of merit of 10.753 RIU⁻¹ and a quality factor of 4.250 at 0.391 THz. Electric field enhancement reached 9.15 × 10⁷ V/m, while a 1D-CNN surrogate model predicted sensor responses with R² > 0.9992 and MAPE < 0.18%. These numerical findings establish a computationally efficient platform with potential for rapid, label-free THz glucose sensing and provide a basis for subsequent experimental validation.

可靠、无创的血糖监测对于改善糖尿病管理至关重要,这推动了高灵敏度太赫兹(THz)生物传感器的发展。本研究提出了一种基于sio2衬底的石墨烯/Au/MXene/Cu混合超表面生物传感器,该传感器具有中心铜矩形谐振器,MXene - ws 2涂层v形谐振器,同心金环和石墨烯层,以增强等离子体场约束。全波COMSOL模拟和参数优化研究了四种结构构型下石墨烯的化学势(0.1-0.9 eV)、入射角(0°-80°)和谐振腔尺寸。优化后的设计在葡萄糖折射率为1.335-1.338范围内的最大局部灵敏度为1000 GHz/RIU,优点系数为10.753 RIU⁻¹,在0.391 THz处的品质因子为4.250。电场增强达到9.15 × 10⁷V/m,而1D-CNN代理模型预测传感器响应的R²>; 0.9992和MAPE <; 0.18%。这些数值结果建立了一个计算效率高的平台,具有快速、无标记的太赫兹葡萄糖传感的潜力,并为后续的实验验证提供了基础。
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引用次数: 0
Ising diatomic molecules in the mean-field and exact recursion relations approach 利用双原子分子的平均场和精确递归关系的方法
IF 1.9 4区 物理与天体物理 Q3 PHYSICS, CONDENSED MATTER Pub Date : 2026-10-15 DOI: 10.1140/epjb/s10051-026-01291-3
Erhan Albayrak

This research utilizes a mean field theory (MFT) on spin-1/2 diatomic molecules for the first time to obtain the thermal changes in magnetizations for each molecule, thus generating the phase diagrams. The same model was also studied using the Bethe lattice (BL) approach in terms of the exact recursion relations (ERR) in order to compare its results with the MFT results. Different types of bilinear interaction parameters between the constituents of a molecule and nearest-neighbor (NN) molecules were assumed, and the coordination number is set to three, corresponding to the honeycomb lattice. It is found that the MFT only gives second-order phase transitions, but the ERR approach gives various phase transitions. The obtained results show that the ERR approach on the BL is superior over the MFT since it provides many more details of the model.

本研究首次利用自旋为1/2的双原子分子的平均场理论(MFT)获得了每个分子的磁化热变化,从而生成了相图。同样的模型也使用Bethe格(BL)方法在精确递归关系(ERR)方面进行了研究,以便与MFT结果进行比较。假设分子各组分与最近邻分子之间存在不同类型的双线性相互作用参数,并设置配位数为3,对应于蜂窝晶格。发现MFT方法只能给出二阶相变,而ERR方法可以给出多种相变。得到的结果表明,在BL上的ERR方法比MFT方法更能提供更多的模型细节。
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引用次数: 0
Structural, dielectric, electrical, and electronic-structure properties of Dy₀.₅Ba₀.₅CrO₃ perovskite Dy 0 .₅Ba 0的结构、介电、电气和电子结构性质。₅CrO₃钙钛矿
IF 3 4区 材料科学 Q3 MATERIALS SCIENCE, MULTIDISCIPLINARY Pub Date : 2026-10-15 DOI: 10.1007/s00339-026-10331-9
Ghada Raddaoui, Karim Souifi, Abdullah Saad Alsubaie, Khasan Berdimuradov, Elyor Berdimurodov, Mansur Radjabov, Okhunjon Khasanov

Dy₀.₅Ba₀.₅CrO₃ was synthesized using a citrate-based sol–gel method and investigated through structural, microstructural, dielectric, impedance, electrical-transport, and electronic-structure analyses. X-ray diffraction and Rietveld refinement indicated the formation of a predominantly single-phase orthorhombic perovskite structure with Pnma symmetry. The refinement produced (Rp = 4.2%, Rwp = 5.6%, χ2 = 2.17), and a goodness-of-fit value of 1.47. Williamson–Hall analysis gave an average crystallite size of approximately 44 nm and a microstrain of. The conductivity increased with temperature, confirming thermally activated semiconducting behavior. Activation energies of approximately eV for DC transport and eV for relaxation were obtained from Arrhenius analysis. The frequency-dependent conductivity followed Jonscher’s universal power law, while the impedance response exhibited thermally activated non-Debye relaxation and a decreasing overall resistance with increasing temperature. Because no equivalent-circuit fitting was performed, separate grain and grain-boundary parameters were not extracted. Oxygen-related defects and chromium mixed valence are discussed as possible contributors to localized transport but are not considered conclusively established without complementary bulk oxygen-stoichiometry measurements.

