Pub Date : 2026-01-24DOI: 10.1016/j.padiff.2026.101340
M.Z. Kiyani , A. Aeman , Sami Ullah Khan , Farkhod Rakhmonov , Mirjalol Ismoilov , M. Ijaz Khan
A two-dimensional flow and heat and mass transfer for Darcy-Forchheimer nanofluid over an exponentially stretching sheet has been studied. The model includes a transverse magnetic field along with Brownian diffusion, significance of thermophoretic and first-order chemical reaction. The concentration phenomenon is further observed with applications of thermophoretic effects. The nonlinear radiated features are used to predicts the thermal inspiration. Convective-Nield's boundary constraints has been followed. The dimensionless representation of problem is obtained. The system is solved numerically via Keller-Box technique. The influence of the exponential stretching rate along with Darcy Forchheimer, Brownian and thermophoresis parameters has been recognized.
{"title":"Darcy-forchheimer bioconvection flow of nanofluid with thermophoretic effects and nonlinear thermal radiation","authors":"M.Z. Kiyani , A. Aeman , Sami Ullah Khan , Farkhod Rakhmonov , Mirjalol Ismoilov , M. Ijaz Khan","doi":"10.1016/j.padiff.2026.101340","DOIUrl":"10.1016/j.padiff.2026.101340","url":null,"abstract":"<div><div>A two-dimensional flow and heat and mass transfer for Darcy-Forchheimer nanofluid over an exponentially stretching sheet has been studied. The model includes a transverse magnetic field along with Brownian diffusion, significance of thermophoretic and first-order chemical reaction. The concentration phenomenon is further observed with applications of thermophoretic effects. The nonlinear radiated features are used to predicts the thermal inspiration. Convective-Nield's boundary constraints has been followed. The dimensionless representation of problem is obtained. The system is solved numerically via Keller-Box technique. The influence of the exponential stretching rate along with Darcy Forchheimer, Brownian and thermophoresis parameters has been recognized.</div></div>","PeriodicalId":34531,"journal":{"name":"Partial Differential Equations in Applied Mathematics","volume":"17 ","pages":"Article 101340"},"PeriodicalIF":0.0,"publicationDate":"2026-01-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146078122","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}
Pub Date : 2025-12-31DOI: 10.1016/j.padiff.2025.101336
Pooja Yadav , Shah Jahan , Kottakkaran Sooppy Nisar
This study introduces a new Bell wavelet matrix method to solve a class of fractional differential equations arising in fluid mechanics. The class under consideration comprises the fractional relaxation-oscillation equation (R-OE) as a special case. In this work, the Bell wavelets are constructed using the Bell polynomials and their properties. The fractional operational matrix of integration is developed using block pulse functions (BPFs). The primary benefit of the suggested approach lies in its ability to convert these fractional R-OE into a set of algebraic equations, making them well-suited for computer programming. The present approach’s effectiveness and performance are shown by four test problems. By comparing the solutions obtained through this method with exact solutions and existing methods, we gain insight into the accuracy and reliability of the approach.
{"title":"Bell wavelets method to solve class of fractional differential equations arising in fluid mechanics","authors":"Pooja Yadav , Shah Jahan , Kottakkaran Sooppy Nisar","doi":"10.1016/j.padiff.2025.101336","DOIUrl":"10.1016/j.padiff.2025.101336","url":null,"abstract":"<div><div>This study introduces a new Bell wavelet matrix method to solve a class of fractional differential equations arising in fluid mechanics. The class under consideration comprises the fractional relaxation-oscillation equation (R-OE) as a special case. In this work, the Bell wavelets are constructed using the Bell polynomials and their properties. The fractional operational matrix of integration is developed using block pulse functions (BPFs). The primary benefit of the suggested approach lies in its ability to convert these fractional R-OE into a set of algebraic equations, making them well-suited for computer programming. The present approach’s effectiveness and performance are shown by four test problems. By comparing the solutions obtained through this method with exact solutions and existing methods, we gain insight into the accuracy and reliability of the approach.</div></div>","PeriodicalId":34531,"journal":{"name":"Partial Differential Equations in Applied Mathematics","volume":"17 ","pages":"Article 101336"},"PeriodicalIF":0.0,"publicationDate":"2025-12-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146038120","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}
Pub Date : 2025-12-15DOI: 10.1016/j.padiff.2025.101327
Ali Raza , F.M. Mahomed , F.D. Zaman , A.H. Kara
We study the non-linear wave equation for arbitrary function with fourth order dispersion. A special case that is analysed exclusively is the model of nerve membranes; we consider this model, both, in the presence and absence of the fourth order dispersion. The equivalence transformations, Lie symmetries and a complete classification is presented. We also discuss the one dimensional optimal system in each case obtained via classification. The reduction of the partial differential equations (PDEs) is carried out and the forms of invariant solutions are presented. The study also include the construction of conservation laws using the direct method. The invariant solutions and some special type of solutions including solitons are presented with their graphical illustrations. we derive homoclinic breather solutions (HBs) and M-shaped rational solutions (MSRs). Their dynamic is shown in figures by selecting appropriate values of parameters.
