Pub Date : 2025-09-01DOI: 10.1016/j.padiff.2025.101273
Takafumi Akahori
The intermediate nonlinear Schrödinger equation (abbreviated to (INS)) is a model equation for envelope waves in a deep stratified fluid and can be thought of as a generalization of the defocusing nonlinear Schrödinger equation. Furthermore, it possesses dark multi-solitons as well as the defocusing nonlinear Schrödinger equation. In this paper, we reveal the asymptotic behavior of dark multi-solitons to (INS). We also give the asymptotic behavior of bright multi-solitons to the intermediate long wave equation. Our analysis relies only on the explicit forms of multi-solitons obtained by Hirota’s bilinear method.
{"title":"Asymptotic behavior of dark multi-solitons to the intermediate nonlinear Schrödinger equation","authors":"Takafumi Akahori","doi":"10.1016/j.padiff.2025.101273","DOIUrl":"10.1016/j.padiff.2025.101273","url":null,"abstract":"<div><div>The intermediate nonlinear Schrödinger equation (abbreviated to (INS)) is a model equation for envelope waves in a deep stratified fluid and can be thought of as a generalization of the defocusing nonlinear Schrödinger equation. Furthermore, it possesses dark multi-solitons as well as the defocusing nonlinear Schrödinger equation. In this paper, we reveal the asymptotic behavior of dark multi-solitons to (INS). We also give the asymptotic behavior of bright multi-solitons to the intermediate long wave equation. Our analysis relies only on the explicit forms of multi-solitons obtained by Hirota’s bilinear method.</div></div>","PeriodicalId":34531,"journal":{"name":"Partial Differential Equations in Applied Mathematics","volume":"15 ","pages":"Article 101273"},"PeriodicalIF":0.0,"publicationDate":"2025-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144919986","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 : 2025-09-01DOI: 10.1016/j.padiff.2025.101281
Ilia Kashchenko, Igor Maslenikov
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.
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.
Also, the situation where two successive bifurcations occur in the system was described.
{"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}
Pub Date : 2025-09-01DOI: 10.1016/j.padiff.2025.101285
Hamida Parvin , Md. Nur Alam , Md. Abdullah Bin Masud , Md. Jakir Hossen
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.
{"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}
Pub Date : 2025-09-01DOI: 10.1016/j.padiff.2025.101295
M. Nurul Islam , M. Al-Amin , M. Ali Akbar
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.
{"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}
Pub Date : 2025-09-01DOI: 10.1016/j.padiff.2025.101276
V. Sowbakiya , R. Nirmalkumar , K. Loganathan , C. Selvamani
In this paper, we study the existence, uniqueness, and stability analysis of non-linear implicit neutral fractional differential equations involving the Atangana–Baleanu derivative in the Caputo sense. The Banach contraction principle theorem is employed to establish the existence and uniqueness of solutions, while Krasnoselskii’s fixed-point theorem is utilized to further analyze the existence of solutions. Stability analysis is also examined, including results for Ulam–Hyers, generalized Ulam–Hyers, Ulam–Hyers–Rassias, and generalized Ulam–Hyers–Rassias stability. Finally, an example is presented to illustrate the existence and uniqueness of solutions, along with a discussion on their stability.
{"title":"Study on existence and stability analysis for implicit neutral fractional differential equations of ABC derivative","authors":"V. Sowbakiya , R. Nirmalkumar , K. Loganathan , C. Selvamani","doi":"10.1016/j.padiff.2025.101276","DOIUrl":"10.1016/j.padiff.2025.101276","url":null,"abstract":"<div><div>In this paper, we study the existence, uniqueness, and stability analysis of non-linear implicit neutral fractional differential equations involving the Atangana–Baleanu derivative in the Caputo sense. The Banach contraction principle theorem is employed to establish the existence and uniqueness of solutions, while Krasnoselskii’s fixed-point theorem is utilized to further analyze the existence of solutions. Stability analysis is also examined, including results for Ulam–Hyers, generalized Ulam–Hyers, Ulam–Hyers–Rassias, and generalized Ulam–Hyers–Rassias stability. Finally, an example is presented to illustrate the existence and uniqueness of solutions, along with a discussion on their stability.</div></div>","PeriodicalId":34531,"journal":{"name":"Partial Differential Equations in Applied Mathematics","volume":"15 ","pages":"Article 101276"},"PeriodicalIF":0.0,"publicationDate":"2025-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144920091","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}
This paper investigates the geometric properties of Smarandache ruled surfaces generated by integral binormal curves in the Euclidean 3-space . Specifically, we study four types of Smarandache ruled surfaces: the , , , and surfaces, each defined by different combinations of the tangent, normal, and binormal vectors of the integral curves. For each type of surface, we derive the parametric representations and compute the fundamental geometric properties, including the striction lines, distribution parameters, and the first and second fundamental forms. Additionally, we provide explicit expressions for the Gaussian and mean curvatures, which characterize the local shape of the surfaces. We also analyze the geodesic curvature, normal curvature, and geodesic torsion associated with the base curves on these surfaces. Furthermore, we establish necessary and sufficient conditions for these surfaces to be developable or minimal. The paper concludes with detailed conditions under which the base curves can be classified as geodesic or asymptotic lines on the surfaces. The results are supported by rigorous proofs and illustrative examples, offering a comprehensive understanding of the geometric behavior of these Smarandache ruled surfaces.
