Partial Differential Equations in Applied Mathematics最新文献_第2页

An improved modified simplest equation method for exact solitary wave solutions of the three-dimensional nonlinear fractional wazwaz-benjamin-bona-mahony model 三维非线性分数阶wawazz -benjamin-bona-mahony模型精确孤波解的改进修正最简方程法

Q1 Mathematics

Partial Differential Equations in Applied Mathematics

Pub Date : 2025-12-10 DOI: 10.1016/j.padiff.2025.101331

M. Al-Amin , M.Nurul Islam , M.Ali Akbar

In this study, we suggest an improved modified simplest equation (IMSE) approach to obtain distinct analytical solutions of the three-dimensional nonlinear fractional Wazwaz-Benjamin-Bona-Mahony (FWBBM) model associated with the conformable derivative. The suggested IMSE approach extends the classical simplest equation approach by introducing four new solutions, enhancing its efficiency and generality for solving nonlinear fractional partial differential equations. This approach yields fifteen solitary wave solutions for each equation of the three-dimensional FWBBM model, including trigonometric, hyperbolic, algebraic, and mixed-function types. The obtained solutions describe diverse soliton shapes such as bell-shaped, anti-bell-shaped, singular, and periodic solitons, which illustrate the rich dynamical behavior of nonlinear dispersive waves. The physical implications of these solutions are analyzed through three-, two-dimensional, and contour plots depicted through Mathematica, showing that the fractional-order parameter significantly affects soliton amplitude, shape, and stability. Comparisons with existing analytical methods, including the tanh-coth and

exp (- ϕ (ω))

-expansion techniques, confirm the precedence and broader applicability of the IMSE method. This approach provides deeper insights into nonlinear wave propagation and soliton dynamics and provides a powerful analytical tool for multidimensional fractional models in plasma physics, fluid mechanics, and optical systems.

在这项研究中，我们提出了一种改进的修正最简单方程（IMSE）方法来获得三维非线性分数阶wazwazi - benjamin - bona - mahony （FWBBM）模型的不同解析解。本文提出的IMSE方法扩展了经典的最简单方程方法，引入了四个新的解，提高了求解非线性分数阶偏微分方程的效率和通用性。这种方法为三维FWBBM模型的每个方程提供了15个孤波解，包括三角、双曲、代数和混合函数类型。得到的解描述了钟形孤子、反钟形孤子、奇异孤子和周期孤子等不同形状的孤子，说明了非线性色散波丰富的动力学行为。通过Mathematica绘制的三维、二维和等高线图分析了这些解的物理含义，表明分数阶参数显著影响孤子振幅、形状和稳定性。与现有的分析方法，包括tanh-coth和exp（−ϕ（ω））-展开技术的比较，证实了IMSE方法的优先性和更广泛的适用性。这种方法为非线性波传播和孤子动力学提供了更深入的见解，并为等离子体物理、流体力学和光学系统中的多维分数模型提供了强大的分析工具。

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引用次数: 0

Fractional mathematical modeling on monkeypox using the Laplace-Adomian decomposition method 用Laplace-Adomian分解法建立猴痘的分数数学模型

Q1 Mathematics

Partial Differential Equations in Applied Mathematics

Pub Date : 2025-12-09 DOI: 10.1016/j.padiff.2025.101326

Sharmin Sultana Shanta , M. Ali Akbar

The monkeypox virus has become a major global health concern due to its rapid spread. Medical intervention and isolation are essential to control the outbreak until an effective treatment is discovered. In this article, we develop a fractional SEIQR model to study the transmission dynamic of the monkeypox virus by including key epidemiological factors and memory effects. The nonlinear model describing the spread of viruses is investigated using the fractional Laplace-Adomian decomposition method (LADM), a powerful analytical technique to address complex infectious disease models. The results are strictly validated by comparing them with those derived from the fractional fourth-order Runge-Kutta (RK4) method. The results demonstrate strong agreement for

ζ = 0.99

, which confirms the reliability of the fractional framework. The error analysis shows that adding more LADM terms increases the accuracy. Positivity and sensitivity analyses confirm the model is biologically valid and show that early detection, isolation, quarantine, and reduced contact strongly affect infection levels. The phase portraits and contour plots provide insight into system behavior and threshold conditions. The study highlights the effectiveness of fractional LADM in describing nonlocal and memory-driven dynamics that cannot be represented in classical models.