{"title":"Invariance and solitons analyses of wave equations with fourth order dispersion","authors":"Ali Raza , F.M. Mahomed , F.D. Zaman , A.H. Kara","doi":"10.1016/j.padiff.2025.101327","DOIUrl":"10.1016/j.padiff.2025.101327","url":null,"abstract":"<div><div>We study the non-linear wave equation for arbitrary function with fourth order dispersion. A special case that is analysed exclusively is the model of nerve membranes; we consider this model, both, in the presence and absence of the fourth order dispersion. The equivalence transformations, Lie symmetries and a complete classification is presented. We also discuss the one dimensional optimal system in each case obtained via classification. The reduction of the partial differential equations (PDEs) is carried out and the forms of invariant solutions are presented. The study also include the construction of conservation laws using the direct method. The invariant solutions and some special type of solutions including solitons are presented with their graphical illustrations. we derive homoclinic breather solutions (HBs) and M-shaped rational solutions (MSRs). Their dynamic is shown in figures by selecting appropriate values of parameters.</div></div>","PeriodicalId":34531,"journal":{"name":"Partial Differential Equations in Applied Mathematics","volume":"17 ","pages":"Article 101327"},"PeriodicalIF":0.0,"publicationDate":"2025-12-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145791940","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}
Pub Date : 2025-12-13DOI: 10.1016/j.padiff.2025.101334
Laurent Tchoualag , Lionel Ouya Ndjansi , Jean Daniel Mukam , Antoine Tambue
In this paper, we present a rapid procedure for approximating the solution to the Laplace equation in a ring domain. We develop a new formulation of boundary integral operators and implement an efficient solution approach using the Galerkin boundary element method for Dirichlet and mixed boundary value problems. The corresponding matrix entries are computed efficiently and accurately, and the resulting circulant block structure allows the matrices of the discrete boundary integral operators to be expressed as a product of sparse matrices. Therefore the fast Fourier transform (FFT) has significantly accelerated matrix-to-vector product. Moreover, the discrete Fourier transform (DFT) enables the construction of efficient preconditioners for conjugate gradient algorithms, and provides a robust direct approach for solving the Dirichlet problem. Numerical experiments for both Dirichlet and mixed problems demonstrate the exceptional efficiency and accuracy of the proposed algorithms.
{"title":"Boundary element method for Laplace equation in a ring domain","authors":"Laurent Tchoualag , Lionel Ouya Ndjansi , Jean Daniel Mukam , Antoine Tambue","doi":"10.1016/j.padiff.2025.101334","DOIUrl":"10.1016/j.padiff.2025.101334","url":null,"abstract":"<div><div>In this paper, we present a rapid procedure for approximating the solution to the Laplace equation in a ring domain. We develop a new formulation of boundary integral operators and implement an efficient solution approach using the Galerkin boundary element method for Dirichlet and mixed boundary value problems. The corresponding matrix entries are computed efficiently and accurately, and the resulting circulant block structure allows the matrices of the discrete boundary integral operators to be expressed as a product of sparse matrices. Therefore the fast Fourier transform (FFT) has significantly accelerated matrix-to-vector product. Moreover, the discrete Fourier transform (DFT) enables the construction of efficient preconditioners for conjugate gradient algorithms, and provides a robust direct approach for solving the Dirichlet problem. Numerical experiments for both Dirichlet and mixed problems demonstrate the exceptional efficiency and accuracy of the proposed algorithms.</div></div>","PeriodicalId":34531,"journal":{"name":"Partial Differential Equations in Applied Mathematics","volume":"17 ","pages":"Article 101334"},"PeriodicalIF":0.0,"publicationDate":"2025-12-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145927153","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}
Pub Date : 2025-12-13DOI: 10.1016/j.padiff.2025.101329
Realeboga Dikole
This article investigates nonlinear Dirac equations (NLD) with cubic-type nonlinearities, that is, vector and scalar self-interaction nonlinearities. We present analytical solutions of gap-solitons, which are self-localised, moving or quiescent pulses existing in the band gaps of nonlinear Dirac models. We also perform the linear stability analysis of the gap-soliton bearing systems and find that the gap-solitons possess some regions of instability. We also extend our studies to planar nonlinear Dirac equations and relate them to light propagation in photonic lattices, such as photonic graphene and present their numerical solutions, in particular, the rotationally symmetric localised radial profiles that rotate about the Brillouin zone.