Dy₀。₅Ba₀。₅CrO₃采用基于柠檬酸盐的溶胶-凝胶法合成,并通过结构、微观结构、介电、阻抗、电输运和电子结构分析进行了研究。x射线衍射和Rietveld细化表明形成了具有Pnma对称的主要单相正交钙钛矿结构。精化得到(Rp = 4.2%, Rwp = 5.6%, χ2 = 2.17),拟合优度值为1.47。Williamson-Hall分析显示,该晶体的平均晶粒尺寸约为44 nm,微应变为。电导率随温度升高而增加,证实了热激活的半导体行为。通过阿伦尼乌斯分析得到了直流输运的约eV活化能和弛豫的eV活化能。频率相关的电导率遵循Jonscher的通用幂律,而阻抗响应表现为热激活的非debye松弛和总电阻随温度升高而降低。由于没有进行等效电路拟合,因此没有提取单独的晶粒和晶界参数。氧相关缺陷和铬混合价被认为是局部输运的可能贡献者,但如果没有补充的大量氧化学计量测量,则不认为最终确定。
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引用次数: 0
Aliovalent Al³⁺ substitution-induced enhancement of Mg²⁺ ionic conductivity in NASICON-type Mg0.5Ti2(PO4)3 solid electrolytes 银价Al³+取代诱导Mg²+在nasicon型Mg0.5Ti2(PO4)3固体电解质中的离子电导率增强
IF 3 4区 材料科学 Q3 MATERIALS SCIENCE, MULTIDISCIPLINARY Pub Date : 2026-10-15 DOI: 10.1007/s00339-026-10269-y
N. A. Wahab, M. H. Shehri, S. B. R. S. Adnan, S. Rudhziah, N. A. Dzulkurnain, N. A. Mustaffa

The Mg₀.₅₊₀.₅ₓAlₓTi₂₋ₓ(PO₄)₃ samples (x = 0.1, 0.3, 0.5, 0.7 and 0.9) were investigated to evaluate the effect of Al³⁺ substitution on the structural and ionic transport properties of Mg₀.₅Ti₂(PO₄)₃. XRD results confirmed that the samples predominantly exhibited a rhombohedral R-3c crystal structure similar to that of the parent compound. The Al³⁺ substitution for Ti⁴⁺ is proposed to promote charge compensation, which may facilitate the incorporation of additional Mg²⁺ ions and consequently enhance ionic transport. Among the investigated compositions, x = 0.5 (AL5) exhibited the highest ionic conductivity, reaching 2.61 × 10⁻⁸ S cm⁻¹ at room temperature and 5.41 × 10⁻⁶ S cm⁻¹ at 500 °C. The enhancement in conductivity is consistent with the proposed charge-compensation mechanism, although direct confirmation of interstitial Mg²⁺ occupancy requires further structural characterization. The frequency-dependent conductivity and temperature dependence of the frequency exponent further indicate thermally activated ionic transport in AL5. The Arrhenius analysis of total ionic conductivity yielded apparent activation energies of 0.04 eV and 0.62 eV for the low and high temperature regions, respectively. These findings demonstrate that Al substitution can effectively enhance the ionic transport properties of Mg₀.₅Ti₂(PO₄)₃ and provide useful insight into the development of NASICON-type magnesium-ion solid electrolytes.

Mg₀。₅₊₀。研究了₅ₓAlₓTi₂₄ₓ(PO₄)₃样品(x = 0.1、0.3、0.5、0.7和0.9),以评估Al³⁺取代对Mg₀.₅Ti₂(PO₄)₃结构和离子传输性能的影响。XRD结果证实,样品主要呈现与母体化合物相似的R-3c菱面体晶体结构。Al³⁺取代Ti⁴⁺是为了促进电荷补偿,这可能促进额外Mg²⁺离子的掺入,从而增强离子传输。在被研究的组合物中,x = 0.5 (AL5)表现出最高的离子电导率,在室温下达到2.61 × 10⁻⁸S cm⁻¹,在500℃时达到5.41 × 10⁻⁶S cm⁻¹。电导率的增强与提出的电荷补偿机制是一致的,尽管直接确认Mg 2 +占据间隙需要进一步的结构表征。频率指数的频率依赖电导率和温度依赖进一步表明AL5中的热激活离子传输。总离子电导率的Arrhenius分析表明,低温区和高温区离子电导率的表观活化能分别为0.04 eV和0.62 eV。这些结果表明,Al取代可以有效地提高Mg 0的离子输运性质。₅Ti₂(PO₄)₃并为nasicon型镁离子固体电解质的开发提供有用的见解。
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引用次数: 0
Prospects for early heavy-quark measurements at the EIC EIC早期重夸克测量的前景
IF 3 3区 物理与天体物理 Q2 PHYSICS, NUCLEAR Pub Date : 2026-10-15 DOI: 10.1140/epja/s10050-026-01974-6
Allencris John Rubesh Rajan, Laboni Manna