猴痘病毒因其迅速传播已成为一个主要的全球卫生问题。在发现有效治疗方法之前，医疗干预和隔离对于控制疫情至关重要。在本文中，我们建立了一个分数SEIQR模型，通过考虑关键流行病学因素和记忆效应来研究猴痘病毒的传播动态。利用分数阶拉普拉斯-阿多米亚分解方法（LADM）研究了描述病毒传播的非线性模型，这是一种处理复杂传染病模型的强大分析技术。将所得结果与分数阶龙格-库塔（RK4）方法的结果进行了比较，得到了严格的验证。结果表明ζ=0.99的强烈协议，这证实了分数框架的可靠性。误差分析表明，增加更多的LADM项可以提高精度。阳性和敏感性分析证实该模型在生物学上是有效的，并表明早期发现、隔离、检疫和减少接触对感染水平有很大影响。相位肖像和等高线图提供了对系统行为和阈值条件的洞察。该研究强调了分数LADM在描述经典模型无法表示的非局部和记忆驱动动力学方面的有效性。

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引用次数: 0

Entropy generation and MHD flow characteristics of unsteady Williamson fluid toward a stagnation point over a vertical Riga plate 竖直Riga板上非定常Williamson流体滞止点的熵生和MHD流动特性

Q1 Mathematics

Partial Differential Equations in Applied Mathematics

Pub Date : 2025-12-01 DOI: 10.1016/j.padiff.2025.101321

Hassan Shahzad , Dur-E-Shehwar Sagheer , Hajra Batool , Maryam Ali Alghafli , Nabil Mlaiki

This study presents a mathematical model to explore two-dimensional, time-dependent fluid flow towards a stagnation point over a Riga plate, under the influence of magnetohydrodynamics (MHD), activation energy, and a higher-order chemical reaction. The surface of the Riga plate is lined with magnets and electrodes, arranged in a structured manner. The research investigates the effects of radiation and Joule heating on fluid motion and includes an entropy generation analysis based on the second law of thermodynamics. The partial differential equations (PDEs) that govern the physical system are reduced to ordinary differential equations (ODEs) via similarity variables, and solved using both the shooting method and the bvp4c algorithm. Results indicate that the unsteadiness parameter increases skin friction by 5.53 %, while the heat source parameter reduces heat transfer by up to 33.4 %. Entropy generation is found to rise with increasing Brinkman number and concentration difference, whereas higher temperature differences lower entropy production. The combined effects of Lorentz force, exponential chemical reaction, internal heat generation, and suction/injection within an unsteady Riga plate configuration have not been explored previously. Furthermore, the inclusion of irreversibility analysis enhances the novelty and provides deeper insight into energy dissipation mechanisms and system efficiency, offering valuable guidance for designing advanced MHD-based thermal control and energy systems. These numerical results are well aligned with existing literature, reinforcing the reliability of the analysis and highlighting its significance for energy-efficient thermal system design.

本研究提出了一个数学模型，用于探索在磁流体力学（MHD）、活化能和高阶化学反应的影响下，二维、随时间变化的流体流向里加板上的一个滞止点。里加板的表面排列着磁铁和电极，以结构化的方式排列。研究了辐射和焦耳加热对流体运动的影响，包括基于热力学第二定律的熵生成分析。将控制物理系统的偏微分方程通过相似变量化简为常微分方程，并采用射击法和bvp4c算法求解。结果表明，非定常参数可使表面摩擦增加5.53%，而热源参数可使传热减少33.4%。熵产随着布林克曼数和浓度差的增加而增加，而温差越大，熵产越低。洛伦兹力、指数化学反应、内部热生成和吸/注入在非定常里加板结构中的联合效应以前没有被探索过。此外，纳入不可逆性分析增强了新颖性，并对能量耗散机制和系统效率提供了更深入的了解，为设计先进的基于mhd的热控制和能源系统提供了有价值的指导。这些数值结果与现有文献吻合较好，增强了分析的可靠性，突出了其对节能热系统设计的意义。

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引用次数: 0

Spatially localized trains of soliton in attractive Bose-Einstein condensates with periodic potential 具有周期势的吸引玻色-爱因斯坦凝聚体中的空间定域孤子列

