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

Pseudo-planar deformations of a linearized elastic solid 线性化弹性固体的拟平面变形

Partial Differential Equations in Applied Mathematics Pub Date : 2025-09-10 DOI: 10.1016/j.padiff.2025.101301

E. Momoniat , C. Harley

{"title":"Pseudo-planar deformations of a linearized elastic solid","authors":"E. Momoniat , C. Harley","doi":"10.1016/j.padiff.2025.101301","DOIUrl":"10.1016/j.padiff.2025.101301","url":null,"abstract":"<div><div>The equations of motion for the pseudo-planar motions of a classical linearized elastic solid and an incompressible linearized elastic solid undergoing non-uniform rotation about a vertical axis are derived. The pseudo-planar motions for both a classical linearized and an incompressible linearized elastic solid are determined numerically. For a classical linearized elastic solid, the non-uniform rotation is time-dependent and is specified. We derive a wave equation that models the non-uniform rotation for an incompressible linearized elastic solid. A pressure Poisson equation is derived and depends on the time derivative of the non-uniform rotation. The locus of the equations of motion coupled with the pseudo-planar motions of a cylindrical solid are plotted and the results are discussed. We show that the pseudo-planar motions of a classical linearized elastic solid with zero rotation are translations of the pseudo-planes about the locus. The pseudo-plane motions for classical and incompressible linearized elastic solids undergo translations and rotations about the locus. The motions are bound and stable when the pressure is symmetric. Unsymmetric pressure, which is just the mechanical pressure, results in a distortion of the pseudo-planar curves.</div></div>","PeriodicalId":34531,"journal":{"name":"Partial Differential Equations in Applied Mathematics","volume":"16 ","pages":"Article 101301"},"PeriodicalIF":0.0,"publicationDate":"2025-09-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145107802","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Dynamic complexity in fractional multispecies ecological systems: A Caputo derivative approach 分数多物种生态系统的动态复杂性：卡普托导数方法

Partial Differential Equations in Applied Mathematics Pub Date : 2025-09-10 DOI: 10.1016/j.padiff.2025.101293

Sonal Jain , Kolade M. Owolabi , Edson Pindza , Eben Mare

{"title":"Dynamic complexity in fractional multispecies ecological systems: A Caputo derivative approach","authors":"Sonal Jain , Kolade M. Owolabi , Edson Pindza , Eben Mare","doi":"10.1016/j.padiff.2025.101293","DOIUrl":"10.1016/j.padiff.2025.101293","url":null,"abstract":"<div><div>In this study, a novel implicit numerical approach is introduced by combining finite-difference techniques with innovative L1 schemes. This method is designed to solve time-fractional reaction–diffusion systems occurring in one and two dimensions. Specifically, the focus is on ecological systems with mixed boundary conditions, which are commonly found in biological and chemical processes. This research focuses on the spatiotemporal behavior of a predator–prey model with a Holling III functional response, taking into account the presence of prey refuges. This study revealed that this model does not exhibit a Turing pattern, which is typically associated with diffusion-driven instability. Consequently, this investigation explored alternative non-Turing patterns using extensive numerical simulations. In scenarios involving two-dimensional subdiffusion, the study observed a variety of spatiotemporal dynamics within the diffusive prey–predator model. When prey refuge availability was low, the system displayed a circular pattern that gradually expanded over time to encompass the entire spatial domain. As the availability of refugees decreased, the system transitioned from a spiral to a chaotic pattern. Furthermore, the research revealed that, as the ratio of predator-to-prey diffusion rates increased, the system exhibited a subdiffusive spiral pattern, which then transformed into a spot-like pattern. Eventually, these spots merged to form stripe-like patterns as the ratio increased. This investigation highlights the rich and intricate dynamics that can emerge in fractional predator–prey interactions when considering both spatial and temporal factors. To further confirm the complexity of the dynamical behaviors, Lyapunov exponents were estimated numerically.</div></div>","PeriodicalId":34531,"journal":{"name":"Partial Differential Equations in Applied Mathematics","volume":"16 ","pages":"Article 101293"},"PeriodicalIF":0.0,"publicationDate":"2025-09-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145048529","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Building novel solitary wave solutions for the generalized non-linear (3+1)-dimensional wave equation with gas bubbles in fluids using an analytic method 用解析法建立流体中含气泡的广义非线性（3+1）维波动方程的孤波解

Partial Differential Equations in Applied Mathematics Pub Date : 2025-09-08 DOI: 10.1016/j.padiff.2025.101272

Abeer S. Khalifa , Niveen M. Badra , Hamdy M. Ahmed , Wafaa B. Rabie , Homan Emadifar , Karim K. Ahmed

