Partial Differential Equations in Applied Mathematics最新文献

{"title":"Polynomial dynamical systems associated with the KdV hierarchy","authors":"V.M. Buchstaber,&nbsp;E. Yu. Bunkova","doi":"10.1016/j.padiff.2024.100928","DOIUrl":"10.1016/j.padiff.2024.100928","url":null,"abstract":"<div><div>In 1974, S.P. Novikov introduced the stationary <span><math><mi>n</mi></math></span>-equations of the Korteweg–de Vries hierarchy, namely the <span><math><mi>n</mi></math></span>-Novikov equations. These are associated with integrable polynomial dynamical systems, with polynomial <span><math><mrow><mn>2</mn><mi>n</mi></mrow></math></span> integrals, in <span><math><msup><mrow><mi>ℂ</mi></mrow><mrow><mn>3</mn><mi>n</mi></mrow></msup></math></span>. In this paper, we construct an infinite-dimensional polynomial dynamical system that is universal for all dynamical systems corresponding to the <span><math><mi>n</mi></math></span>-Novikov equations. Thus, we solve the well-known problem of the relationship between the <span><math><mi>n</mi></math></span>-Novikov equations for different <span><math><mi>n</mi></math></span>.</div></div>","PeriodicalId":34531,"journal":{"name":"Partial Differential Equations in Applied Mathematics","volume":"12 ","pages":"Article 100928"},"PeriodicalIF":0.0,"publicationDate":"2024-09-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142318675","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"On the study of double dispersive equation in the Murnaghan’s rod: Dynamics of diversity wave structures","authors":"Jan Muhammad ,&nbsp;Usman Younas ,&nbsp;Aziz Khan ,&nbsp;Thabet Abdeljawad ,&nbsp;D.K. Almutairi","doi":"10.1016/j.padiff.2024.100916","DOIUrl":"10.1016/j.padiff.2024.100916","url":null,"abstract":"<div><div>This article secures the various wave structures of the fractional double dispersive equation, a significant nonlinear equation that describes the propagation of nonlinear waves within the elastic, uniform, and inhomogeneous Murnaghan’s rod. The model under discussion has a wide range of applications in science and engineering. Two recently developed analytical techniques known as the improved generalized Riccati equation mapping method and the multivariate generalized exponential rational integral function method have been applied to the proposed equation for the first time. A variety of solutions have been revealed such that dark, singular, bright-dark, bright, complex, and combined solitons. Furthermore, we include a diverse array of plots that illustrate the physical interpretation of the obtained solutions in relation to a number of significant parameters, thereby highlighting the impact of fractional derivatives. Within the context of the proposed model, these visualizations give a clear understanding of the behavior and characteristics of the solutions. This study’s results have the potential to enhance comprehension of the nonlinear dynamic characteristics exhibited by the specified system and validate the efficacy of the implemented techniques. The achieved results significantly enhance our understanding of nonlinear science and the nonlinear wave fields associated with more complex nonlinear models.</div></div>","PeriodicalId":34531,"journal":{"name":"Partial Differential Equations in Applied Mathematics","volume":"12 ","pages":"Article 100916"},"PeriodicalIF":0.0,"publicationDate":"2024-09-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142357947","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Diverse soliton wave profile analysis in ion-acoustic wave through an improved analytical approach","authors":"U.H.M. Zaman ,&nbsp;Mohammad Asif Arefin ,&nbsp;M. Ali Akbar ,&nbsp;M. Hafiz Uddin","doi":"10.1016/j.padiff.2024.100932","DOIUrl":"10.1016/j.padiff.2024.100932","url":null,"abstract":"<div><div>In engineering and applied sciences, several physical phenomena can be more precisely characterized by employing nonlinear fractional partial differential equations. The primary goal of this research is to examine the traveling wave solution in closed form for the nonlinear acoustic wave propagation model known as the time fractional simplified modified Camassa–Holm equation, which is used to explain the unidirectional propagation of shallow-water waves with non-hydrostatic pressure and explains the dispersion properties of numerous phenomena like fluid flow, control theory, liquid drop patterning in plasma, acoustics, fusion, and fission processes, etc. The utmost potential approach, namely the new auxiliary equation technique, is applied for analyzing the time nonlinear fractional simplified modified Camassa-Holm equation in the logic of the newest established truncated M-fractional derivative. The