Q1 Mathematics

Partial Differential Equations in Applied Mathematics

Pub Date : 2025-11-14 DOI: 10.1016/j.padiff.2025.101322

Nkeh Oma Nfor , Akoni Brikly Njinabo , Francois Marie Moukam Kakmeni

We investigate the spatial profiles of periodic localized modes in attractive Bose-Einstein condensates, by solving the mean-field Gross-Pitaevskii equation in the presence of elliptic-type periodic potential. By considering a one-dimensional time independent linearized Gross-Pitaevskii equation, we obtained three bound state solutions and energies emanating from the first order Lamé equation. When the nonlinearity induced by the two body inter-atomic interactions are fully activated, spatially localized trivial phase periodic solutions of the attractive condensates are analytically obtained using the ansatz technique coupled with the direct integral method. Results of numerical simulation depicts trivial phase solutions, which are uniform train of spatially localized modes that are insensitive to variation of the elliptic modulus. However in the non-trivial phase regime, the spatially localized trains of soliton become very structurally unstable. This work underscores the spontaneous generation of periodic potential by the condensate wave function, determine the band structure of the lattice and basic properties of periodic matter waves under linear conditions, and highlight various spatial nonlinear periodic modes in the condensate. Finally, our investigation provides a solid theoretical framework that finds potential application in the fabrication of atomic lasers, periodic matter-wave gratings and quantum logic gates.

通过求解椭圆型周期势存在下的平均场Gross-Pitaevskii方程，研究了吸引玻色-爱因斯坦凝聚中周期局域模式的空间分布。通过考虑一维时间无关线性化的Gross-Pitaevskii方程，我们得到了一阶lam方程的三个束缚态解和能量。当两体原子间相互作用引起的非线性被完全激活时，利用ansatz技术结合直接积分法解析得到了吸引凝聚物的空间定域平凡相周期解。数值模拟结果描述了平凡的相位解，它们是对椭圆模量变化不敏感的空间局域模态的均匀序列。然而，在非平凡相域中，空间局域孤子序列在结构上变得非常不稳定。本工作强调了凝聚波函数自发产生周期势，确定了晶格的带结构和线性条件下周期物质波的基本性质，并强调了凝聚中各种空间非线性周期模式。最后，我们的研究为原子激光器、周期性物质波光栅和量子逻辑门的制造提供了一个坚实的理论框架。

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引用次数: 0

Numerical simulation of multilane traffic flow model based on exponential velocity-density function 基于指数速度-密度函数的多车道交通流模型数值模拟

Q1 Mathematics

Partial Differential Equations in Applied Mathematics

Pub Date : 2025-11-10 DOI: 10.1016/j.padiff.2025.101323

Md Rasel Ahmed , Bitu Joydhar , Dr. Md. Laek Sazzad Andallah , Prokriti Biswas , Jannatul Ferdous

In this paper, we study a multilane traffic flow model incorporating the exponential velocity-density relationship, which yields a nonlinear first-order system of hyperbolic partial differential (PDEs) equations formulated as an initial-boundary value problem (IBVP). This study seeks to construct a physically consistent and computationally efficient model for a multilane traffic flow model, which captures nonlinear vehicular interactions and lane-changing dynamics. Numerical solutions of the multilane traffic flow model, under the specified initial and boundary conditions, are obtained using the finite difference method. The numerical simulations are performed by employing the well-known first-order Explicit Upwind Scheme, the Lax-Friedrichs Scheme, and the second-order Lax-Wendroff Scheme. We evaluate the convergence rate of the numerical solutions, along with detailed well-posedness and stability analysis. To assess the stability and accuracy of three numerical schemes, we compare the velocity and density profiles derived from different schemes. The outcomes of our study have significant applications in traffic management in the real world, including predicting the effect of congestion, optimizing the lane-change effects, and enhancing efficiency through intelligent transportation system intelligent transportation system (ITS) and safety on multilane highways.

本文研究了一个包含指数速度-密度关系的多车道交通流模型，得到了一个一阶非线性双曲型偏微分方程系统，其形式为初边值问题（IBVP）。本研究旨在建立一个物理上一致且计算效率高的多车道交通流模型，以捕获非线性车辆相互作用和变道动力学。利用有限差分法得到了给定初始条件和边界条件下多车道交通流模型的数值解。采用著名的一阶显式迎风格式、Lax-Friedrichs格式和二阶Lax-Wendroff格式进行了数值模拟。我们评估了数值解的收敛速度，以及详细的适定性和稳定性分析。为了评估三种数值格式的稳定性和准确性，我们比较了从不同格式得到的速度和密度曲线。研究结果在多车道高速公路的交通管理中具有重要的应用价值，包括预测拥堵效应、优化变道效果以及通过智能交通系统提高效率和安全性。

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引用次数: 0

Numerical study for inelastic fluid flow in a contraction-expansion axisymmetric channel by using the finite element method 用有限元法对收缩-膨胀轴对称通道内非弹性流体流动进行数值研究

Q1 Mathematics

Partial Differential Equations in Applied Mathematics

Pub Date : 2025-10-28 DOI: 10.1016/j.padiff.2025.101311

Alaa A. Sharhan , Adnan K. Farhood , Alaa H. Al-Muslimawi

This research looks at the flow of inelastic fluids in an axisymmetric 4:1:4 contraction-expansion with a sharp corner. The finite element approach is used to simulate the flow of inelastic fluid numerically. The continuity equation and the conversation equation of momentum equation are used in combination with the power law model. This study presents the extent of the influence of many factors, including the Reynolds number (Re) and the power law index

(n)

, on the solution behavior. Our focus in this work is specifically on how these parameters effect the component of the solution and the convergence rate. The values of pressure and velocity were on of the interests of our research paper, as was the extent to which these are effected by the power law index and the Reynolds number. The influence of index

(n)

of power law model on viscosity was also one of the subjects of the investigation.