We assess the prospects for inclusive heavy-quark-pair electroproduction in electron–proton (ep) and electron–nucleus (eA) collisions, alongside double-charm-pair ((D^0 bar{D}^0) and (D^0D^0)) electroproduction in ep collisions, during the early operational phase of the Electron-Ion Collider (EIC). Based on the anticipated beam energies and luminosities of the EIC, we estimate the total cross sections and differential distributions for photon virtuality (Q^2), heavy-quark transverse momentum, and rapidity. This analysis evaluates different Bjorken-x ((x_textrm{Bj})) intervals across a range of (Q^2) values. Expected event yields are estimated from the projected integrated luminosities of the early science programme, demonstrating the substantial improvement in statistical precision over previous HERA measurements at moderate and large (x_{textrm{Bj}}). For electron–nucleus collisions, we compute the nuclear modification ratio (R^{etext {A}}) within collinear factorisation using nuclear parton distribution functions, and identify the kinematic regimes in which shadowing, anti-shadowing, and EMC-like suppression are accessible with early EIC data. These results are intended to serve as a parton-level baseline to support feasibility studies and to provide a reference for future higher-order theoretical and experimental investigations at the EIC.

在电子-离子对撞机(EIC)的早期运行阶段,我们评估了电子-质子(ep)和电子-核(eA)碰撞中包含重夸克对产生电的前景,以及电子-离子对撞机(EIC)碰撞中双粲对((D^0 bar{D}^0)和(D^0D^0))产生电的前景。基于EIC的预期光束能量和光度,我们估计了光子虚性(Q^2)、重夸克横向动量和速度的总横截面和微分分布。该分析在(Q^2)值范围内评估不同的Bjorken-x ((x_textrm{Bj}))区间。预期的事件产量是根据早期科学方案预测的综合光度来估计的,这表明与以前的中大型HERA测量相比,统计精度有了实质性的提高(x_{textrm{Bj}})。对于电子-核碰撞,我们使用核部分子分布函数计算共线分解中的核修饰比(R^{etext {A}}),并确定早期EIC数据可以获得阴影,反阴影和类似emc的抑制的运动状态。这些结果旨在作为支持可行性研究的部分级基线,并为未来EIC的高阶理论和实验研究提供参考。
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引用次数: 0
25th EPJE anniversary: vision piece on EPJE role today and tomorrow EPJE成立25周年:展望EPJE今天和明天的作用
IF 2.6 4区 物理与天体物理 Q4 CHEMISTRY, PHYSICAL Pub Date : 2026-10-15 DOI: 10.1140/epje/s10189-026-00630-7
Fabrizio Croccolo, Giovanna Fragneto, Holger Stark

On the occasion of the 25th anniversary of The European Physical Journal E—Soft Matter and Biological Physics, we reflect on the journal’s origins, rooted in Pierre-Gilles de Gennes’ vision of soft matter as a unifying field of physics, and trace its evolution to encompass biological and active systems. We review EPJE’s current position as a journal combining strong European roots with global reach, publishing original research, topical issues, reviews, and experimentally focused Tips and Tricks papers. Looking ahead, we outline our vision: deepening coverage of non-equilibrium and active matter, expanding into functional soft materials, reinforcing our strength in rheology, prioritizing experimental innovation, and embracing sustainability-related research, while remaining committed to Open Access and to bridging generations of scientists in the field.

