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Mathematical Methods in the Applied Sciences最新文献

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The analysis of traveling wave structures and chaos of the cubic–quartic perturbed Biswas–Milovic equation with Kudryashov's nonlinear form and two generalized nonlocal laws 带有库德亚绍夫非线性形式和两个广义非局部定律的立方-方波扰动比斯瓦斯-米洛维奇方程的行波结构和混沌分析
IF 2.9 3区 数学
Mathematical Methods in the Applied Sciences Pub Date : 2024-08-31 DOI: 10.1002/mma.10462
Shuang Li, Xing‐Hua Du
{"title":"The analysis of traveling wave structures and chaos of the cubic–quartic perturbed Biswas–Milovic equation with Kudryashov's nonlinear form and two generalized nonlocal laws","authors":"Shuang Li, Xing‐Hua Du","doi":"10.1002/mma.10462","DOIUrl":"https://doi.org/10.1002/mma.10462","url":null,"abstract":"The cubic–quartic perturbed Biswas–Milovic equation, which contains Kudryashov's nonlinear form and two generalized nonlocal laws, has been explored qualitatively and quantitatively, as demonstrated in the present work. The research methods used include the complete discrimination system for polynomial method and the trial equation method. The results show that the Hamiltonian has the conservation property, and the global phase diagrams obtained via the bifurcation method reveal the existence of periodic and soliton solutions. Furthermore, we fully classify all the single traveling wave solutions to substantiate our findings, covering singular solutions, solitons, and Jacobian elliptic function solutions. We analyze their topological stabilities and present two‐dimensional graphs of solutions. We also delve deeper into the dynamic system by incorporating the perturbation item to explore the chaotic phenomena associated with the equation. These outcomes are valuable for studying the propagation of high‐order dispersive optical solitons and have potential applications in optimizing optical communication systems to improve efficiency.","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":"11 1","pages":""},"PeriodicalIF":2.9,"publicationDate":"2024-08-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142220053","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}
引用次数: 0
A family of quadrature formulas with their error bounds for convex functions and applications 凸函数的一系列正交公式及其误差范围和应用
IF 2.9 3区 数学
Mathematical Methods in the Applied Sciences Pub Date : 2024-08-31 DOI: 10.1002/mma.10460
Muhammad Toseef, Abdul Mateen, Muhammad Aamir Ali, Zhiyue Zhang
{"title":"A family of quadrature formulas with their error bounds for convex functions and applications","authors":"Muhammad Toseef, Abdul Mateen, Muhammad Aamir Ali, Zhiyue Zhang","doi":"10.1002/mma.10460","DOIUrl":"https://doi.org/10.1002/mma.10460","url":null,"abstract":"In numerical analysis, the quadrature formulas serve as a pivotal tool for approximating definite integrals. In this paper, we introduce a family of quadrature formulas and analyze their associated error bounds for convex functions. The main advantage of these new error bounds is that from these error bounds, we can find the error bounds of different quadrature formulas. This work extends the traditional quadrature formulas such as the midpoint formula, trapezoidal formula, Simpson's formula, and Boole's formula. We also use the power mean and Hölder's integral inequalities to find more general and sharp bounds. Furthermore, we give numerical example and applications to quadrature formulas of the newly established inequalities.","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":"38 1","pages":""},"PeriodicalIF":2.9,"publicationDate":"2024-08-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142220052","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}
引用次数: 0
Nonlinear dynamics in a fear-driven predator–prey system: Bistability, bifurcations, hydra effect, and optimal harvesting 恐惧驱动的捕食者-猎物系统的非线性动力学：双稳态、分岔、九头蛇效应和最优收获
IF 2.1 3区 数学
Mathematical Methods in the Applied Sciences Pub Date : 2024-08-31 DOI: 10.1002/mma.10431
Anuj Kumar Umrao, Sonu Lamba, Prashant K. Srivastava
