Partial Differential Equations in Applied Mathematics最新文献_第3页

An investigation of novel closed form soliton solutions of the space-time fractional nonlinear Schrödinger model in optical fibers 光纤中时空分数阶非线性Schrödinger模型新颖闭型孤子解的研究

Partial Differential Equations in Applied Mathematics Pub Date : 2026-03-01 Epub Date: 2025-12-11 DOI: 10.1016/j.padiff.2025.101328

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

{"title":"An investigation of novel closed form soliton solutions of the space-time fractional nonlinear Schrödinger model in optical fibers","authors":"M. Nurul Islam , M. Al-Amin , M. Ali Akbar","doi":"10.1016/j.padiff.2025.101328","DOIUrl":"10.1016/j.padiff.2025.101328","url":null,"abstract":"<div><div>In this study, we examine the conformal space-time fractional nonlinear Schrödinger (NLS) model and derive several new closed-form optical soliton solutions using an interoperable auxiliary-equation method. By applying a fractional wave transformation, the original model is converted into a nonlinear equation formulated in terms of conventional derivatives. The NLS model serves as an essential framework for characterizing wave propagation in nonlinear optical media, accounting for the factors that influence signal integrity and data transmission in optical fiber networks. For this model, we obtain new exact soliton solutions expressed through exponential, trigonometric, hyperbolic, and rational function forms. These optical soliton solutions are then employed to analyze how various model parameters affect their behavior, with numerical simulations carried out in Wolfram Mathematica. The numerical simulations of the derived solutions reveal periodic, kink-type, singular periodic, and other soliton-like behaviors. The findings indicate that the proposed method is both robust and efficient, making it a valuable tool for deriving optical soliton solutions in other fractional nonlinear models, especially those relevant to optical fiber communication systems.</div></div>","PeriodicalId":34531,"journal":{"name":"Partial Differential Equations in Applied Mathematics","volume":"17 ","pages":"Article 101328"},"PeriodicalIF":0.0,"publicationDate":"2026-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145791938","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

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

Partial Differential Equations in Applied Mathematics Pub Date : 2026-03-01 Epub Date: 2025-12-10 DOI: 10.1016/j.padiff.2025.101331

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

{"title":"An improved modified simplest equation method for exact solitary wave solutions of the three-dimensional nonlinear fractional wazwaz-benjamin-bona-mahony model","authors":"M. Al-Amin , M.Nurul Islam , M.Ali Akbar","doi":"10.1016/j.padiff.2025.101331","DOIUrl":"10.1016/j.padiff.2025.101331","url":null,"abstract":"<div><div>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 <span><math><mrow><mtext>exp</mtext><mo>(</mo><mrow><mo>−</mo><mi>ϕ</mi><mo>(</mo><mi>ω</mi><mo>)</mo></mrow><mo>)</mo></mrow></math></span>-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.</div></div>","PeriodicalId":34531,"journal":{"name":"Partial Differential Equations in Applied Mathematics","volume":"17 ","pages":"Article 101331"},"PeriodicalIF":0.0,"publicationDate":"2026-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145792018","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

Darcy-forchheimer bioconvection flow of nanofluid with thermophoretic effects and nonlinear thermal radiation 具有热泳效应和非线性热辐射的纳米流体的Darcy-forchheimer生物对流

Partial Differential Equations in Applied Mathematics Pub Date : 2026-03-01 Epub Date: 2026-01-24 DOI: 10.1016/j.padiff.2026.101340

M.Z. Kiyani , A. Aeman , Sami Ullah Khan , Farkhod Rakhmonov , Mirjalol Ismoilov , M. Ijaz Khan

引用次数: 0

Heat generation effect on 3D MHD flow of Casson fluid via stretching/shrinking surface with velocity slip Condition 速度滑移条件下卡森流体拉伸/收缩表面三维MHD流动产热效应

Partial Differential Equations in Applied Mathematics Pub Date : 2026-03-01 Epub Date: 2026-02-11 DOI: 10.1016/j.padiff.2026.101343

B. Jagadeesh Kumar, Nainaru Tarakaramu

引用次数: 0

Spinor solitons in one-dimensional and planar nonlinear Dirac equations 一维及平面非线性狄拉克方程中的旋量孤子

Partial Differential Equations in Applied Mathematics Pub Date : 2026-03-01 Epub Date: 2025-12-13 DOI: 10.1016/j.padiff.2025.101329

Realeboga Dikole

引用次数: 0

Lie symmetry and memory-driven dynamics of a (2+1)-dimensional time-fractional nonlinear wave equation in memory media 存储介质中（2+1）维时间分数阶非线性波动方程的Lie对称性和记忆驱动动力学

Partial Differential Equations in Applied Mathematics Pub Date : 2026-03-01 Epub Date: 2026-02-14 DOI: 10.1016/j.padiff.2026.101347