在《欧洲物理杂志e-软物质与生物物理学》创刊25周年之际,我们回顾了该杂志的起源,它植根于皮埃尔-吉尔勒·德热纳(Pierre-Gilles de Gennes)关于软物质作为物理学统一领域的愿景,并追溯了它的演变,涵盖了生物和活动系统。我们回顾了EPJE目前的地位,作为一个结合强大的欧洲根基和全球影响力的期刊,发表原创研究,专题问题,评论和实验重点提示和技巧论文。展望未来,我们概述了我们的愿景:深化非平衡和活性物质的覆盖范围,扩展到功能软材料,加强我们在流变学方面的实力,优先考虑实验创新,拥抱与可持续性相关的研究,同时继续致力于开放获取并在该领域架起几代科学家的桥梁。
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引用次数: 0
In-plane magnetic field dependent energy spectrum of isolated GaAs-AlGaAs quantum well: numerical calculation 孤立GaAs-AlGaAs量子阱的面内磁场依赖能谱:数值计算
IF 3 4区 材料科学 Q3 MATERIALS SCIENCE, MULTIDISCIPLINARY Pub Date : 2026-10-14 DOI: 10.1007/s00339-026-10279-w
Shahajan Miah, Nujhat Nuri Sultana, Sujaul Chowdhury

We have numerically calculated energy spectrum of electron in isolated GaAs-AlGaAs Quantum Well in conduction band in presence of uniform static magnetic field applied parallel to GaAs-AlGaAs interfaces. We have numerically solved eigenvalue equation of energy using a two-point boundary value problem in this regard. This is the first use of the numerical method to this classic problem of nanostructure physics. There is no need to use any analytical expression for eigenfunctions in the calculations. We have also shown that results of our method agree very well with known standard results where available; we analyzed two different cases in this regard. Thus the work introduces a novel numerical approach in computational nanostructure physics.

在平行于GaAs-AlGaAs界面的均匀静态磁场作用下,我们数值计算了导带中孤立GaAs-AlGaAs量子阱中电子能谱。在这方面,我们用两点边值问题数值解出了能量的特征值方程。这是第一次使用数值方法来解决纳米结构物理学的经典问题。在计算中不需要使用特征函数的解析表达式。我们还表明,我们的方法的结果与已知的标准结果非常一致。我们在这方面分析了两个不同的案例。因此,这项工作在计算纳米结构物理中引入了一种新的数值方法。
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引用次数: 0
Exploring the dark sector through galaxy dynamics in clusters 通过星系团中的星系动力学来探索黑暗区域
IF 20.1 1区 物理与天体物理 Q1 ASTRONOMY & ASTROPHYSICS Pub Date : 2026-10-14 DOI: 10.1007/s00159-026-00174-x
Andrea Biviano, Lorenzo Pizzuti, Antonaldo Diaferio

Galaxy clusters are among the most powerful laboratories to probe fundamental physics, from the formation of cosmic structures to the nature of dark matter, dark energy, and gravity. Realizing their full potential requires accurate and unbiased determinations of their mass profiles, a longstanding challenge in cluster cosmology. In this context, the kinematics of member galaxies in clusters has become a key tool to reconstruct the mass distribution and investigate the dynamical properties of clusters. The advent of large spectroscopic datasets has enabled the application of increasingly sophisticated models and robust techniques, which make kinematic analyses competitive with other probes of cluster dynamics. In this review, we provide a comprehensive overview of cluster kinematics, covering the main methods to infer dynamical masses and mass profiles, their physical assumptions, and the impact of systematics, such as deviation from dynamical equilibrium, triaxiality, and substructures. We discuss the complementarity with other techniques to investigate the structure of clusters and highlight recent applications to tests cosmological models. We focus in particular on the role of kinematical studies in constraining the dark sector (dark matter and dark energy) and in providing novel insights into the behavior of gravity at Mpc scales. Finally, we outline current limitations and future prospects, emphasizing that the combination of improved modeling and forthcoming spectroscopic surveys will establish cluster kinematics as a fundamental probe in the era of precision cosmology.

从宇宙结构的形成到暗物质、暗能量和引力的本质,星系团是探索基础物理学最强大的实验室之一。要充分发挥它们的潜力,就需要对它们的质量曲线进行准确而公正的测定,这是星系团宇宙学中一个长期存在的挑战。在此背景下,星系团成员星系的运动学已成为重建星系团质量分布和研究星系团动力学性质的关键工具。大型光谱数据集的出现使得越来越复杂的模型和强大的技术得以应用,这使得运动学分析与其他簇动力学探测具有竞争力。在这篇综述中,我们提供了一个全面的概述,包括主要的方法来推断动态质量和质量轮廓,他们的物理假设,以及系统的影响,如偏离动态平衡,三轴性,和子结构。我们讨论了与其他研究星系团结构的技术的互补性,并强调了最近在测试宇宙模型方面的应用。我们特别关注运动学研究在限制暗物质(暗物质和暗能量)方面的作用,以及在Mpc尺度上提供对引力行为的新见解。最后,我们概述了当前的局限性和未来的前景,强调改进的建模和即将到来的光谱调查的结合将使星系团运动学成为精确宇宙学时代的基本探测。
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引用次数: 0
A new perspective for obtaining analytical solitons of the fractional Kaup–Kupershmidt equation 获得分数阶kup - kupershmidt方程解析孤子的新视角
IF 2.3 4区 物理与天体物理 Q2 PHYSICS, MULTIDISCIPLINARY Pub Date : 2026-10-14 DOI: 10.1007/s12043-026-03177-6
Francis Tuffour, Benedict Barnes

