Pub Date : 2025-09-23DOI: 10.1016/j.aml.2025.109769
Tao Xu, Yaonan Shan
The ()-dimensional Wazwaz–Kaur–Boussinesq equation, which always describe shallow water wave interactions, is researched by the Wronskian technique. To guarantee the Wronskian determinant solves the objective equation in Hirota bilinear form, we construct some sufficient conditions consisting of linear differential equations. Based on the received Wronskian conditions, the general Wronskian solutions can be successfully derived. Choosing the matrix in the Wronskian conditions as diagonal or Jordan forms, three kinds of exact solutions including -bright, -dark solitons and rational solutions are skillfully reduced from the resulted general solutions.
{"title":"Wronskian solutions for the (3+1)-dimensional Wazwaz–Kaur–Boussinesq equation","authors":"Tao Xu, Yaonan Shan","doi":"10.1016/j.aml.2025.109769","DOIUrl":"10.1016/j.aml.2025.109769","url":null,"abstract":"<div><div>The (<span><math><mrow><mn>3</mn><mo>+</mo><mn>1</mn></mrow></math></span>)-dimensional Wazwaz–Kaur–Boussinesq equation, which always describe shallow water wave interactions, is researched by the Wronskian technique. To guarantee the Wronskian determinant solves the objective equation in Hirota bilinear form, we construct some sufficient conditions consisting of linear differential equations. Based on the received Wronskian conditions, the general Wronskian solutions can be successfully derived. Choosing the matrix in the Wronskian conditions as diagonal or Jordan forms, three kinds of exact solutions including <span><math><mi>N</mi></math></span>-bright, <span><math><mi>N</mi></math></span>-dark solitons and rational solutions are skillfully reduced from the resulted general solutions.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"173 ","pages":"Article 109769"},"PeriodicalIF":2.8,"publicationDate":"2025-09-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145158741","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-09-22DOI: 10.1016/j.aml.2025.109765
Zhong-Zhi Bai, Yan-Qi Chen
The admissibly randomized coordinate descent method is an effective iteration solver for computing the smallest eigenpairs of symmetric matrices of very large sizes. This randomized iteration method is, however, only proved to be convergent locally. In this work, we are going to demonstrate its global convergence by proving that it always converges to a certain eigenpair of the target matrix for any normalized initial vector. Hence, the convergence theory of this randomized iteration method is further enriched and completed.
{"title":"On global convergence of admissibly randomized coordinate descent method","authors":"Zhong-Zhi Bai, Yan-Qi Chen","doi":"10.1016/j.aml.2025.109765","DOIUrl":"10.1016/j.aml.2025.109765","url":null,"abstract":"<div><div>The admissibly randomized coordinate descent method is an effective iteration solver for computing the smallest eigenpairs of symmetric matrices of very large sizes. This randomized iteration method is, however, only proved to be convergent locally. In this work, we are going to demonstrate its global convergence by proving that it always converges to a certain eigenpair of the target matrix for any normalized initial vector. Hence, the convergence theory of this randomized iteration method is further enriched and completed.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"173 ","pages":"Article 109765"},"PeriodicalIF":2.8,"publicationDate":"2025-09-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145158745","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-09-22DOI: 10.1016/j.aml.2025.109733
Zhan Wang, Shengjie Li
In this paper, we present a Gauss–Newton-like conjugate gradient method for solving large-scale nonlinear equations. This new method can essentially be regarded as a spectral three-term conjugate gradient method, where the spectral parameter is designed based on an approximate Gauss–Newton direction and the secant equation. Global convergence is established under appropriate conditions. Numerical experiments demonstrate that the presented method is more effective than other existing methods in solving large-scale nonlinear equations. Moreover, this new method exhibits significant advantages in image restoration problems.