{"title":"Building novel solitary wave solutions for the generalized non-linear (3+1)-dimensional wave equation with gas bubbles in fluids using an analytic method","authors":"Abeer S. Khalifa , Niveen M. Badra , Hamdy M. Ahmed , Wafaa B. Rabie , Homan Emadifar , Karim K. Ahmed","doi":"10.1016/j.padiff.2025.101272","DOIUrl":"10.1016/j.padiff.2025.101272","url":null,"abstract":"<div><div>This article investigates the generalized nonlinear (3+1)-dimensional wave equation using an analytical technique — the Extended F-expansion method — to derive a variety of exact wave solutions and analyze the dynamic behavior of distinct wave profiles. The study presents several types of soliton solutions, including dark, bright, singular, periodic, and singular periodic forms. To the best of our knowledge, these specific solutions have not been previously reported in the literature. By assigning appropriate values to the free parameters, the behavior of the obtained solutions is illustrated through two- and three-dimensional plots, as well as corresponding contour diagrams. The proposed analytical method not only contributes to the theoretical understanding of nonlinear wave phenomena but also demonstrates practical relevance in applied sciences, particularly in fluid mechanics and engineering contexts involving gas-liquid interactions.</div></div>","PeriodicalId":34531,"journal":{"name":"Partial Differential Equations in Applied Mathematics","volume":"16 ","pages":"Article 101272"},"PeriodicalIF":0.0,"publicationDate":"2025-09-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145061380","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Exploring solitary wave structures and bifurcation dynamics in the (2+1)-dimensional generalized Hietarinta equation 探索（2+1）维广义Hietarinta方程中的孤波结构和分岔动力学

Partial Differential Equations in Applied Mathematics Pub Date : 2025-09-08 DOI: 10.1016/j.padiff.2025.101283

Yeşim Sağlam Özkan , Esra Ünal Yılmaz

{"title":"Exploring solitary wave structures and bifurcation dynamics in the (2+1)-dimensional generalized Hietarinta equation","authors":"Yeşim Sağlam Özkan , Esra Ünal Yılmaz","doi":"10.1016/j.padiff.2025.101283","DOIUrl":"10.1016/j.padiff.2025.101283","url":null,"abstract":"<div><div>This study investigates the <span><math><mrow><mo>(</mo><mn>2</mn><mo>+</mo><mn>1</mn><mo>)</mo></mrow></math></span>-dimensional generalized Hietarinta equation, which models the propagation of waves on water surfaces in the presence of gravity and surface tension. Solitary wave solutions are obtained using the <span><math><mrow><mi>e</mi><mi>x</mi><mi>p</mi><mrow><mo>(</mo><mo>−</mo><mi>w</mi><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow><mo>)</mo></mrow></mrow></math></span> method and the <span><math><mi>F</mi></math></span>-expansion method, and are expressed in terms of hyperbolic, trigonometric, exponential and rational functions. Two- and three-dimensional plots illustrate various wave structures, such as dark, kinked, and singular kinked waves, highlighting their dynamic behaviors under different parameter settings. Hamiltonian functions and bifurcation theory are employed to analyze phase portraits and nonlinear wave dynamics, including chaotic behavior. Numerical simulations has been conducted using Mathematica and Maple confirm the theoretical findings. Additionally, the results have been compared with other existing results in the literature to show their uniqueness. The proposed techniques are effective, computationally efficient and reliable. In this context, considering previous studies, the findings of this research contribute to the existing literature.</div></div>","PeriodicalId":34531,"journal":{"name":"Partial Differential Equations in Applied Mathematics","volume":"16 ","pages":"Article 101283"},"PeriodicalIF":0.0,"publicationDate":"2025-09-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145044691","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

A study on intuitionistic fuzzy neutral functional integro-differential PDEs with impulses 带有脉冲的直觉模糊中立泛函积分微分偏微分方程的研究

Partial Differential Equations in Applied Mathematics Pub Date : 2025-09-01 DOI: 10.1016/j.padiff.2025.101296

T. Gunasekar , K. Nithyanandhan , Hanumagowda B. N , Jagadish V. Tawade , Nashwan Adnan Othman , Barno Abdullaeva , Nadia Batool , Khayrilla Kurbonov