{"title":"Nonlinear dynamics in a fear-driven predator–prey system: Bistability, bifurcations, hydra effect, and optimal harvesting","authors":"Anuj Kumar Umrao,&nbsp;Sonu Lamba,&nbsp;Prashant K. Srivastava","doi":"10.1002/mma.10431","DOIUrl":"10.1002/mma.10431","url":null,"abstract":"<p>The impact of predator-driven fear on ecosystems is significant and can encompass both trophic (direct) and nontrophic (indirect) effects. Previous studies have shown that nontrophic fear effects have an important role in predator–prey dynamics. This study investigates the nontrophic fear effect on prey caused by generalist predators and explores optimal harvesting. We assume that the reproduction rate of prey is reduced due to the fear effect, and generalist predator follows Holling type II foraging strategy for predation. Additionally, we assume that predators are commercially valuable and harvested proportionately to their density. We demonstrate the existence of equilibrium points, their local and global stability, and bifurcation analysis. We observe that the model system undergoes a sequence of codimension one and codimension two bifurcations. Our results show that in the absence of predator harvesting, increasing levels of fear destabilize the predator–prey system, and controlled harvesting is beneficial for the coexistence of both populations. Also, the harvesting of predators may produce hydra and multiple hydra effects. We identify different types of bistability phenomena, which emphasize the importance of initial population size. Further, an optimal harvesting policy is also explored by formulating an optimal control problem (OCP). The harvesting cost-functional is designed by incorporating the bionomic equilibrium state. We use Pontryagin's maximum principle and solve the OCP numerically. It is observed that implementing optimal harvesting not only contributes to the ecological benefits by maintaining a sustainable balance of predator–prey evolution but also plays a significant role in maximizing the economic benefits.</p>","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":"48 2","pages":"2194-2223"},"PeriodicalIF":2.1,"publicationDate":"2024-08-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/mma.10431","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142220051","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}
引用次数: 0
Spectral properties for discontinuous Dirac system with eigenparameter-dependent boundary condition 具有特征参数相关边界条件的不连续狄拉克系统的频谱特性
IF 2.1 3区 数学
Mathematical Methods in the Applied Sciences Pub Date : 2024-08-30 DOI: 10.1002/mma.10364
Jiajia Zheng, Kun Li, Zhaowen Zheng
{"title":"Spectral properties for discontinuous Dirac system with eigenparameter-dependent boundary condition","authors":"Jiajia Zheng,&nbsp;Kun Li,&nbsp;Zhaowen Zheng","doi":"10.1002/mma.10364","DOIUrl":"10.1002/mma.10364","url":null,"abstract":"<p>In this paper, Dirac system with interface conditions and spectral parameter dependent boundary conditions is investigated. By introducing a new Hilbert space, the original problem is transformed into an operator problem. Then the continuity and differentiability of the eigenvalues with respect to the parameters in the problem are showed. In particular, the differential expressions of eigenvalues for each parameter are given. These results would provide theoretical support for the calculation of eigenvalues of the corresponding problems.</p>","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":"48 1","pages":"870-889"},"PeriodicalIF":2.1,"publicationDate":"2024-08-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142220048","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}
引用次数: 0
Sharp estimates of solution of an elliptic problem on a family of open non-convex planar sectors 开放非凸平面扇形族上椭圆问题解法的锐估计
IF 2.1 3区 数学
Mathematical Methods in the Applied Sciences Pub Date : 2024-08-30 DOI: 10.1002/mma.10449
Abdelaziz Douah, Abdelkader Tami, Mounir Tlemcani
{"title":"Sharp estimates of solution of an elliptic problem on a family of open non-convex planar sectors","authors":"Abdelaziz Douah,&nbsp;Abdelkader Tami,&nbsp;Mounir Tlemcani","doi":"10.1002/mma.10449","DOIUrl":"10.1002/mma.10449","url":null,"abstract":"<p>Based on partial Fourier series analysis, we adapt on a model case a new approach to classical results obtained in the literature describing the singularities of a family a solutions of a second-order elliptic problems on open non-convex planar sectors. The method allows the exhibition of singular and regular frequencies, explicit decomposition, and description of coefficients of singularities of the solution. As a main result, explicit and sharp estimates with respect to the opening angle parameter are obtained via this method. They are not uniform near \u0000<span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>π</mi>\u0000 </mrow>\u0000 <annotation>$$ pi $$</annotation>\u0000 </semantics></math> where corners have opening angle generating a jump of singularity in Sobolev exponent, contrarily to the results obtained for harmonic and/or biharmonic problems on a family of convex planar sectors.