Faiza Arif , Adil Jhangeer , F.D. Zaman , F.M. Mahomed

{"title":"Lie symmetry and memory-driven dynamics of a (2+1)-dimensional time-fractional nonlinear wave equation in memory media","authors":"Faiza Arif , Adil Jhangeer , F.D. Zaman , F.M. Mahomed","doi":"10.1016/j.padiff.2026.101347","DOIUrl":"10.1016/j.padiff.2026.101347","url":null,"abstract":"<div><div>In the present work, we focus on discussing detailed analysis and important features of a (2+1)-dimensional nonlinear time-fractional diffusion-wave equation. The equation models wave phenomena in materials where memory effects play an important role, for example porous mediums and viscoelastic structures. We use the Lie symmetry methods together with the traveling wave reductions to obtain the exact solutions. Some of the solutions are expressed using special functions, like the Mittag-Leffler function and the Lambert <em>W</em> function. These functions describe the role of nonlinearity and fractional-order temporal damping on wave propagation. The graphical representation of the solutions suggest that the parameter <em>α</em> more or less dictates the behavior of the wave by affecting its concentration in space, decay rate, and speed at which it propagates. Further, the system correspond to distinct physical behaviors depending on different values of <em>α</em>, for example, sub-diffusive (0 < <em>α</em> < 1), diffusive <span><math><mrow><mo>(</mo><mi>α</mi><mo>=</mo><mn>1</mn><mo>)</mo></mrow></math></span>, or wave-like motion with memory effects (1 < <em>α</em> ≤ 2). From these observation, it becomes clear that the dynamics of the system strongly gets affected when fractional memory combines with nonlinearity. This effect may have possible applications in modeling transportation processes as well as viscoelastic wave propagation arising in biological systems and porous materials.</div></div>","PeriodicalId":34531,"journal":{"name":"Partial Differential Equations in Applied Mathematics","volume":"17 ","pages":"Article 101347"},"PeriodicalIF":0.0,"publicationDate":"2026-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147397038","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

Exact difference approach on the Shishkin mesh for solving time fractional singularly perturbed parabolic PDE 求解时间分数阶奇摄动抛物型偏微分方程的Shishkin网格精确差分法

Partial Differential Equations in Applied Mathematics Pub Date : 2026-03-01 Epub Date: 2026-02-13 DOI: 10.1016/j.padiff.2026.101344

Mesfin Mekuria Woldaregay, Tibebu Worku Hunde

引用次数: 0

Promoted analytical solutions of conformable Ginzburg-Landau applied in Bose-Einstein condensate with external potentials 具有外部势的玻色-爱因斯坦凝聚体中可调金兹堡-朗道的提升解析解

Partial Differential Equations in Applied Mathematics Pub Date : 2026-03-01 Epub Date: 2026-02-13 DOI: 10.1016/j.padiff.2026.101345

Shaher Momani , Fatimah Noor Harun , Rasha Amryeen , Shrideh Al-Omari , Mohammed Al-Smadi

{"title":"Promoted analytical solutions of conformable Ginzburg-Landau applied in Bose-Einstein condensate with external potentials","authors":"Shaher Momani , Fatimah Noor Harun , Rasha Amryeen , Shrideh Al-Omari , Mohammed Al-Smadi","doi":"10.1016/j.padiff.2026.101345","DOIUrl":"10.1016/j.padiff.2026.101345","url":null,"abstract":"<div><div>This work concerns the construction of the approximate analytical solutions for the nonlinear complex conformable Ginzburg-Landau equations with external potential using the conformable residual series method. The governing model plays a pivotal role in modeling complex physical phenomena such as Bose-Einstein condensation and building approximate analytical solutions for this model, which is considered a distinctive addition given the scarcity of work presented in the literature in this context. The methodology lies in combines of generalized multivariable power series and residual error function. Convergence analysis is provided to illustrate the theoretical framework of our scheme in handling the projected nonlinear models. For a sake of practical computation, several naturalistic applications for Bose-Einstein condensates are examined involving zero trapping, periodic box, optical lattice, and harmonic potentials. In this orientation, numeric computations and graphical representations are provided to verify the correctness and accuracies of the tested applications. The dynamic behaviors of wave soliton solutions are captured at different parameters in addition to the comparison of acquired wave solutions with previous studies. The overall impact of this work lies in the ease with which the proposed approach can be applied to construct efficient and systematic approximate analytical solutions for complex nonlinear partial differential equations arising in quantum optics, quantum gases, quantum fluids, and other quantum mechanical phenomena.</div></div>","PeriodicalId":34531,"journal":{"name":"Partial Differential Equations in Applied Mathematics","volume":"17 ","pages":"Article 101345"},"PeriodicalIF":0.0,"publicationDate":"2026-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147397042","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

Retraction Notice to “Heat and mass transfer analysis of Williamson nanofluids under the influence of magnetic field and Joule's heating” [Partial Differential Equations in Applied Mathematics 13 (2025) 101148] “磁场和焦耳加热影响下Williamson纳米流体的传热传质分析”的撤回通知[应用数学偏微分方程13 (2025)101148]

Partial Differential Equations in Applied Mathematics Pub Date : 2026-03-01 Epub Date: 2026-03-06 DOI: 10.1016/j.padiff.2026.101349

Sharanayya Swami , Suresh Biradar , Jagadish V. Tawade , Nitiraj V. Kulkarni , Barno Sayfutdinovna Abdullaeva , Dana Mohammad Khidhir , Nadia Batool , Taoufik Saidani

引用次数: 0

Retraction Notice to “Analysis of MHD radiative flow of ternary hybrid nanofluid over a porous stretching surface” [Partial Differential Equations in Applied Mathematics 15 (2025) 101267] “三元混合纳米流体在多孔拉伸表面上的MHD辐射流分析”的撤回通知[应用数学偏微分方程15 (2025)101267]

Partial Differential Equations in Applied Mathematics Pub Date : 2026-03-01 Epub Date: 2026-03-07 DOI: 10.1016/j.padiff.2026.101350

Shital Sobale , Jagadish V. Tawade , Pooja Bagane , Vediyappn Govindan , Barno Abdullaeva , Hawzhen Fateh M. Ameen , Manish Gupta , Nadia Batool

引用次数: 0