{"title":"A study on intuitionistic fuzzy neutral functional integro-differential PDEs with impulses","authors":"T. Gunasekar , K. Nithyanandhan , Hanumagowda B. N , Jagadish V. Tawade , Nashwan Adnan Othman , Barno Abdullaeva , Nadia Batool , Khayrilla Kurbonov","doi":"10.1016/j.padiff.2025.101296","DOIUrl":"10.1016/j.padiff.2025.101296","url":null,"abstract":"<div><div>This paper investigates the existence and uniqueness of solutions for a nonlocal intuitionistic fuzzy impulsive integro-differential equation, employing intuitionistic fuzzy semigroups and the contraction mapping principle. Through a systematic theoretical framework, it establishes that, under certain conditions, a distinct solution is ensured. Additionally, the study expands its analysis to explore the existence results for intuitionistic fuzzy impulsive neutral integro-differential equations, broadening its research focus. This approach introduces a new perspective on understanding intuitionistic fuzzy integro-differential equations, introducing innovative methodologies and significant discoveries that advance theoretical exploration in this field. The findings underscore that, subject to specific assumptions, a singular fuzzy solution emerges for these problems marked by nonlocal conditions, effectively addressing crucial challenges in the analysis of fuzzy systems.</div></div>","PeriodicalId":34531,"journal":{"name":"Partial Differential Equations in Applied Mathematics","volume":"15 ","pages":"Article 101296"},"PeriodicalIF":0.0,"publicationDate":"2025-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144931557","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Machine learning analysis of tangent hyperbolic nanofluid with radiation and Arrhenius activation energy over falling cone under gravity 重力作用下落锥上具有辐射和Arrhenius活化能的正切双曲纳米流体的机器学习分析

Partial Differential Equations in Applied Mathematics Pub Date : 2025-09-01 DOI: 10.1016/j.padiff.2025.101280

Muhammad Zubair , Hamid Qureshi , Usman Khaliq , Taoufik Saidani , Waqar Azeem Khan

{"title":"Machine learning analysis of tangent hyperbolic nanofluid with radiation and Arrhenius activation energy over falling cone under gravity","authors":"Muhammad Zubair , Hamid Qureshi , Usman Khaliq , Taoufik Saidani , Waqar Azeem Khan","doi":"10.1016/j.padiff.2025.101280","DOIUrl":"10.1016/j.padiff.2025.101280","url":null,"abstract":"<div><div>This study is a machine learning investigation of the advance level nanofluidic coolant through a cone in a two-dimensional transitory boundary layer. The model accounts for both radiation absorption and the Arrhenius activation energy. Synthetic datasets from governing mathematical model are used in Artificial Intelligence (AI) based Levenberg Marquardt Back Propagation algorithm (LM-BP). Multiple scenarios of Tangent Hyperbolic Nanofluidic (THNF) coolant are framed with variation of influencing characteristics like Magnetic field <em>M</em>, power law index <em>n</em>, permeability <em>k</em>, Radiation absorption <em>Q</em>, Prandtl ratio <em>Pr</em>, Brownian motion <em>Nb</em>, Lewis number <em>Le</em> and Chemical reaction parameter γ. Convergence parameters of AI-based feed routing Neural Network computing is presented through graphs and numerical tables. Results indicate that flow slows when the Lorentz force and surface permeability grow, but it gets stronger when thermal absorption and momentum to thermal diffusivity ratio Pr increase. Meanwhile, the temperature increases when thermal absorption rises and drops when thermal to mass diffusivity ratio Le increases so that temperature falls for greater chemical reaction influence.</div></div>","PeriodicalId":34531,"journal":{"name":"Partial Differential Equations in Applied Mathematics","volume":"15 ","pages":"Article 101280"},"PeriodicalIF":0.0,"publicationDate":"2025-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144920092","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Local dynamics of second-order differential equation with delayed derivative 二阶时滞微分方程的局部动力学

Partial Differential Equations in Applied Mathematics Pub Date : 2025-09-01 DOI: 10.1016/j.padiff.2025.101281

Ilia Kashchenko, Igor Maslenikov

{"title":"Local dynamics of second-order differential equation with delayed derivative","authors":"Ilia Kashchenko, Igor Maslenikov","doi":"10.1016/j.padiff.2025.101281","DOIUrl":"10.1016/j.padiff.2025.101281","url":null,"abstract":"<div><div>We study the nonlinear dynamics of second-order differential equation with delayed feedback depending on the derivative. The problem in question contains a small multiplier at the highest derivative, so it is singularly perturbed. We determine the stability of equilibrium depending on the parameters and find critical (bifurcation) cases. In each critical case, asymptotic approximations for the spectrum points (roots of the characteristic equation) are determined. The main feature of the problem under consideration is that in critical cases the spectrum consists of two parts: an infinite chain of points that tend to the imaginary axis and one or two more points located near the imaginary axis.</div><div>Using methods of asymptotic analysis to study bifurcations, in the critical cases we construct special equations – quasinormal forms. Quasinormal form is an analog of normal form. It does not depends on small parameter and its solutions provide the main part of the asymptotic approximation of the solutions of the original problem. Each quasinormal form is a partial differential equation with an antiderivative operator and integral term in nonlinearity. For the constructed forms stable periodic solutions are determined, asymptotic approximations on stable periodic solutions of original problem is obtained and the bifurcations that occur are described.</div><div>Also, the situation where two successive bifurcations occur in the system was described.</div></div>","PeriodicalId":34531,"journal":{"name":"Partial Differential Equations in Applied Mathematics","volume":"15 ","pages":"Article 101281"},"PeriodicalIF":0.0,"publicationDate":"2025-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144987919","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Asymptotic behavior of dark multi-solitons to the intermediate nonlinear Schrödinger equation 暗多孤子对中间非线性Schrödinger方程的渐近行为