fractional partial differential equations have been transformed to the ordinary differential equation using the complex wave transformation in the sense of truncated M-fractional derivative. A variety of soliton solutions, including anti-kink, single soliton, anti-bell, bell, kink, multiple soliton, double soliton, singular-kink, compacton shape, periodic shape, and so many, are displayed in the diagram of 3D and contour plots by taking into account a number of various parameters. It is essential to point out that all derived outcomes are directly compared to the original solutions to certify their exactness. Results show that the used scheme is capable, simple, and straightforward and can be useful to a variety of complex phenomena. The acquired results are unique for the model equation and could be applied to the analysis of several nonlinear study fields.</div></div>","PeriodicalId":34531,"journal":{"name":"Partial Differential Equations in Applied Mathematics","volume":"12 ","pages":"Article 100932"},"PeriodicalIF":0.0,"publicationDate":"2024-09-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142419542","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Convective diffusive thermal flow over an inclined surface with viscous dissipation and aligned magnetic field applications","authors":"Obulesu Mopuri ,&nbsp;Kamel Al-Khaled ,&nbsp;Vediyappan Govindan ,&nbsp;Charankumar Ganteda ,&nbsp;Aruna Ganjikunta ,&nbsp;Barno Abdullaeva ,&nbsp;Furqan Ahmad ,&nbsp;Sami Ullah Khan ,&nbsp;M. Waqas ,&nbsp;D. Piriadarshani","doi":"10.1016/j.padiff.2024.100924","DOIUrl":"10.1016/j.padiff.2024.100924","url":null,"abstract":"<div><div>This investigation incorporating the fluctuation in heat and mass transfer associated to the mixed convection magnetized flow of viscous fluid due to inclined surface with porous media. The contribution of Soret effects and viscous dissipation appliances is addressed. Furthermore, the heat transfer improvement is also assessed by thermal radiation, heat source and joule heating effects. The chemical reaction enrollment is also studied for concentration phenomenon. The convection of problem into non-dimensional framework is based on implication of new variables. The perturbation technique is followed to tracking the analytical outcomes. Physical visualization and interpretation of results under the influence of perturbed parameters have been studied. It is observed that heat and mass transfer enhances due to Soret number. Presence of chemical reaction leads to decrement of concentration profile. Claimed results presents applications in heat and mass transfer processes, chemical reaction, manufacturing systems, chemical engineering, extrusion processes etc.</div></div>","PeriodicalId":34531,"journal":{"name":"Partial Differential Equations in Applied Mathematics","volume":"12 ","pages":"Article 100924"},"PeriodicalIF":0.0,"publicationDate":"2024-09-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142322330","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"The nanoparticles aggregation aspects on the chemically reactive unsteady flow of alumina-water based nanofluid: A Keller box approach with applications of wavelet physics inspired neural networks","authors":"Sumanta Shagolshem ,&nbsp;Chandan K ,&nbsp;Malatesh Akkur ,&nbsp;Bharti Kumari ,&nbsp;Chander Prakash ,&nbsp;T.V. Smitha ,&nbsp;Naveen Kumar R","doi":"10.1016/j.padiff.2024.100931","DOIUrl":"10.1016/j.padiff.2024.100931","url":null,"abstract":"<div><div>The present study explores the unsteady flow of a nanoliquid past a stretching cylinder with the consequence of heat source/sink and chemical reaction. Additionally, the effect of nanoparticle aggregation, convective boundary conditions, and magnetic field on the liquid flow is taken into consideration. Utilizing similarity variables, the modeled equations are transformed into dimensionless ordinary differential equations (ODEs). Further, the obtained ODEs are numerically solved by using the Keller box method. Moreover, the physics-informed neural network (PINN) is applied to analyze the flow, heat, and mass transport features. Graphical illustrations are used to display the influence of various parameters on the velocity, concentration, and temperature profiles for aggregation and without aggregation cases. As the value of the magnetic parameter increases, the temperature and concentration profile upsurge, but the reverse trend can be seen in the velocity profile. The concentration and temperature profiles rise as the unsteadiness parameter increases, but the velocity profile declines. The concentration, velocity, and temperature profiles are strengthened by an improvement in the curvature parameter value. The intensification in the values of the chemical reaction parameter declines the concentration.