{"title":"Geometric properties of Smarandache ruled surfaces generated by integral binormal curves in Euclidean 3-space","authors":"Ayman Elsharkawy , Hanene Hamdani , Clemente Cesarano , Noha Elsharkawy","doi":"10.1016/j.padiff.2025.101298","DOIUrl":"10.1016/j.padiff.2025.101298","url":null,"abstract":"<div><div>This paper investigates the geometric properties of Smarandache ruled surfaces generated by integral binormal curves in the Euclidean 3-space <span><math><msup><mrow><mi>E</mi></mrow><mrow><mn>3</mn></mrow></msup></math></span>. Specifically, we study four types of Smarandache ruled surfaces: the <span><math><mrow><mi>t</mi><mi>n</mi></mrow></math></span>, <span><math><mrow><mi>t</mi><mi>b</mi></mrow></math></span>, <span><math><mrow><mi>n</mi><mi>b</mi></mrow></math></span>, and <span><math><mrow><mi>t</mi><mi>n</mi><mi>b</mi></mrow></math></span> surfaces, each defined by different combinations of the tangent, normal, and binormal vectors of the integral curves. For each type of surface, we derive the parametric representations and compute the fundamental geometric properties, including the striction lines, distribution parameters, and the first and second fundamental forms. Additionally, we provide explicit expressions for the Gaussian and mean curvatures, which characterize the local shape of the surfaces. We also analyze the geodesic curvature, normal curvature, and geodesic torsion associated with the base curves on these surfaces. Furthermore, we establish necessary and sufficient conditions for these surfaces to be developable or minimal. The paper concludes with detailed conditions under which the base curves can be classified as geodesic or asymptotic lines on the surfaces. The results are supported by rigorous proofs and illustrative examples, offering a comprehensive understanding of the geometric behavior of these Smarandache ruled surfaces.</div></div>","PeriodicalId":34531,"journal":{"name":"Partial Differential Equations in Applied Mathematics","volume":"15 ","pages":"Article 101298"},"PeriodicalIF":0.0,"publicationDate":"2025-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144931558","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 : 2025-09-01DOI: 10.1016/j.padiff.2025.101286
Nauman Ahmed , Sidra Ghazanfar , Zunaira , Muhammad Z. Baber , Ilyas Khan , Osama Oqilat , Wei Sin Kohh
This work suggests single-wave solutions for the Estevez-Mansfield-Clarkson (EMC) and linked sine-Gordon equations. The shape generation process in droplet form is studied using these model equations. For accurate wave and solitary wave solutions, in addition to many mathematical and physical research methods. There is nonlinear dispersion according to the EMC equation. It is feasible to generalize the Estevez-Mansfield integrable. Precise wave solutions, including kink, solitary, rational, single, and anti-kink, may be obtained by modifying the generalized exponential rational function technique. These changes may be advantageous in several scientific and technological domains. A novel approach to the precise solution of nonlinear partial differential equations is presented in this paper. The strategy’s main objective is to increase the applicability of the exponential rational function technique.