The Kaup–Kupershmidt equation is used to study nonlinear wave propagation associated with ocean currents, capturing the combined effects of nonlinearity and dispersion. Due to the many solitons exhibited by the fractional Kaup–Kupershmidt (K–K) equation, which represent the many solitary waves observed in ocean currents, plasma physics, and optics, several analytical methods have been developed and consistently applied to study these phenomena. One such method is the homogeneous balance method (HBM), which invariably relies on the embedded Riccati equation. Thus, the workability of the HBM largely depends on the embedded Riccati equation, which by and large determines the number and type of solitons yielded when the HBM is applied to the fractional K–K equation. Undeniably, several Riccati equations appear in the literature, each with unique properties. Therefore, if the HBM is embedded with a particular Riccati equation for solving the fractional K–K equation, the underlying mechanisms of the solitary waves in ocean current, plasma physics and optics are unveiled. The HBM and its modified methods explored only by the researchers have not been exhaustively observed a fractional Riccati equation with a quadratic term as the dependent variable, where coefficient of the second term is one and coefficient of the linear term is zero, (frac{d^{gamma }phi }{dxi ^{gamma }} = p + phi ^2(xi ),) quadratic term as the dependent variable and applied this modified homogeneous balance method (MHBM) to obtain the exact solitons of the fractional K–K equation. Applying the MHBM in solving the fractional K–K equation yielded five solitons: a bright soliton with a flat top, a gray soliton, a dark soliton with a flat bottom, an L-tilted soliton, and a halfway dark soliton. Three of the five solitons, a bright soliton with a flat bottom, a dark soliton with a flat bottom, and an L-tilted soliton, were new solitons that have not been observed in literature. These three new solitons of the fractional K–K equation have been observed in this paper as a result of a new embedded Riccati equation in HBM. The soliton properties, such as the kinetic and potential energies of the gray soliton and L-tilted soliton, are similar, whereas in the bright soliton and in the flat top and dark soliton with flat bottom, the potential and kinetic energies are in opposite directions. Lastly, the kinetic energy of the halfway dark soliton increases exponentially.

kap - kupershmidt方程用于研究与洋流有关的非线性波传播,捕捉非线性和色散的综合效应。由于分数阶kup - kupershmidt (K-K)方程显示了许多孤子,它们代表了在洋流、等离子体物理和光学中观察到的许多孤立波,因此已经开发了几种分析方法并一直应用于研究这些现象。其中一种方法是齐次平衡法(HBM),它总是依赖于内嵌的Riccati方程。因此,HBM的可操作性在很大程度上取决于嵌入的Riccati方程,该方程在很大程度上决定了HBM应用于分数阶K-K方程时产生的孤子的数量和类型。不可否认,文献中出现了几个里卡第方程,每个方程都有独特的性质。因此,如果在HBM中嵌入求解分数K-K方程的特定Riccati方程,则可以揭示洋流中孤立波的潜在机制,等离子体物理和光学。仅研究人员探索的HBM及其改进方法尚未详尽地观察到以二次项为因变量的分数阶Riccati方程,其中第二项系数为1,线性项系数为零,(frac{d^{gamma }phi }{dxi ^{gamma }} = p + phi ^2(xi ),)二次项为因变量,并应用这种改进的齐次平衡法(MHBM)获得分数阶K-K方程的精确孤子。用MHBM求解分数K-K方程得到了五个孤子:一个平顶亮孤子、一个灰孤子、一个平底暗孤子、一个l倾斜孤子和一个半暗孤子。五个孤子中的三个,一个底部平坦的亮孤子,一个底部平坦的暗孤子和一个l倾斜的孤子,是文献中未观察到的新孤子。本文通过在HBM中嵌入一个新的Riccati方程,观察到了分数阶K-K方程的这三个新的孤子。灰色孤子和l倾斜孤子的动能和势能是相似的,而明亮孤子、平顶孤子和平底暗孤子的动能和势能方向相反。最后,半暗孤子的动能呈指数增长。
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引用次数: 0
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