{"title":"A Gauss–Newton-like conjugate gradient method for large-scale nonlinear equations and image restoration problems","authors":"Zhan Wang, Shengjie Li","doi":"10.1016/j.aml.2025.109733","DOIUrl":"10.1016/j.aml.2025.109733","url":null,"abstract":"<div><div>In this paper, we present a Gauss–Newton-like conjugate gradient method for solving large-scale nonlinear equations. This new method can essentially be regarded as a spectral three-term conjugate gradient method, where the spectral parameter is designed based on an approximate Gauss–Newton direction and the secant equation. Global convergence is established under appropriate conditions. Numerical experiments demonstrate that the presented method is more effective than other existing methods in solving large-scale nonlinear equations. Moreover, this new method exhibits significant advantages in image restoration problems.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"173 ","pages":"Article 109733"},"PeriodicalIF":2.8,"publicationDate":"2025-09-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145158744","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-09-20DOI: 10.1016/j.aml.2025.109767
Carlos Lizama , Marina Murillo-Arcila
We investigate a class of abstract fractional evolution equations governed by convolution-type derivatives associated with Sonine kernels. These generalized derivatives encompass several known fractional operators, including the Caputo–Dzhrbashyan and distributed-order derivatives. We analyze the Cauchy problem where is a Sonine kernel, is a closed linear operator generating a bounded analytic semigroup, and . Using functional analytic techniques and subordination theory, we establish well-posedness in the space of infinitely smooth vectors and derive explicit representations for the solution via Laplace transforms and fractional semigroup theory. Several examples involving the Laplacian on different function spaces are discussed to illustrate the theory.
我们研究了一类抽象的分数阶演化方程，该方程由与Sonine核相关的卷积型导数所控制。这些广义导数包含了几个已知的分数算子，包括Caputo-Dzhrbashyan和分布阶导数。我们分析了柯西问题∂t(k∗(u−u0))(t)= - a αu(t)，其中k是Sonine核，a是生成有界解析半群的闭线性算子，α∈(0,1)。利用泛函解析技术和隶属理论，建立了无限光滑向量空间的适定性，并利用拉普拉斯变换和分数阶半群理论推导了其解的显式表示。讨论了不同函数空间上的拉普拉斯算子的几个例子来说明这一理论。
{"title":"Fundamental solutions for abstract fractional evolution equations with generalized convolution operators","authors":"Carlos Lizama , Marina Murillo-Arcila","doi":"10.1016/j.aml.2025.109767","DOIUrl":"10.1016/j.aml.2025.109767","url":null,"abstract":"<div><div>We investigate a class of abstract fractional evolution equations governed by convolution-type derivatives associated with Sonine kernels. These generalized derivatives encompass several known fractional operators, including the Caputo–Dzhrbashyan and distributed-order derivatives. We analyze the Cauchy problem <span><span><span><math><mrow><msub><mrow><mi>∂</mi></mrow><mrow><mi>t</mi></mrow></msub><mrow><mo>(</mo><mi>k</mi><mo>∗</mo><mrow><mo>(</mo><mi>u</mi><mo>−</mo><msub><mrow><mi>u</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>)</mo></mrow><mo>)</mo></mrow><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow><mo>=</mo><mo>−</mo><msup><mrow><mi>A</mi></mrow><mrow><mi>α</mi></mrow></msup><mi>u</mi><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow><mo>,</mo></mrow></math></span></span></span>where <span><math><mi>k</mi></math></span> is a Sonine kernel, <span><math><mi>A</mi></math></span> is a closed linear operator generating a bounded analytic semigroup, and <span><math><mrow><mi>α</mi><mo>∈</mo><mrow><mo>(</mo><mn>0</mn><mo>,</mo><mn>1</mn><mo>)</mo></mrow></mrow></math></span>. Using functional analytic techniques and subordination theory, we establish well-posedness in the space of infinitely smooth vectors and derive explicit representations for the solution via Laplace transforms and fractional semigroup theory. Several examples involving the Laplacian on different function spaces are discussed to illustrate the theory.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"173 ","pages":"Article 109767"},"PeriodicalIF":2.8,"publicationDate":"2025-09-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145121223","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-09-19DOI: 10.1016/j.aml.2025.109768
Linlin Gui, Yufeng Zhang
Manakov and Santini, etc., have solved inverse scattering problem for dispersionless integrable partial differential equations (PDEs), and used these to construct the formal solutions for integrable equations. In this paper, we derive a new equation from a pair of two-dimensional vector fields, termed the generalized r-th dispersionless Harry Dym (g-rdDym) equation, which reduces to the standard (2+1)-dimensional r-th dispersionless Harry Dym (rdDym) equation. Then we construct large behaviour of formal solution of Cauchy problem by applying associated Riemann-Hilbert (RH) inverse problem, and describe a new class of particular solutions via the exponential functions. This paper investigates not only the rdDym equation, but also its corresponding generalized equation, i.e. the g-rdDym equation.