本文研究了轴对称4:1:4缩胀带尖角的非弹性流体流动。采用有限元方法对非弹性流体的流动进行了数值模拟。将动量方程的连续性方程和对话方程与幂律模型结合使用。本研究提出了包括雷诺数（Re）和幂律指数(n)在内的许多因素对溶液行为的影响程度。我们在这项工作中特别关注这些参数如何影响解的组成部分和收敛速度。压力和速度的值是我们研究论文的兴趣所在，幂律指数和雷诺数对它们的影响程度也是我们研究的兴趣所在。幂律模型的指数(n)对黏度的影响也是研究的主题之一。

引用次数: 0

Traveling synchronized asymmetric two-waves in the propagation of the KdV and mKdV equations incorporating time-space dispersion terms 含时空色散项的KdV和mKdV方程的行同步非对称双波传播

Q1 Mathematics

Partial Differential Equations in Applied Mathematics

Pub Date : 2025-10-25 DOI: 10.1016/j.padiff.2025.101319

Marwan Alquran, Imad Jaradat

Joseph and Egri revised the standard Korteweg-de Vries equation by replacing its third-order space dispersion term by space-time dispersions aiming to adjust the wave speed and preserve frequency stability. The aim of the current study is twofold. First, it demonstrates that the Joseph-Egri equation exhibits dynamical behavior similar to the Boussinesq model, particularly in the propagation of synchronized asymmetric two-wave structures. Second, it presents and investigates a modified extension of the Joseph-Egri equation, inspired by similar modifications of the Korteweg-de Vries and Benjamin-Bona-Mahony equations. Effective schemes, including the trigonometric and hyperbolic rational functions method and the extended tanh-coth expansion method, are implemented to extract diverse explicit solutions for both models. These analytical results are further supported by 2D and 3D plots. The obtained findings reveal distinct physical structures for the Joseph-Egri and its modified counterparts. Specifically, the Joseph-Egri equation supports cusp soliton, bell-shaped soliton, and periodic concave-pattern solutions, while the modified Joseph-Egri equation admits kink soliton, periodic kink-pattern, and periodic concave-convex wave solutions. We believe the reported results will contribute to a deeper understanding of the synchronized propagation of bidirectional waves in various nonlinear media and related physical applications.

Joseph和Egri修改了标准的Korteweg-de Vries方程，将其三阶空间色散项替换为时空色散项，旨在调整波速并保持频率稳定性。目前这项研究的目的是双重的。首先，它证明了Joseph-Egri方程表现出与Boussinesq模型相似的动力学行为，特别是在同步非对称双波结构的传播中。其次，在Korteweg-de Vries方程和Benjamin-Bona-Mahony方程的类似修正的启发下，提出并研究了Joseph-Egri方程的修正扩展。采用三角和双曲有理函数法、扩展tanh-coth展开法等有效的方法来提取两种模型的多种显式解。这些分析结果进一步得到了二维和三维图的支持。所获得的发现揭示了不同的物理结构，约瑟夫- egri和其改良的同类。其中，Joseph-Egri方程支持尖孤子、钟形孤子和周期凹型解，而改进的Joseph-Egri方程支持扭结孤子、周期扭结孤子和周期凹凸波解。我们相信报告的结果将有助于深入理解各种非线性介质中双向波的同步传播及其相关的物理应用。

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引用次数: 0

Caputo approach to transmission dynamics of paragonimiasis in humans, snails, and crustaceans 人类、蜗牛和甲壳类动物中吸虫病传播动力学的卡普托方法