{"title":"Spinor solitons in one-dimensional and planar nonlinear Dirac equations","authors":"Realeboga Dikole","doi":"10.1016/j.padiff.2025.101329","DOIUrl":"10.1016/j.padiff.2025.101329","url":null,"abstract":"<div><div>This article investigates nonlinear Dirac equations (NLD) with cubic-type nonlinearities, that is, vector and scalar self-interaction nonlinearities. We present analytical solutions of gap-solitons, which are self-localised, moving or quiescent pulses existing in the band gaps of nonlinear Dirac models. We also perform the linear stability analysis of the gap-soliton bearing systems and find that the gap-solitons possess some regions of instability. We also extend our studies to planar nonlinear Dirac equations and relate them to light propagation in photonic lattices, such as photonic graphene and present their numerical solutions, in particular, the rotationally symmetric localised radial profiles that rotate about the Brillouin zone.</div></div>","PeriodicalId":34531,"journal":{"name":"Partial Differential Equations in Applied Mathematics","volume":"17 ","pages":"Article 101329"},"PeriodicalIF":0.0,"publicationDate":"2025-12-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145791939","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}
Pub Date : 2025-12-13DOI: 10.1016/j.padiff.2025.101332
G. Shylaja , V. Kesavulu Naidu , B. Venkatesh , S.M. Mallikarjunaiah
This paper presents an explicit integration scheme that incorporates septic-order triangular elements. Cubic arcs are utilized to approximate the curved edges of these elements. This methodology is particularly effective for discretizing curved domains, and its primary objective is the approximation of equations involving differential operators. A 36-node septic-order triangular element with a curved boundary, which consists of one curved edge and two straight edges, is introduced in this study. This element serves as the foundation for the isoparametric coordinate transformation discussed herein. A standard triangle in the local coordinate system is mapped onto the curved triangular element in the global coordinate system by means of a unique point transformation. The curved triangular element is replaced by septic arcs, and the coordinates located on the curved edge are embedded within the parameters that define these arc equations. Each arc consistently represents a distinct cubic arc due to the relationships involved in the parameter calculations. Consequently, the overall numerical approximation is highly accurate. For higher-order curved triangular elements, the finite element method, in conjunction with numerical integration that utilizes curved boundary point transformations (applicable to both the exterior and interior of each curved triangular element), will act as a robust subparametric coordinate transformation and, as a result, a formidable numerical technique. The efficacy of this method is demonstrated through the resolution of three boundary value problems. Numerical outcomes affirm that the proposed technique significantly surpasses existing methods in the approximation of boundary value problems.