{"title":"The large t behaviour of solutions for a new generalized r-th dispersionless Harry Dym equation","authors":"Linlin Gui, Yufeng Zhang","doi":"10.1016/j.aml.2025.109768","DOIUrl":"10.1016/j.aml.2025.109768","url":null,"abstract":"<div><div>Manakov and Santini, etc., have solved inverse scattering problem for dispersionless integrable partial differential equations (PDEs), and used these to construct the formal solutions for integrable equations. In this paper, we derive a new equation from a pair of two-dimensional vector fields, termed the generalized r-th dispersionless Harry Dym (g-rdDym) equation, which reduces to the standard (2+1)-dimensional r-th dispersionless Harry Dym (rdDym) equation. Then we construct large <span><math><mi>t</mi></math></span> behaviour of formal solution of Cauchy problem by applying associated Riemann-Hilbert (RH) inverse problem, and describe a new class of particular solutions via the exponential functions. This paper investigates not only the rdDym equation, but also its corresponding generalized equation, i.e. the g-rdDym equation.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"173 ","pages":"Article 109768"},"PeriodicalIF":2.8,"publicationDate":"2025-09-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145097041","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-09-19DOI: 10.1016/j.aml.2025.109766
Roberto Cavoretto
In this article we enhance the rational RBF partition of unity (RBF-PU) method presented in Farazandeh and Mirzaei (2021) for shape parameter free RBFs. Here, we propose a leave-one-out cross-validation technique to optimize the RBF shape parameter in the context of rational interpolation. This approach enables us to obtain remarkable results in the rational RBF-PU scheme for shape parameter dependent RBFs. Numerical experiments highlight performance of the rational RBF-PU interpolation, also in comparison to that of the standard method.
{"title":"Optimizing the shape parameter in rational RBF partition of unity interpolation","authors":"Roberto Cavoretto","doi":"10.1016/j.aml.2025.109766","DOIUrl":"10.1016/j.aml.2025.109766","url":null,"abstract":"<div><div>In this article we enhance the rational RBF partition of unity (RBF-PU) method presented in Farazandeh and Mirzaei (2021) for shape parameter free RBFs. Here, we propose a leave-one-out cross-validation technique to optimize the RBF shape parameter in the context of rational interpolation. This approach enables us to obtain remarkable results in the rational RBF-PU scheme for shape parameter dependent RBFs. Numerical experiments highlight performance of the rational RBF-PU interpolation, also in comparison to that of the standard method.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"173 ","pages":"Article 109766"},"PeriodicalIF":2.8,"publicationDate":"2025-09-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145097042","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-09-19DOI: 10.1016/j.aml.2025.109764
Yixuan Ge , Zhenyu Chen , Baochang Shi , Yong Zhao
In this paper, we propose a regularized lattice Boltzmann model for one-dimensional nonlinear scalar hyperbolic conservation laws which can convert to convection–diffusion equation through introducing a dissipation term. Then, a rigorous Chapman–Enskog analysis is conducted to show that this models can recover the correct governing equation. Finally, we also conduct some simulations to test the model and find that the numerical results not only agree with the exact solutions but also exhibits superior performance in solving hyperbolic conservation laws with discontinuous initial conditions.
{"title":"Regularized lattice Boltzmann model for one-dimensional nonlinear scalar hyperbolic conservation laws","authors":"Yixuan Ge , Zhenyu Chen , Baochang Shi , Yong Zhao","doi":"10.1016/j.aml.2025.109764","DOIUrl":"10.1016/j.aml.2025.109764","url":null,"abstract":"<div><div>In this paper, we propose a regularized lattice Boltzmann model for one-dimensional nonlinear scalar hyperbolic conservation laws which can convert to convection–diffusion equation through introducing a dissipation term. Then, a rigorous Chapman–Enskog analysis is conducted to show that this models can recover the correct governing equation. Finally, we also conduct some simulations to test the model and find that the numerical results not only agree with the exact solutions but also exhibits superior performance in solving hyperbolic conservation laws with discontinuous initial conditions.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"173 ","pages":"Article 109764"},"PeriodicalIF":2.8,"publicationDate":"2025-09-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145097040","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-09-18DOI: 10.1016/j.aml.2025.109763
Leonid Shaikhet
To readers attention two known theorems on the stabilization of a controlled inverted pendulum under stochastic perturbations in the form of a combination of white noise and Poisson’s jumps are presented. As unsolved problems, a generalization of these theorems is proposed for a mathematical model, described two coupled controlled inverted pendulums.