Partial Differential Equations in Applied Mathematics Pub Date : 2025-09-01 DOI: 10.1016/j.padiff.2025.101273

Takafumi Akahori

引用次数: 0

Investigating traveling wave structures in the van der Waals normal form for fluidized granular matter through the modified S-expansion method 用改进的s -膨胀法研究流化颗粒物质范德华范式的行波结构

Partial Differential Equations in Applied Mathematics Pub Date : 2025-09-01 DOI: 10.1016/j.padiff.2025.101285

Hamida Parvin , Md. Nur Alam , Md. Abdullah Bin Masud , Md. Jakir Hossen

{"title":"Investigating traveling wave structures in the van der Waals normal form for fluidized granular matter through the modified S-expansion method","authors":"Hamida Parvin , Md. Nur Alam , Md. Abdullah Bin Masud , Md. Jakir Hossen","doi":"10.1016/j.padiff.2025.101285","DOIUrl":"10.1016/j.padiff.2025.101285","url":null,"abstract":"<div><div>This research discovers traveling wave solutions (TWSs) of the van der Waals normal form for fluidized granular matter using the modified S-expansion (MS-E) method. The model captures key behaviors such as phase transitions, clustering, and shock structures in granular flows. Applying a traveling wave transformation reduces the governing equation to a nonlinear ordinary differential equation (NODE), enabling the construction of TWSs relevant to geophysical and industrial applications. The MS-E technique is implemented to systematically derive TWSs—such as kink, bright, and dark solitons—that model density waves, shock fronts, and clustering in granular media. Comprehensive 2D, 3D, and contour plots are presented to validate and visualize the results, offering insights into wave behavior and soliton stability. This work highlights the MS-E method as a powerful tool for solving nonlinear integral and fractional partial differential equations (NLIFPDEs), with broad applications in granular physics, fluid mechanics, plasma waves, and nonlinear optics. This experiment offers a novel procedure to explore additional compound nonlinear wave phenomena by integrating the MS-E method, opening novel opportunities for additional expansions in soliton-driven knowledge. This method offers a promising pathway for future researchers to explore closed-form traveling wave solutions of other NLIFPDEs.</div></div>","PeriodicalId":34531,"journal":{"name":"Partial Differential Equations in Applied Mathematics","volume":"15 ","pages":"Article 101285"},"PeriodicalIF":0.0,"publicationDate":"2025-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145018631","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Mathematical analysis of novel soliton solutions of the space-time fractional Chen-Lee-Liu model in optical fibers communication systems 光纤通信系统中时空分数陈-李-刘模型新孤子解的数学分析

Partial Differential Equations in Applied Mathematics Pub Date : 2025-09-01 DOI: 10.1016/j.padiff.2025.101295

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

{"title":"Mathematical analysis of novel soliton solutions of the space-time fractional Chen-Lee-Liu model in optical fibers communication systems","authors":"M. Nurul Islam , M. Al-Amin , M. Ali Akbar","doi":"10.1016/j.padiff.2025.101295","DOIUrl":"10.1016/j.padiff.2025.101295","url":null,"abstract":"<div><div>The space-time fractional Chen-Lee-Liu (CLL) model is a significant optical fiber model utilized to analyze the performance of communication systems in optical fibers. It studies numerous features that may have impacts on the data transmission rates and signal excellence in optical fibers networks, nonlinearity, and noise. By developing this model, the engineers and researchers can optimize the design and performance in optical fiber communication systems. The optical solitons pulses of the CLL model are the fundamental construction block of soliton transmission technology, the telecommunication sector, and data transfer of optical fiber. In this study, we establish the significant soliton solutions which can be functional in optics of the stated model through the beta derivative employing the generalized exponential rational function technique (GERFT) which are not been investigated in the recent literature. The numerical simulations of the establishing solitons illustrates the bell-shaped, periodic, and some other soliton-like feature sand the examined shapes show the structure and influence of the fractional parameters. The results of this study exhibits that the implemented technique is efficient, reliable, and capable of establishing solutions to other complex nonlinear models in optical fiber communication systems.</div></div>","PeriodicalId":34531,"journal":{"name":"Partial Differential Equations in Applied Mathematics","volume":"15 ","pages":"Article 101295"},"PeriodicalIF":0.0,"publicationDate":"2025-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144996471","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0