</div></div>","PeriodicalId":34531,"journal":{"name":"Partial Differential Equations in Applied Mathematics","volume":"12 ","pages":"Article 100931"},"PeriodicalIF":0.0,"publicationDate":"2024-09-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142318793","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Optimal feedback stabilization of fractional output in semilinear distributed systems","authors":"Marouane Karim ,&nbsp;Issam Khaloufi ,&nbsp;Imane Dehaj ,&nbsp;Rachik Mostafa","doi":"10.1016/j.padiff.2024.100911","DOIUrl":"10.1016/j.padiff.2024.100911","url":null,"abstract":"<div><p>This study explores the stabilization of state–space fractional derivatives in semilinear distributed systems, using the Riemann–Liouville derivative of order <span><math><mi>α</mi></math></span>, where <span><math><mi>α</mi></math></span> lies within the interval <span><math><mfenced><mrow><mn>0</mn><mo>,</mo><mn>1</mn></mrow></mfenced></math></span>. The main objective is to develop effective feedback control strategies that ensure both strong and weak stabilization of fractional outputs. Additionally, we tackle a fractional minimization problem to enhance the system’s performance. A numerical simulation example is provided to demonstrate the practical significance of the proposed stabilization theorems.</p></div>","PeriodicalId":34531,"journal":{"name":"Partial Differential Equations in Applied Mathematics","volume":"12 ","pages":"Article 100911"},"PeriodicalIF":0.0,"publicationDate":"2024-09-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S2666818124002973/pdfft?md5=eff1e9b7eb37d27adc7d3dd250722e2d&pid=1-s2.0-S2666818124002973-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142238680","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Modification of Adomian decomposition technique in multiplicative calculus and application for nonlinear equations","authors":"Farooq Ahmed Shah ,&nbsp;Muhammad Waseem ,&nbsp;Alexey Mikhaylov ,&nbsp;Gabor Pinter","doi":"10.1016/j.padiff.2024.100902","DOIUrl":"10.1016/j.padiff.2024.100902","url":null,"abstract":"<div><p>Multiplicative calculus is a mathematical system that offers an alternative to traditional calculus. Instead of using addition and subtraction to measure change, as in traditional calculus, it uses multiplication and division. The framework of nonlinear equations is an incredibly powerful tool that has proven invaluable in advancing our understanding of various phenomena across a wide range of applied sciences. This framework has enabled researchers to gain deeper insights into a vast array of scientific problems. The physical interpretation of iterative methods for nonlinear equations using multiplicative calculus offers a unique perspective on solving such equations and opens up potential applications across various scientific disciplines. Multiplicative calculus naturally aligns with processes characterized by exponential growth or decay. In many physical, biological, and economic systems, quantities change in a manner proportional to their current state. Multiplicative calculus models these processes more accurately than traditional additive approaches. For example, population growth, radioactive decay, and compound interest are all better described multiplicatively. The primary objective of this work is to modify and implement the Adomian decomposition method within the multiplicative calculus framework and to develop an effective class of multiplicative numerical algorithms for obtaining the best approximation of the solution of nonlinear equations. We build up the convergence criteria of the multiplicative iterative methods. To demonstrate the application and effectiveness of these new recurrence relations, we consider some numerical examples. Comparison of the multiplicative iterative methods with the similar ordinary existing methods is presented. Graphical comparison is also provided by plotting log of residuals. The purpose in constructing new algorithms is to show the implementation and effectiveness of multiplicative calculus.