{"title":"About unsolved problems in stabilization of two coupled controlled inverted pendulums under stochastic perturbations","authors":"Leonid Shaikhet","doi":"10.1016/j.aml.2025.109763","DOIUrl":"10.1016/j.aml.2025.109763","url":null,"abstract":"<div><div>To readers attention two known theorems on the stabilization of a controlled inverted pendulum under stochastic perturbations in the form of a combination of white noise and Poisson’s jumps are presented. As unsolved problems, a generalization of these theorems is proposed for a mathematical model, described two coupled controlled inverted pendulums.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"173 ","pages":"Article 109763"},"PeriodicalIF":2.8,"publicationDate":"2025-09-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145097038","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-09-17DOI: 10.1016/j.aml.2025.109762
Yarong Xia , Wenjie Huang , Ruoxia Yao
This paper mainly studies the interaction structures of lump wave and other types of localized wave for (2+ 1)-dimensional Sawada–Kotera-like (SK-Like) equation. Firstly, the -soliton solutions are constructed via the Hirota bilinear method. Subsequently, using the long-wave limit method, we derive several distinct hybrid solutions which include lump-line waves, lump-breather waves, and hybrid solution among lump, line and breather waves. At the same time, we discuss that the lump wave neither collides with line waves or breather waves nor always lies on them under the conditions and . In addition, based on the mixed solutions obtained above, by leveraging the velocity resonance mechanism, we construct the soliton molecular bound states among lump wave, line wave, and breather wave. Furthermore, through numerical simulation, vivid pictures of the superposition of lump wave and other nonlinear waves are presented.
{"title":"Interaction structures of (2+1)-dimensional Sawada–Kotera-like equation","authors":"Yarong Xia , Wenjie Huang , Ruoxia Yao","doi":"10.1016/j.aml.2025.109762","DOIUrl":"10.1016/j.aml.2025.109762","url":null,"abstract":"<div><div>This paper mainly studies the interaction structures of lump wave and other types of localized wave for (2+ 1)-dimensional Sawada–Kotera-like (SK-Like) equation. Firstly, the <span><math><mi>N</mi></math></span>-soliton solutions are constructed via the Hirota bilinear method. Subsequently, using the long-wave limit method, we derive several distinct hybrid solutions which include lump-line waves, lump-breather waves, and hybrid solution among lump, line and breather waves. At the same time, we discuss that the lump wave neither collides with line waves or breather waves nor always lies on them under the conditions <span><math><mrow><msub><mrow><mi>λ</mi></mrow><mrow><mn>3</mn></mrow></msub><mo>=</mo><mn>0</mn></mrow></math></span> and <span><math><mrow><msub><mrow><mi>λ</mi></mrow><mrow><mn>4</mn></mrow></msub><mo>=</mo><mn>0</mn></mrow></math></span>. In addition, based on the mixed solutions obtained above, by leveraging the velocity resonance mechanism, we construct the soliton molecular bound states among lump wave, line wave, and breather wave. Furthermore, through numerical simulation, vivid pictures of the superposition of lump wave and other nonlinear waves are presented.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"173 ","pages":"Article 109762"},"PeriodicalIF":2.8,"publicationDate":"2025-09-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145109586","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-09-16DOI: 10.1016/j.aml.2025.109760
Henghui Tang, Liquan Mei
For the Allen–Cahn equation, it is highly desirable to develop numerical schemes that achieve both high-order temporal accuracy and energy stability. In this work, we propose a high-order energy-stable scheme by combining an explicit time integration method inspired by the Adams–Bashforth method with the scalar auxiliary variable (SAV) framework. The resulting time-stepping scheme is capable of attaining arbitrarily high orders of accuracy while preserving energy stability, a property that is rigorously proven in this paper. Numerical experiments are conducted to validate the stability and convergence behavior of the proposed method.
{"title":"An arbitrarily high-order energy-stabilized Adams–Bashforth-type-SAV scheme for the Allen–Cahn equation","authors":"Henghui Tang, Liquan Mei","doi":"10.1016/j.aml.2025.109760","DOIUrl":"10.1016/j.aml.2025.109760","url":null,"abstract":"<div><div>For the Allen–Cahn equation, it is highly desirable to develop numerical schemes that achieve both high-order temporal accuracy and energy stability. In this work, we propose a high-order energy-stable scheme by combining an explicit time integration method inspired by the Adams–Bashforth method with the scalar auxiliary variable (SAV) framework. The resulting time-stepping scheme is capable of attaining arbitrarily high orders of accuracy while preserving energy stability, a property that is rigorously proven in this paper. Numerical experiments are conducted to validate the stability and convergence behavior of the proposed method.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"173 ","pages":"Article 109760"},"PeriodicalIF":2.8,"publicationDate":"2025-09-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145097039","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
扫码关注我们
求助内容：
应助结果提醒方式：
京公网安备 11010802042870号