{"title":"Campatibility of solitons within the frame work of Estevez-Mansfield-Clarkson equation","authors":"Nauman Ahmed , Sidra Ghazanfar , Zunaira , Muhammad Z. Baber , Ilyas Khan , Osama Oqilat , Wei Sin Kohh","doi":"10.1016/j.padiff.2025.101286","DOIUrl":"10.1016/j.padiff.2025.101286","url":null,"abstract":"<div><div>This work suggests single-wave solutions for the Estevez-Mansfield-Clarkson (EMC) and linked sine-Gordon equations. The shape generation process in droplet form is studied using these model equations. For accurate wave and solitary wave solutions, in addition to many mathematical and physical research methods. There is nonlinear dispersion according to the EMC equation. It is feasible to generalize the Estevez-Mansfield integrable. Precise wave solutions, including kink, solitary, rational, single, and anti-kink, may be obtained by modifying the generalized exponential rational function technique. These changes may be advantageous in several scientific and technological domains. A novel approach to the precise solution of nonlinear partial differential equations is presented in this paper. The strategy’s main objective is to increase the applicability of the exponential rational function technique.</div></div>","PeriodicalId":34531,"journal":{"name":"Partial Differential Equations in Applied Mathematics","volume":"15 ","pages":"Article 101286"},"PeriodicalIF":0.0,"publicationDate":"2025-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145018459","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 : 2025-09-01DOI: 10.1016/j.padiff.2025.101271
Alemu Senbeta Bekela , Mesfin Mekuria Woldaregay
Nonlinear time-fractional diffusion equations (NTFDEs) are widely applied for modeling various natural processes like volcanic eruption, diffusion processes, earthquakes, brain tumors, and the dynamics of soil in water. Solving these problems is quite challenging. So, designing effective numerical approaches is an active research area. The fractional derivative used is the Caputo type. In this paper, we develop the hybrid series based method by combining the Formable transform and Adomian decomposition method (ADM) for treating the NTFDEs. The stability and convergence of the developed series based method have been investigated. The effectiveness of the introduced method is investigated by solving two test examples. The obtained numerical results show that the proposed method is efficient for solving NTFDEs and gives accurate results.
{"title":"Formable transform Adomian decomposition method for solving nonlinear time-fractional diffusion equation","authors":"Alemu Senbeta Bekela , Mesfin Mekuria Woldaregay","doi":"10.1016/j.padiff.2025.101271","DOIUrl":"10.1016/j.padiff.2025.101271","url":null,"abstract":"<div><div>Nonlinear time-fractional diffusion equations (NTFDEs) are widely applied for modeling various natural processes like volcanic eruption, diffusion processes, earthquakes, brain tumors, and the dynamics of soil in water. Solving these problems is quite challenging. So, designing effective numerical approaches is an active research area. The fractional derivative used is the Caputo type. In this paper, we develop the hybrid series based method by combining the Formable transform and Adomian decomposition method (ADM) for treating the NTFDEs. The stability and convergence of the developed series based method have been investigated. The effectiveness of the introduced method is investigated by solving two test examples. The obtained numerical results show that the proposed method is efficient for solving NTFDEs and gives accurate results.</div></div>","PeriodicalId":34531,"journal":{"name":"Partial Differential Equations in Applied Mathematics","volume":"15 ","pages":"Article 101271"},"PeriodicalIF":0.0,"publicationDate":"2025-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145018460","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 : 2025-09-01DOI: 10.1016/j.padiff.2025.101300
Attia Rani , Muhammad Shakeel , Muhammad Sohail , Ibrahim Mahariq
In this work, we examine the Heimburg model, which describes how electromechanical pulses are transmitted through nerves by using the generalizing Riccati equation mapping method. This approach is regarded as one of the most recent efficient analytical approaches for nonlinear evolution equations, yielding numerous different types of solutions for the model under consideration. We get novel analytic exact solitary wave solutions, including exponential, hyperbolic, and trigonometric functions. These solutions comprises solitary wave, kink, singular kink, periodic, singular soliton, combined dark bright soliton, and breather soliton. To understand the physical principles and significance of the technique the well-furnished results are ultimately displayed in a variety of 2D, 3D, and contour profiles. Additionally, a stability study of the derived solutions is conducted, demonstrating that the steady state is stable under specific parameter restrictions, however the breach of these requirements results in instability due to the exponential increase of perturbations. The results of this work shed light on the importance of studying various nonlinear wave phenomena in nonlinear optics and physics by showing how important it is to understand the behaviour and physical meaning of the studied model. The employed methodology possesses sufficient capability, efficacy, and brevity to enable further research.