</p></div>","PeriodicalId":34531,"journal":{"name":"Partial Differential Equations in Applied Mathematics","volume":"12 ","pages":"Article 100902"},"PeriodicalIF":0.0,"publicationDate":"2024-09-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S2666818124002882/pdfft?md5=605dedd4d9d4bc8599d66b01e67b4b18&pid=1-s2.0-S2666818124002882-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142274056","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Vibrations of a vertical beam rotating with variable angular velocity","authors":"Mehmet Pakdemirli","doi":"10.1016/j.padiff.2024.100929","DOIUrl":"10.1016/j.padiff.2024.100929","url":null,"abstract":"<div><div>An Euler-Bernoulli beam in vertical position rotating about its symmetry axis along its length is considered. The angular velocity is assumed to have small fluctuations about a constant mean velocity. The partial differential equation of motion is derived first. The equation is cast into a non-dimensional form. The natural frequencies are calculated for the pinned-pinned case. Principle parametric resonances such that the fluctuation frequency being close to two times one of the natural frequencies are considered. By employment of the Method of Multiple Scales, an approximate perturbation solution is found. The frequency response diagrams are drawn and the bifurcation points for transition from the trivial solution to the non-trivial solution are calculated. The conditions for which such resonances occur are exploited in the numerical results.</div></div>","PeriodicalId":34531,"journal":{"name":"Partial Differential Equations in Applied Mathematics","volume":"12 ","pages":"Article 100929"},"PeriodicalIF":0.0,"publicationDate":"2024-09-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S2666818124003152/pdfft?md5=2a729d1f83b2bb06bf4f725d98ccf481&pid=1-s2.0-S2666818124003152-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142310679","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Investigating multi-soliton patterns and dynamical characteristics of the (3+1)-dimensional equation via phase portraits","authors":"Muhammad Bilal Riaz ,&nbsp;Adil Jhangeer ,&nbsp;Tomas Kozubek ,&nbsp;Syeda Sarwat Kazmi","doi":"10.1016/j.padiff.2024.100926","DOIUrl":"10.1016/j.padiff.2024.100926","url":null,"abstract":"<div><p>In this study, we investigate the deeper characteristics of the modified Ito equation, which can be applied across various scientific domains to represent systems influenced by noise and randomness. Multi-solitons, including 1-wave, 2-wave, and 3-wave solitons, have been successfully generated using a multiple exponential-function approach. For visual representation, the outcomes are displayed through 3D, 2D, density, and contour plots. The wave transformation is then applied to convert the studied model into an ordinary differential equation. Following this, the dynamic nature of the model is examined from various viewpoints, including bifurcation, chaotic phenomena, multistability, and sensitivity analysis. Bifurcation shows how the solution of a planar system depends on equilibrium points, and when an outward periodic force is implemented to the unperturbed planar system, it reveals chaotic characteristics. These are analyzed using tools such as 3-dimensional and 2-dimensional plots, time scale plots, and Poincaré maps. Additionally, the model’s sensitivity is assessed with varying initial values. The results underscore the effectiveness and relevance of the proposed approaches for examining solitons within a broad spectrum of nonlinear systems.</p></div>","PeriodicalId":34531,"journal":{"name":"Partial Differential Equations in Applied Mathematics","volume":"12 ","pages":"Article 100926"},"PeriodicalIF":0.0,"publicationDate":"2024-09-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S2666818124003127/pdfft?md5=ebe498884be147f2fba753ac825fcfac&pid=1-s2.0-S2666818124003127-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142273886","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"A novel approach for solving weakly singular fractional integro-differential equations","authors":"Ali Jalal Ali,&nbsp;Mostafa Eslami,&nbsp;Ali Tavakoli","doi":"10.1016/j.padiff.2024.100922","DOIUrl":"10.1016/j.padiff.2024.100922","url":null,"abstract":"<div><p>In this essay, we introduce a novel idea to tackle the challenges of fractional integro-differential equations (FIDEs) featuring weakly singular kernels (WSKs). New idea leverages B-splines for solving such equations, offering a robust numerical solution technique. We delve into the operational matrices integral to this method, providing comprehensive insights into their functionality. Furthermore, we establish the convergence of our approach and substantiate its effectiveness through various numerical examples.</p></div>","PeriodicalId":34531,"journal":{"name":"Partial Differential Equations in Applied Mathematics","volume":"12 ","pages":"Article 100922"},"PeriodicalIF":0.0,"publicationDate":"2024-09-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S2666818124003085/pdfft?md5=993d5ac7cae4b379852574ce6443e170&pid=1-s2.0-S2666818124003085-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142273885","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}