Mathematical Methods in the Applied Sciences最新文献

{"title":"On the Periodic Cauchy Problem for the \u0000 \u0000 μ\u0000 -Modified Camassa-Holm-Novikov Type Equation","authors":"Li Yang,&nbsp;Hongli Sun,&nbsp;Shanshan Zheng","doi":"10.1002/mma.70953","DOIUrl":"https://doi.org/10.1002/mma.70953","url":null,"abstract":"<div>\u0000 \u0000 <p>This paper delves into the intricate periodic Cauchy problem associated with the <span></span><math>\u0000 <mrow>\u0000 <mi>μ</mi>\u0000 </mrow></math>-modified Camassa-Holm-Novikov equation. We first rigorously demonstrate that the occurrence of blow-up phenomena in this equation is exclusively manifested through the formation of breaking waves and elucidate a comprehensive wave-breaking mechanism of the solutions under certain initial data conditions. Subsequently, the existence of peaked travelling wave solutions is established, thereby enriching the understanding of the dynamical behavior of this remarkable equation. Finally, it is shown that the data-to-solution map <span></span><math>\u0000 <mrow>\u0000 <msub>\u0000 <mrow>\u0000 <mi>u</mi>\u0000 </mrow>\u0000 <mrow>\u0000 <mn>0</mn>\u0000 </mrow>\u0000 </msub>\u0000 <mo>↦</mo>\u0000 <mi>u</mi>\u0000 </mrow></math> is Hölder continuous in the <span></span><math>\u0000 <mrow>\u0000 <msup>\u0000 <mrow>\u0000 <mi>H</mi>\u0000 </mrow>\u0000 <mrow>\u0000 <mi>r</mi>\u0000 </mrow>\u0000 </msup>\u0000 </mrow></math>, with <span></span><math>\u0000 <mrow>\u0000 <mi>r</mi>\u0000 <mo>∈</mo>\u0000 <mo>[</mo>\u0000 <mn>1</mn>\u0000 <mo>,</mo>\u0000 <mi>s</mi>\u0000 <mo>)</mo>\u0000 </mrow></math>.</p>\u0000 </div>","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":"49 17","pages":"17848-17872"},"PeriodicalIF":2.0,"publicationDate":"2026-11-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149311751","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Fragmentation–Coagulation Processes With Advection or Diffusion in Space","authors":"Jacek Banasiak,&nbsp;Nduduzo Majozi","doi":"10.1002/mma.70956","DOIUrl":"https://doi.org/10.1002/mma.70956","url":null,"abstract":"&lt;p&gt;In this paper, we consider a continuous fragmentation–coagulation model in which the reacting particles can be transported in physical space through either advection or diffusion. We prove new results on the generation of &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;mrow&gt;\u0000 &lt;msub&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;C&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mn&gt;0&lt;/mn&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/msub&gt;\u0000 &lt;/mrow&gt;&lt;/math&gt;-semigroups with parameter and use them to show that the abstract Cauchy problem associated with a more general version of the advection/diffusion–fragmentation problem generates a positive &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;mrow&gt;\u0000 &lt;msub&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;C&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mn&gt;0&lt;/mn&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/msub&gt;\u0000 &lt;/mrow&gt;&lt;/math&gt;-semigroup in spaces &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;mrow&gt;\u0000 &lt;msub&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;L&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mn&gt;1&lt;/mn&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/msub&gt;\u0000 &lt;mo&gt;(&lt;/mo&gt;\u0000 &lt;msub&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;ℝ&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mo&gt;+&lt;/mo&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/msub&gt;\u0000 &lt;mo&gt;,&lt;/mo&gt;\u0000 &lt;msub&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;X&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;x&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/msub&gt;\u0000 &lt;mo&gt;,&lt;/mo&gt;\u0000 &lt;mo&gt;(&lt;/mo&gt;\u0000 &lt;mn&gt;1&lt;/mn&gt;\u0000 &lt;mo&gt;+&lt;/mo&gt;\u0000 &lt;msup&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;m&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;r&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/msup&gt;\u0000 &lt;mo&gt;)&lt;/mo&gt;\u0000 &lt;mi&gt;d&lt;/mi&gt;\u0000 &lt;mi&gt;m&lt;/mi&gt;\u0000 &lt;mo&gt;)&lt;/mo&gt;\u0000 &lt;mo&gt;,&lt;/mo&gt;\u0000 &lt;/mrow&gt;&lt;/math&gt; where &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;m&lt;/mi&gt;\u0000 &lt;/mrow&gt;&lt;/math&gt; is the particle mass, &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;mrow&gt;\u0000 &lt;msub&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;X&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;x&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/msub&gt;\u0000 &lt;/mrow&gt;&lt;/math&gt; is the space of either integrable or continuous functions with respect to the spatial variable, and the weight exponent &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;r","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":"49 17","pages":"17952-17982"},"PeriodicalIF":2.0,"publicationDate":"2026-11-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/mma.70956","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149311791","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"A Qualitative Study of a Diffusive HIV/AIDS Model With Screening Effects","authors":"M. Chinnadurai,&nbsp;S. Chandru","doi":"10.1002/mma.70947","DOIUrl":"https://doi.org/10.1002/mma.70947","url":null,"abstract":"&lt;div&gt;\u0000 \u0000 &lt;p&gt;In this article, we investigated a diffusive HIV/AIDS model with the effect of screening of infectives among adults and female sex workers. In the deterministic compartmental model without spatial movement, we determined the basic reproduction number &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;mrow&gt;\u0000 &lt;msub&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;ℛ&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mn&gt;0&lt;/mn&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/msub&gt;\u0000 &lt;/mrow&gt;&lt;/math&gt; and proved the existence of disease-free and endemic equilibria. We also analyzed the long-term behavior of the system through the global stability of the model. To understand how infection fronts propagate spatially, we extended the HIV system to the reaction–diffusion model. We analyzed the properties of critical spreading speed &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;mrow&gt;\u0000 &lt;msup&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;ω&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mo&gt;∗&lt;/mo&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/msup&gt;\u0000 &lt;/mrow&gt;&lt;/math&gt;, as well as the existence of a traveling wave linking disease-free equilibrium and endemic equilibrium for &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;ω&lt;/mi&gt;\u0000 &lt;mo&gt;≥&lt;/mo&gt;\u0000 &lt;msup&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;ω&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mo&gt;∗&lt;/mo&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/msup&gt;\u0000 &lt;/mrow&gt;&lt;/math&gt; with &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;mrow&gt;\u0000 &lt;msub&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;ℛ&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mn&gt;0&lt;/mn&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/msub&gt;\u0000 &lt;mo&gt;&gt;&lt;/mo&gt;\u0000 &lt;mn&gt;1&lt;/mn&gt;\u0000 &lt;/mrow&gt;&lt;/math&gt;, and their non-existence for &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;ω&lt;/mi&gt;\u0000 &lt;mo&gt;∈&lt;/mo&gt;\u0000 &lt;mo&gt;[&lt;/mo&gt;\u0000 &lt;mn&gt;0&lt;/mn&gt;\u0000 &lt;mo&gt;,&lt;/mo&gt;\u0000 &lt;msup&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;ω&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mo&gt;∗&lt;/mo&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/msup&gt;\u0000 &lt;mo&gt;)&lt;/mo&gt;\u0000 &lt;/mrow&gt;&lt;/math&gt; with &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;mrow&gt;\u0000 &lt;msub&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;ℛ&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mn&gt;0&lt;/mn&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/msub&gt;\u0000 &lt;mo&gt;&gt;&lt;/mo&gt;\u0000 &lt;mn&gt;1&lt;/mn&gt;\u0000 &lt;/mrow&gt;&lt;/math&gt;, and for &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;ω&lt;/mi&gt;\u0000 &lt;mo&gt;&gt;&lt;/mo&gt;\u0000 &lt;mn&gt;0&lt;/mn&gt;\u0000 &lt;/mrow&gt;&lt;/math&gt; with &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;mrow&gt;\u0000 &lt;msub&gt;\u0000 &lt;mrow&gt;\u0000 ","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":"49 17","pages":"17658-17699"},"PeriodicalIF":2.0,"publicationDate":"2026-11-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149312070","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Optimal Design of Elastic Plates: Hybrid Numerical Method Based on Homogenization and Shape Derivative","authors":"Ivana Crnjac,&nbsp;Jelena Jankov Pavlović,&nbsp;Petar Kunštek","doi":"10.1002/mma.70951","DOIUrl":"https://doi.org/10.1002/mma.70951","url":null,"abstract":"<p>This paper focuses on optimal design problems in the context of the Kirchhoff-Love model for pure bending of a thin, solid, symmetric plate under a transverse load. The objective is to simultaneously determine the optimal outer shape of the domain and the distribution of two isotropic materials within the domain in order to minimize compliance. The proposed optimization strategy integrates homogenization techniques with shape optimization. The level-set function is utilized to propagate the movement of the outer boundary through a calculated shape derivative, while the interior is optimized using a known optimality criteria method for the single-state compliance minimization problem. A numerical scheme implementing this coupled approach is presented and validated through several examples. Finally, the proposed method is compared with the pure homogenization and the pure shape optimization method and is shown to yield improved performance.</p>","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":"49 17","pages":"17793-17815"},"PeriodicalIF":2.0,"publicationDate":"2026-11-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/mma.70951","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149312816","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Global Existence and Exponential Stability for 3D Nonhomogeneous Micropolar Fluid System With Density-Dependent Viscosities and Vacuum","authors":"Mingyu Zhang","doi":"10.1002/mma.70944","DOIUrl":"https://doi.org/10.1002/mma.70944","url":null,"abstract":"<div>\u0000 \u0000 <p>We consider the global well-posedness and large-time asymptotic behavior of strong solutions to the Cauchy problem of three-dimensional (3D) nonhomogeneous incompressible micropolar fluids with density-dependent viscosities and vacuum. More precisely, based on the energy method, some key a priori exponential decay-in-time rates of strong solutions are obtained in the whole space, provided that the initial velocity and initial micro-rotational velocity are suitably small in some homogeneous Sobolev space which may be optimal compared with the case of homogeneous micropolar fluid equations. Note that this result is obtained without any compatibility and smallness conditions on the initial density.</p>\u0000 </div>","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":"49 17","pages":"17627-17657"},"PeriodicalIF":2.0,"publicationDate":"2026-11-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149312068","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Wave-Breaking and Persistence Property for a Two-Component Shallow-Water Wave System With Higher-Order Nonlinearities","authors":"Leyi Zhang,&nbsp;Yue Chen,&nbsp;Xingxing Liu","doi":"10.1002/mma.70952","DOIUrl":"https://doi.org/10.1002/mma.70952","url":null,"abstract":"<div>\u0000 \u0000 <p>This paper investigates wave-breaking and persistence properties for a two-component shallow-water wave system with higher-order nonlinearities, derived from the rotational Green-Naghdi equations under the Camassa-Holm regime. We first establish a new wave-breaking criterion that directly links the initial slope of the velocity to the system's conserved quantities and a bound on the component <span></span><math>\u0000 <mrow>\u0000 <mi>ρ</mi>\u0000 </mrow></math>. Next, utilizing the framework of moderate weight functions, we demonstrate the persistence of strong solutions in weighted <span></span><math>\u0000 <mrow>\u0000 <msup>\u0000 <mrow>\u0000 <mi>L</mi>\u0000 </mrow>\u0000 <mrow>\u0000 <mi>p</mi>\u0000 </mrow>\u0000 </msup>\u0000 </mrow></math> spaces for a general class of weights. As a consequence of this persistence, we derive the precise spatial asymptotic profiles of solutions that exhibit exponential decay. These results extend classical findings for the Camassa-Holm equation to a more complex system with higher-order nonlinearities.