{"title":"The generalizing riccati equation mapping method's application for detecting soliton solutions in biomembranes and nerves","authors":"Attia Rani , Muhammad Shakeel , Muhammad Sohail , Ibrahim Mahariq","doi":"10.1016/j.padiff.2025.101300","DOIUrl":"10.1016/j.padiff.2025.101300","url":null,"abstract":"<div><div>In this work, we examine the Heimburg model, which describes how electromechanical pulses are transmitted through nerves by using the generalizing Riccati equation mapping method. This approach is regarded as one of the most recent efficient analytical approaches for nonlinear evolution equations, yielding numerous different types of solutions for the model under consideration. We get novel analytic exact solitary wave solutions, including exponential, hyperbolic, and trigonometric functions. These solutions comprises solitary wave, kink, singular kink, periodic, singular soliton, combined dark bright soliton, and breather soliton. To understand the physical principles and significance of the technique the well-furnished results are ultimately displayed in a variety of 2D, 3D, and contour profiles. Additionally, a stability study of the derived solutions is conducted, demonstrating that the steady state is stable under specific parameter restrictions, however the breach of these requirements results in instability due to the exponential increase of perturbations. The results of this work shed light on the importance of studying various nonlinear wave phenomena in nonlinear optics and physics by showing how important it is to understand the behaviour and physical meaning of the studied model. The employed methodology possesses sufficient capability, efficacy, and brevity to enable further research.</div></div>","PeriodicalId":34531,"journal":{"name":"Partial Differential Equations in Applied Mathematics","volume":"15 ","pages":"Article 101300"},"PeriodicalIF":0.0,"publicationDate":"2025-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145018632","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 : 2025-09-01DOI: 10.1016/j.padiff.2025.101288
Sajid Shafique , Muhammad Afzal , Muhammad Arsalan Ahmad , Mohammad Mahtab Alam
Parametric analysis of different choices of acoustic absorbent liners in a bicameral acoustic duct is presented in the current research study. Bicameral is characterized by two expansion chambers but functions as a single duct in practice, that is widely used in various engineering applications, particularly in the field of exhaust systems and to mitigate noise. The current research intends to examine the acoustic behavior in an acoustic duct when it is equipped with fibrous and perforated liners in bicameral configurations. The comparison study of rigid vertical walls of the bicameral with absorbent liner materials is addressed particularly to optimize the design of an acoustic duct to accomplish the desired acoustic performance. The current physical challenge is modeled mathematically and solved by a semi-analytical Mode-Matching (MM) approach. However, the root findings of the derived dispersion relations and recasting the system of linear algebraic equations are tackled numerically. The power fluxes, transmission-loss (TL), and absorption power () as a function of frequency and against horizontal spacing of the chambers (L) are achieved and displayed graphically. Also, the comparison discussion is provided for both vertical rigid and vertical lining cases by assuming the various choices of fibrous absorbent liner (FAL) and perforated absorbent liner (PAL). Ahead of this, the computational validation of the analytical perspective also depends on satisfying matching continuity criteria.
{"title":"Parametric analysis of acoustic liner in bicameral duct: An analytical perspective","authors":"Sajid Shafique , Muhammad Afzal , Muhammad Arsalan Ahmad , Mohammad Mahtab Alam","doi":"10.1016/j.padiff.2025.101288","DOIUrl":"10.1016/j.padiff.2025.101288","url":null,"abstract":"<div><div>Parametric analysis of different choices of acoustic absorbent liners in a bicameral acoustic duct is presented in the current research study. Bicameral is characterized by two expansion chambers but functions as a single duct in practice, that is widely used in various engineering applications, particularly in the field of exhaust systems and to mitigate noise. The current research intends to examine the acoustic behavior in an acoustic duct when it is equipped with fibrous and perforated liners in bicameral configurations. The comparison study of rigid vertical walls of the bicameral with absorbent liner materials is addressed particularly to optimize the design of an acoustic duct to accomplish the desired acoustic performance. The current physical challenge is modeled mathematically and solved by a semi-analytical Mode-Matching (MM) approach. However, the root findings of the derived dispersion relations and recasting the system of linear algebraic equations are tackled numerically. The power fluxes, transmission-loss (TL), and absorption power (<span><math><msub><mrow><mi>P</mi></mrow><mrow><mi>a</mi><mi>b</mi><mi>s</mi></mrow></msub></math></span>) as a function of frequency and against horizontal spacing of the chambers (L) are achieved and displayed graphically. Also, the comparison discussion is provided for both vertical rigid and vertical lining cases by assuming the various choices of fibrous absorbent liner (FAL) and perforated absorbent liner (PAL). Ahead of this, the computational validation of the analytical perspective also depends on satisfying matching continuity criteria.</div></div>","PeriodicalId":34531,"journal":{"name":"Partial Differential Equations in Applied Mathematics","volume":"15 ","pages":"Article 101288"},"PeriodicalIF":0.0,"publicationDate":"2025-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144923055","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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