</p>","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":"48 2","pages":"2529-2544"},"PeriodicalIF":2.1,"publicationDate":"2024-08-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142220059","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}
引用次数: 0
Global solvability for semidiscrete Kirchhoff equation 半离散基尔霍夫方程的全局可解性
IF 2.1 3区 数学
Mathematical Methods in the Applied Sciences Pub Date : 2024-08-30 DOI: 10.1002/mma.10453
Fumihiko Hirosawa
{"title":"Global solvability for semidiscrete Kirchhoff equation","authors":"Fumihiko Hirosawa","doi":"10.1002/mma.10453","DOIUrl":"10.1002/mma.10453","url":null,"abstract":"<p>It is effective to consider discretized problems for partial differential equations that are difficult to analyze themselves. The global solvability of the initial value problem of the Kirchhoff equation is still unsolved except in cases where the initial value is a specially restricted class. In this paper, we prove the global solvability of the semidiscrete Kirchhoff equation, which is obtained by discretizing the Kirchhoff equation with respect to spatial variables.</p>","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":"48 2","pages":"2600-2611"},"PeriodicalIF":2.1,"publicationDate":"2024-08-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142220057","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}
引用次数: 0
Instability of H1-stable periodic peakons for the Novikov equation 诺维科夫方程 H1$$ {H}&#x0005E;1 $$ 稳定周期峰子的不稳定性
IF 2.1 3区 数学
Mathematical Methods in the Applied Sciences Pub Date : 2024-08-30 DOI: 10.1002/mma.10436
Gezi Chong, Ying Fu, Hao Wang
{"title":"Instability of \u0000H1-stable periodic peakons for the Novikov equation","authors":"Gezi Chong,&nbsp;Ying Fu,&nbsp;Hao Wang","doi":"10.1002/mma.10436","DOIUrl":"10.1002/mma.10436","url":null,"abstract":"<p>Periodic peaked waves of the Novikov equation have been proved to be \u0000<span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <msup>\u0000 <mrow>\u0000 <mi>H</mi>\u0000 </mrow>\u0000 <mrow>\u0000 <mn>1</mn>\u0000 </mrow>\u0000 </msup>\u0000 </mrow>\u0000 <annotation>$$ {H}&amp;amp;amp;#x0005E;1 $$</annotation>\u0000 </semantics></math>-orbital stable. Utilizing the method of characteristics, we establish that the periodic peakons of the Novikov equation are linearly unstable under \u0000<span></span><math>\u0000 <msup>\u0000 <mrow>\u0000 <mi>W</mi>\u0000 </mrow>\u0000 <mrow>\u0000 <mn>1</mn>\u0000 <mo>,</mo>\u0000 <mi>∞</mi>\u0000 </mrow>\u0000 </msup>\u0000 <mo>(</mo>\u0000 <mi>𝕋</mi>\u0000 <mo>)</mo></math> perturbations. Moreover, it is proved that the small initial \u0000<span></span><math>\u0000 <msup>\u0000 <mrow>\u0000 <mi>W</mi>\u0000 </mrow>\u0000 <mrow>\u0000 <mn>1</mn>\u0000 <mo>,</mo>\u0000 <mi>∞</mi>\u0000 </mrow>\u0000 </msup>\u0000 <mo>(</mo>\u0000 <mi>𝕋</mi>\u0000 <mo>)</mo></math> perturbations of the above periodic peakons can lead to the blow-up phenomenon in finite time in the nonlinear evolution of the Novikov equation.</p>","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":"48 2","pages":"2294-2317"},"PeriodicalIF":2.1,"publicationDate":"2024-08-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142220050","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}
引用次数: 0
Distributed order hantavirus model and its nonstandard discretizations and stability analysis 分布式阶梯汉坦病毒模型及其非标准离散化和稳定性分析
IF 2.1 3区 数学
Mathematical Methods in the Applied Sciences Pub Date : 2024-08-30 DOI: 10.1002/mma.10442
Mehmet Kocabiyik, Mevlüde Yakit Ongun