</p>\u0000 </div>","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":"49 17","pages":"17816-17825"},"PeriodicalIF":2.0,"publicationDate":"2026-11-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149310910","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Weak Solutions and Uniqueness Results for Sequential q-Fractional Pantograph Equations Under Weak Topology","authors":"Alireza Hatami","doi":"10.1002/mma.70962","DOIUrl":"https://doi.org/10.1002/mma.70962","url":null,"abstract":"<div>\u0000 \u0000 <p>The purpose of this paper is to investigate the existence and uniqueness of weak solutions for a nonlinear sequential quantum Liouville–Caputo fractional differential equation subject to a nonlocal initial condition, where the initial value is defined through a continuous function rather than a constant. The main novelty of this work lies in the combination of a sequential quantum fractional operator with a functional nonlocal initial condition. By employing Mönch's fixed point theorem together with the De Blasi measure of weak noncompactness, we establish the existence of a weak solution. Moreover, by imposing suitable Lipschitz conditions and applying Banach's contraction principle, we prove the uniqueness of the weak solution.</p>\u0000 </div>","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":"49 17","pages":"17873-17887"},"PeriodicalIF":2.0,"publicationDate":"2026-11-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149311500","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Hyperbolic Rotations With Hybrid Numbers","authors":"İskender Öztürk,&nbsp;Hasan Çakır,&nbsp;Mustafa Özdemir","doi":"10.1002/mma.70963","DOIUrl":"https://doi.org/10.1002/mma.70963","url":null,"abstract":"<p>This paper presents a geometric and algebraic analysis of hyperbolic hybrid numbers, which combine structural features of the complex, dual, and hyperbolic number systems. Based on the algebraic properties of the hybrid number set, hyperbolic rotations in both the plane and space are investigated. The study constructs mutually orthogonal hyperbolic planes in the hybrid setting and examines the left-hand, right-hand, and sandwich multiplication maps that produce hyperbolic rotational transformations. In addition, Rodrigues and Cayley type formulas are formulated within the hybrid number system to obtain explicit hyperbolic rotation matrices in three dimensions. These results show that hyperbolic hybrid numbers provide a consistent algebraic setting for modeling Lorentzian-type geometries and clarify the relationship between algebraic operations and geometric motions.</p>","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":"49 17","pages":"17918-17932"},"PeriodicalIF":2.0,"publicationDate":"2026-11-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/mma.70963","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149311704","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Propagation of Stochastic Wave Structures of the Kaup–Newell Optical Fiber Equation With Multiplicative Noise Excitation","authors":"Sonia Akram,&nbsp;Mati ur Rahman,&nbsp;Laila A. AL-Essa,&nbsp;Khalid Aldawsari","doi":"10.1002/mma.70885","DOIUrl":"https://doi.org/10.1002/mma.70885","url":null,"abstract":"<div>\u0000 \u0000 <p>This paper investigates a comprehensive analytical and numerical examination of the stochastic Kaup–Newell equation, including multiplicative white-noise perturbations, which serves as a prominent model for nonlinear pulse propagation in birefringent optical fibers. By applying the modified Sardar Sub equation method in conjunction with the Kumar–Malik technique, a broad class of exact traveling-wave solutions is obtained, including