{"title":"Septic-order triangular finite elements: An explicit method with cubic arc subparametric transformations","authors":"G. Shylaja , V. Kesavulu Naidu , B. Venkatesh , S.M. Mallikarjunaiah","doi":"10.1016/j.padiff.2025.101332","DOIUrl":"10.1016/j.padiff.2025.101332","url":null,"abstract":"<div><div>This paper presents an explicit integration scheme that incorporates septic-order triangular elements. Cubic arcs are utilized to approximate the curved edges of these elements. This methodology is particularly effective for discretizing curved domains, and its primary objective is the approximation of equations involving differential operators. A 36-node septic-order triangular element with a curved boundary, which consists of one curved edge and two straight edges, is introduced in this study. This element serves as the foundation for the isoparametric coordinate transformation discussed herein. A standard triangle in the local coordinate system is mapped onto the curved triangular element in the global coordinate system by means of a unique point transformation. The curved triangular element is replaced by septic arcs, and the coordinates located on the curved edge are embedded within the parameters that define these arc equations. Each arc consistently represents a distinct cubic arc due to the relationships involved in the parameter calculations. Consequently, the overall numerical approximation is highly accurate. For higher-order curved triangular elements, the finite element method, in conjunction with numerical integration that utilizes curved boundary point transformations (applicable to both the exterior and interior of each curved triangular element), will act as a robust subparametric coordinate transformation and, as a result, a formidable numerical technique. The efficacy of this method is demonstrated through the resolution of three boundary value problems. Numerical outcomes affirm that the proposed technique significantly surpasses existing methods in the approximation of boundary value problems.</div></div>","PeriodicalId":34531,"journal":{"name":"Partial Differential Equations in Applied Mathematics","volume":"17 ","pages":"Article 101332"},"PeriodicalIF":0.0,"publicationDate":"2025-12-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145791937","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}
Pub Date : 2025-12-12DOI: 10.1016/j.padiff.2025.101325
Dian K. Palagachev
The non-homogeneous conormal derivative problems for nonlinear, second-order divergence form elliptic equations with singular data appear naturally in mathematical modeling of real phenomena involving problems of image recovery, the thermistor problem, or studies of non-Newtonian fluids.
We prove suitable estimates for certain surface integrals, related to non-homogeneous conormal derivative problems, which lead to essential boundedness of the weak solutions under quite general hypotheses on the data.
{"title":"On certain surface integrals related to the conormal derivative problem","authors":"Dian K. Palagachev","doi":"10.1016/j.padiff.2025.101325","DOIUrl":"10.1016/j.padiff.2025.101325","url":null,"abstract":"<div><div>The non-homogeneous conormal derivative problems for nonlinear, second-order divergence form elliptic equations with singular data appear naturally in mathematical modeling of real phenomena involving problems of image recovery, the thermistor problem, or studies of non-Newtonian fluids.</div><div>We prove suitable estimates for certain surface integrals, related to non-homogeneous conormal derivative problems, which lead to essential boundedness of the weak solutions under quite general hypotheses on the data.</div></div>","PeriodicalId":34531,"journal":{"name":"Partial Differential Equations in Applied Mathematics","volume":"17 ","pages":"Article 101325"},"PeriodicalIF":0.0,"publicationDate":"2025-12-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145760656","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}
Pub Date : 2025-12-11DOI: 10.1016/j.padiff.2025.101333
M.M. Nour , Abdur Rehman , Abdallah aldurayhim , Muhammad Ashraf , A.M. Rashad , Hossam A. Nabwey
This study investigates the effects of non-linear motion on mixed convection viscous fluid flow, incorporating thermal conductivity inversely proportional to a linear function of temperature under the influence of oscillating thermal waves. To provide a comprehensive understanding, the research explores convective heat transfer in the presence of vorticity. The governing equations, including continuity, momentum, and heat equations, are formulated to represent the intricate non-linear dynamics of fluid flow and heat transfer. These equations are rendered dimensionless using appropriate scaling variables and subsequently transformed into steady and unsteady forms to address varying thermal and flow conditions. A Gaussian elimination approach, combined with a primitive variable formulation, is employed for numerical computation, alongside the finite difference method. Computational solutions are developed using FORTRAN Laher-90, with graphical and tabular results presented via Tecplot-360 to analyze transient shear stress (τs) and transient heat transfer (τt) influenced by oscillating thermal waves. The findings reveal critical insights into the interplay between vorticity, non-linear fluid behavior, and thermal oscillations, contributing to advancements in optimizing convective heat transfer mechanisms. The findings show that in steady-state conditions, temperature distribution and flow velocity increase with higher values of the thermal conductivity variation parameter (ς). In the unsteady state, transient shear stress τₛ exhibits higher wave amplitude at ς = 0.2, followed by slight changes in phase angle at different values. However, transient heat transfer τt decreases in wave magnitude as ς increases.