{"title":"Distributed order hantavirus model and its nonstandard discretizations and stability analysis","authors":"Mehmet Kocabiyik,&nbsp;Mevlüde Yakit Ongun","doi":"10.1002/mma.10442","DOIUrl":"10.1002/mma.10442","url":null,"abstract":"<p>It is crucial to understand the effects of deadly viruses on humans in advance. One such virus is the infectious hantavirus. Since the effects of viruses vary under different conditions, this study models the virus using distributed order differential equations. Because distributed order differential equations effectively capture variable effects in different conditions through the incorporated density function, this study aims to achieve a solution via the discretization method after presenting the equation system. A nonstandard finite difference scheme (NSFD) is used for the discretization. Then the stability analysis of the discretized system is investigated.</p>","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":"48 2","pages":"2404-2420"},"PeriodicalIF":2.1,"publicationDate":"2024-08-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/mma.10442","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142220055","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}
引用次数: 0
Application of Chelyshkov wavelets and least squares support vector regression to solve fractional differential equations arising in optics and engineering 应用切利什科夫小波和最小二乘支持向量回归求解光学和工程学中出现的分数微分方程
IF 2.1 3区 数学
Mathematical Methods in the Applied Sciences Pub Date : 2024-08-30 DOI: 10.1002/mma.10420
Yadollah Ordokhani, Sedigheh Sabermahani, Parisa Rahimkhani
{"title":"Application of Chelyshkov wavelets and least squares support vector regression to solve fractional differential equations arising in optics and engineering","authors":"Yadollah Ordokhani,&nbsp;Sedigheh Sabermahani,&nbsp;Parisa Rahimkhani","doi":"10.1002/mma.10420","DOIUrl":"10.1002/mma.10420","url":null,"abstract":"<p>Fractional-order ray equations and fractional Duffing-van der Pol oscillator equations are relationships utilized as a reliable means of modeling some phenomena in optics and engineering. The main motivation of this study is to introduce a new hybrid technique utilizing Chelyshkov wavelets and least squares-support vector regression (LS-SVR) for determining the approximate solution of fractional ray equations and fractional Duffing-van der Pol oscillator equations (D-v POEs). With the help of the Riemann-Liouville operator for Chelyshkov wavelets and LS-SVR (called Chw-Ls-SVR), the mentioned problems transform into systems of algebraic equations. The convergence analysis is discussed. Finally, the numerical results are proposed and compared with some schemes to display the capability of the numerical technique proposed here.</p>","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":"48 2","pages":"1996-2010"},"PeriodicalIF":2.1,"publicationDate":"2024-08-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142220058","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}
引用次数: 0
Persistence of the solution to the Euler equations in an end-point critical Triebel–Lizorkin space 端点临界特里贝尔-利佐尔金空间中欧拉方程解的持久性
IF 2.1 3区 数学
Mathematical Methods in the Applied Sciences Pub Date : 2024-08-30 DOI: 10.1002/mma.10443
JunSeok Hwang, Hee Chul Pak
{"title":"Persistence of the solution to the Euler equations in an end-point critical Triebel–Lizorkin space","authors":"JunSeok Hwang,&nbsp;Hee Chul Pak","doi":"10.1002/mma.10443","DOIUrl":"10.1002/mma.10443","url":null,"abstract":"<p>Local stay of the solutions to the Euler equations for an ideal incompressible fluid in the end-point Triebel–Lizorkin space \u0000<span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <msubsup>\u0000 <mrow>\u0000 <mi>F</mi>\u0000 </mrow>\u0000 <mrow>\u0000 <mn>1</mn>\u0000 <mo>,</mo>\u0000 <mi>∞</mi>\u0000 </mrow>\u0000 <mrow>\u0000 <mi>s</mi>\u0000 </mrow>\u0000 </msubsup>\u0000 <mfenced>\u0000 <mrow>\u0000 <msup>\u0000 <mrow>\u0000 <mi>ℝ</mi>\u0000 </mrow>\u0000 <mrow>\u0000 <mi>d</mi>\u0000 </mrow>\u0000 </msup>\u0000 </mrow>\u0000 </mfenced>\u0000 </mrow>\u0000 <annotation>$$ {F}_{1,infty}&amp;amp;amp;#x0005E;sleft({mathbb{R}}&amp;amp;amp;#x0005E;dright) $$</annotation>\u0000 </semantics></math> with \u0000<span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>s</mi>\u0000 <mo>≥</mo>\u0000 <mi>d</mi>\u0000 <mo>+</mo>\u0000 <mn>1</mn>\u0000 </mrow>\u0000 <annotation>$$ sge d&amp;amp;amp;#x0002B;1 $$</annotation>\u0000 </semantics></math> is clarified.</p>","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":"48 2","pages":"2421-2433"},"PeriodicalIF":2.1,"publicationDate":"2024-08-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/mma.10443","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142220056","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}
引用次数: 0
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