elliptic, dark, bright, singular, exponential, combo, and rational wave profiles. The influence of stochastic forcing on the stability and qualitative structure of these wave patterns is studied in detail. The obtained stochastic wave structures reveal how multiplicative noise modifies nonlinear pulse evolution and wave stability, providing a deeper understanding of realistic optical fiber dynamics. Moreover, the ability of the modified Sardar Sub-equation and Kumar–Malik methods to generate a wide spectrum of exact stochastic solutions confirms their effectiveness for the analytical investigation of nonlinear stochastic optical systems. Additionally, a sensitivity analysis is performed using the classical fourth-order Runge–Kutta scheme to demonstrate the effects of parameter variations and initial conditions on the system dynamics. The determined results emphasize the crucial role of noise-induced modulation in shaping nonlinear pulse evolution and polarization dynamics in birefringent fibers. The significance of this work lies in suggesting deeper insight into the interplay between randomness and nonlinearity, providing valuable guidance for the design of robust high-speed optical communication systems and advanced photonic devices.</p>\u0000 </div>","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":"49 17","pages":"17700-17726"},"PeriodicalIF":2.0,"publicationDate":"2026-11-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149311911","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"RBF-FD Method for Solving the Generalized Time-Fractional Burgers Equation With Initial Weak Singularity","authors":"Ziyu Guo,&nbsp;Kaysar Rahman,&nbsp;Junping Guan","doi":"10.1002/mma.70961","DOIUrl":"https://doi.org/10.1002/mma.70961","url":null,"abstract":"<div>\u0000 \u0000 <p>This paper develops an efficient numerical algorithm for solving the generalized time-fractional Burgers equation subject to three classes of boundary conditions, whose solutions possess weak singularities in the vicinity of the initial instant <span></span><math>\u0000 <mrow>\u0000 <mi>t</mi>\u0000 <mo>=</mo>\u0000 <mn>0</mn>\u0000 </mrow></math>. Traditional numerical approaches employ uniform temporal grids, which inevitably results in deteriorated numerical accuracy. To overcome this defect, the nonuniform <span></span><math>\u0000 <mrow>\u0000 <mi>L</mi>\u0000 <mn>2</mn>\u0000 </mrow></math>-<span></span><math>\u0000 <mrow>\u0000 <msub>\u0000 <mrow>\u0000 <mn>1</mn>\u0000 </mrow>\u0000 <mrow>\u0000 <mi>σ</mi>\u0000 </mrow>\u0000 </msub>\u0000 </mrow></math> formula is utilized for the discretization of the Caputo fractional derivative. For the spatial component, the radial basis function finite difference scheme is adopted. The established algorithm attains a global convergence accuracy of <span></span><math>\u0000 <mrow>\u0000 <mi>O</mi>\u0000 <mo>(</mo>\u0000 <msup>\u0000 <mrow>\u0000 <mi>N</mi>\u0000 </mrow>\u0000 <mrow>\u0000 <mo>−</mo>\u0000 <mi>min</mi>\u0000 <mo>{</mo>\u0000 <mi>r</mi>\u0000 <mi>γ</mi>\u0000 <mo>,</mo>\u0000 <mn>2</mn>\u0000 <mo>}</mo>\u0000 </mrow>\u0000 </msup>\u0000 <mo>+</mo>\u0000 <mi>Δ</mi>\u0000 <msup>\u0000 <mrow>\u0000 <mi>x</mi>\u0000 </mrow>\u0000 <mrow>\u0000 <mn>2</mn>\u0000 </mrow>\u0000 </msup>\u0000 <mo>)</mo>\u0000 </mrow></math>, with <span></span><math>\u0000 <mrow>\u0000 <mi>r</mi>\u0000 </mrow></math> representing the mesh grading parameter, and <span></span><math>\u0000 <mrow>\u0000 <mi>γ</mi>\u0000 </mrow></math> standing for the order of the Caputo fractional derivative. The stability of the presented scheme is strictly proven through energy analysis, and its convergence property is also investigated systematically. A series of numerical tests and comparative analyses with existing benchmark methods verify the remarkable performance of the proposed algorithm. Moreover, the computational efficiency is demonstrated by the CPU times.</p>\u0000 </div>","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":"49 17","pages":"17826-17847"},"PeriodicalIF":2.0,"publicationDate":"2026-11-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149311142","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}