{"title":"Influence of non-linear motion on mixed convection in viscous fluids with temperature-dependent thermal conductivity and oscillating thermal wave","authors":"M.M. Nour , Abdur Rehman , Abdallah aldurayhim , Muhammad Ashraf , A.M. Rashad , Hossam A. Nabwey","doi":"10.1016/j.padiff.2025.101333","DOIUrl":"10.1016/j.padiff.2025.101333","url":null,"abstract":"<div><div>This study investigates the effects of non-linear motion on mixed convection viscous fluid flow, incorporating thermal conductivity inversely proportional to a linear function of temperature under the influence of oscillating thermal waves. To provide a comprehensive understanding, the research explores convective heat transfer in the presence of vorticity. The governing equations, including continuity, momentum, and heat equations, are formulated to represent the intricate non-linear dynamics of fluid flow and heat transfer. These equations are rendered dimensionless using appropriate scaling variables and subsequently transformed into steady and unsteady forms to address varying thermal and flow conditions. A Gaussian elimination approach, combined with a primitive variable formulation, is employed for numerical computation, alongside the finite difference method. Computational solutions are developed using FORTRAN Laher-90, with graphical and tabular results presented via Tecplot-360 to analyze transient shear stress (τ<sub><em>s</em></sub>) and transient heat transfer (τ<sub><em>t</em></sub>) influenced by oscillating thermal waves. The findings reveal critical insights into the interplay between vorticity, non-linear fluid behavior, and thermal oscillations, contributing to advancements in optimizing convective heat transfer mechanisms. The findings show that in steady-state conditions, temperature distribution and flow velocity increase with higher values of the thermal conductivity variation parameter (ς). In the unsteady state, transient shear stress τₛ exhibits higher wave amplitude at ς = 0.2, followed by slight changes in phase angle at different values. However, transient heat transfer τ<sub>t</sub> decreases in wave magnitude as ς increases.</div></div>","PeriodicalId":34531,"journal":{"name":"Partial Differential Equations in Applied Mathematics","volume":"17 ","pages":"Article 101333"},"PeriodicalIF":0.0,"publicationDate":"2025-12-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145791934","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}
Pub Date : 2025-12-11DOI: 10.1016/j.padiff.2025.101330
Md. Towhiduzzaman , Md. Abdul Al Mohit , A.Z.M. Asaduzzaman
This paper presents an in-depth analytical and computational study of the (3 + 1)-dimensional Fornberg-Whitham (FW) equation, a highly nonlinear partial differential equation modeling complex wave interactions in multidimensional dispersive media. Employing Hirota’s bilinear method, we derive explicit lump and multi-soliton solutions, elucidating their dynamic interaction patterns and stability properties. To complement these findings, we develop a robust physics-informed neural network (PINN) framework to numerically solve the FW equation, capturing challenging rogue and breather wave phenomena with high accuracy. Comprehensive numerical experiments validate the PINN model against analytical benchmarks, demonstrating its capability to handle high-dimensional nonlinearities and mixed derivatives. These results provide critical insights into multidimensional wave dynamics and establish a hybrid approach that effectively blends classical soliton theory with modern machine learning, paving the way for future research in nonlinear wave propagation, fluid dynamics, and applied physics.
{"title":"Modeling lump and soliton wave interactions in the (3 + 1)D Fornberg-Whitham equation using a physics-informed neural network framework","authors":"Md. Towhiduzzaman , Md. Abdul Al Mohit , A.Z.M. Asaduzzaman","doi":"10.1016/j.padiff.2025.101330","DOIUrl":"10.1016/j.padiff.2025.101330","url":null,"abstract":"<div><div>This paper presents an in-depth analytical and computational study of the (3 + 1)-dimensional Fornberg-Whitham (FW) equation, a highly nonlinear partial differential equation modeling complex wave interactions in multidimensional dispersive media. Employing Hirota’s bilinear method, we derive explicit lump and multi-soliton solutions, elucidating their dynamic interaction patterns and stability properties. To complement these findings, we develop a robust physics-informed neural network (PINN) framework to numerically solve the FW equation, capturing challenging rogue and breather wave phenomena with high accuracy. Comprehensive numerical experiments validate the PINN model against analytical benchmarks, demonstrating its capability to handle high-dimensional nonlinearities and mixed derivatives. These results provide critical insights into multidimensional wave dynamics and establish a hybrid approach that effectively blends classical soliton theory with modern machine learning, paving the way for future research in nonlinear wave propagation, fluid dynamics, and applied physics.</div></div>","PeriodicalId":34531,"journal":{"name":"Partial Differential Equations in Applied Mathematics","volume":"17 ","pages":"Article 101330"},"PeriodicalIF":0.0,"publicationDate":"2025-12-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145792019","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}
Pub Date : 2025-12-11DOI: 10.1016/j.padiff.2025.101328
M. Nurul Islam , M. Al-Amin , M. Ali Akbar
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.
{"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":"2025-12-11","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}
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