Q1 Mathematics

Partial Differential Equations in Applied Mathematics

Pub Date : 2025-10-24 DOI: 10.1016/j.padiff.2025.101313

Stephen Edward

Paragonimiasis, a parasitic infection caused by trematodes of the genus Paragonimus, is characterized by chronic cough, chest pain, and hemoptysis. This study introduces a novel fractional-order modelling technique to capture the impact of memory effects and control strategies on the transmission dynamics of Paragonimiasis. We develop a system of Caputo fractional differential equations supplemented with constant control measures–specifically, human treatment to reduce infection prevalence and snail molluscicide to target intermediate hosts. We analyze the fundamental properties of the model, including positivity, boundedness, existence, and uniqueness of solutions. Local stability of equilibrium states is investigated via Routh’s criterion, while Ulam-Hyer’s stability concepts confirm global stability. Numerical solutions obtained through the Adams-Bashforth-Moulton predictor-corrector method highlight the considerable influence of memory on disease progression. The results underscore the importance of integrating memory effects into control strategies: enhanced human treatment combined with improved snail molluscicide can significantly mitigate infection levels. These findings suggest that fractional derivatives offer a flexible, detailed lens for examining nonlocal disease dynamics processes and refining practical intervention approaches.

吸虫病是由吸虫病属吸虫引起的一种寄生虫感染，其特征是慢性咳嗽、胸痛和咯血。本研究引入了一种新的分数阶建模技术，以捕捉记忆效应和控制策略对肺吸虫病传播动力学的影响。我们开发了一个卡普托分数阶微分方程系统，辅以恒定的控制措施-具体来说，人类治疗以减少感染流行，并针对中间宿主使用杀螺剂。我们分析了该模型的基本性质，包括解的正性、有界性、存在性和唯一性。通过Routh准则研究了平衡态的局部稳定性，而Ulam-Hyer稳定性概念证实了平衡态的全局稳定性。通过Adams-Bashforth-Moulton预测校正方法获得的数值解突出了记忆对疾病进展的重要影响。结果强调了将记忆效应整合到控制策略中的重要性：强化人类治疗结合改良的蜗牛杀螺剂可以显著降低感染水平。这些发现表明，分数衍生物为检查非局部疾病动力学过程和改进实际干预方法提供了灵活、详细的视角。

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引用次数: 0

Intrinsic dynamics of lumps and multi-soliton solutions to the higher dimensional Boussinesq model 块的内在动力学和高维Boussinesq模型的多孤子解

Q1 Mathematics

Partial Differential Equations in Applied Mathematics

Pub Date : 2025-10-21 DOI: 10.1016/j.padiff.2025.101320

M. Belal Hossen , Md. Towhiduzzaman , Mst. Shekha Khatun , Harun-Or- Roshid , Md. Amanat Ullah

This research investigates diverse wave behaviors of innovative higher dimensional Boussinesq model (BM) based on Hirota bi-linear technique. From this, firstly we derive lump and multiple soliton solutions. The study explores various dynamic behaviors, including interactions involving one up to four solitons. Additionally, the study analyzes breather waves, twofold periodic wave, periodic line lump wave, and the interactions among bell solitons. Other interactions analyze include lump wave with periodic wave, 1-stripe soliton and 2-stripe solitons. Many of these dynamic properties not yet explored in previous research. The trajectories of these solutions are visualized using Maple software, providing deeper insights into the model's dynamical behavior.

本文研究了基于Hirota双线性技术的创新型高维Boussinesq模型（BM）的多种波动行为。在此基础上，首先导出了整体解和多孤子解。该研究探索了各种动态行为，包括涉及一个到四个孤子的相互作用。此外，研究还分析了呼吸波、双周期波、周期线块状波以及钟孤子之间的相互作用。其他相互作用的分析包括块波与周期波、1条孤子和2条孤子。许多这些动态特性在以前的研究中尚未被探索。这些解决方案的轨迹使用Maple软件可视化，提供对模型动态行为的更深入的见解。

引用次数: 0

Construction of an infinite-dimensional family of exact solutions of the Klein–Gordon equation by the hypercomplex method 用超复方法构造Klein-Gordon方程无穷维精确解族

Q1 Mathematics

Partial Differential Equations in Applied Mathematics

Pub Date : 2025-10-20 DOI: 10.1016/j.padiff.2025.101312

Vitalii Shpakivskyi

The Klein–Gordon equation is one of the fundamental equations of mathematical physics. Therefore, it is important to have exact solutions to this equation. There are many methods for constructing exact solutions to the Klein–Gordon equation. Naturally, that different methods give different exact solutions. In this paper, by the hypercomplex method, we construct an infinite-dimensional new family of exact solutions of the polynomial–exponential type to the Klein–Gordon equation.

克莱恩-戈登方程是数学物理的基本方程之一。因此，得到这个方程的精确解是很重要的。有许多方法可以构造Klein-Gordon方程的精确解。当然，不同的方法给出不同的精确解。本文利用超复方法，构造了Klein-Gordon方程的无穷维多项式-指数型精确解族。

引用次数: 0