Pub Date : 2026-02-04DOI: 10.1016/j.aml.2026.109879
Chunxue Zhao, Xingjie Yan, Xiubin Wang
{"title":"Vector rogue waves and their dynamic patterns of the coupled nonlocal nonlinear Schrödinger equations in the focusing regime","authors":"Chunxue Zhao, Xingjie Yan, Xiubin Wang","doi":"10.1016/j.aml.2026.109879","DOIUrl":"https://doi.org/10.1016/j.aml.2026.109879","url":null,"abstract":"","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"293 1","pages":""},"PeriodicalIF":3.7,"publicationDate":"2026-02-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146134777","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 : 2026-02-03DOI: 10.1016/j.aml.2026.109881
Jishan Fan, Fucai Li
{"title":"A note on L p estimates of the n -dimensional incompressible magnetohydrodynamic equations","authors":"Jishan Fan, Fucai Li","doi":"10.1016/j.aml.2026.109881","DOIUrl":"https://doi.org/10.1016/j.aml.2026.109881","url":null,"abstract":"","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"79 1","pages":""},"PeriodicalIF":3.7,"publicationDate":"2026-02-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146110512","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 : 2026-01-29DOI: 10.1016/j.aml.2026.109883
Jifeng Chu , Kateryna Marynets , Zihao Wang
We analyse a second-order boundary value problem arising from the motion of stratified ocean flows in Antarctica. Using a Lyapunov-type function and the monotonicity properties of the density function and of the oceanic vorticity, we prove results on the existence and uniqueness of solutions of the problem under consideration. Finally, we discuss possible extensions of the model that admit unique solutions for more general cases of density distribution.
{"title":"Existence and uniqueness of stratified Antarctic flows","authors":"Jifeng Chu , Kateryna Marynets , Zihao Wang","doi":"10.1016/j.aml.2026.109883","DOIUrl":"10.1016/j.aml.2026.109883","url":null,"abstract":"<div><div>We analyse a second-order boundary value problem arising from the motion of stratified ocean flows in Antarctica. Using a Lyapunov-type function and the monotonicity properties of the density function and of the oceanic vorticity, we prove results on the existence and uniqueness of solutions of the problem under consideration. Finally, we discuss possible extensions of the model that admit unique solutions for more general cases of density distribution.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"177 ","pages":"Article 109883"},"PeriodicalIF":2.8,"publicationDate":"2026-01-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146072040","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 : 2026-01-29DOI: 10.1016/j.aml.2026.109878
Fei Sun, Hongxing Rui
{"title":"Mixed finite element method for nonlinear hybrid-dimensional fracture model with varying aperture","authors":"Fei Sun, Hongxing Rui","doi":"10.1016/j.aml.2026.109878","DOIUrl":"https://doi.org/10.1016/j.aml.2026.109878","url":null,"abstract":"","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"77 1","pages":""},"PeriodicalIF":3.7,"publicationDate":"2026-01-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146072042","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 : 2026-01-28DOI: 10.1016/j.aml.2026.109880
Zejun Liu, Minxin Jia, Yihao Li
This paper investigates a (3+1)-dimensional higher-order Kadomtsev–Petviashvili (hKP) equation within the Hirota bilinear framework. Motivated by recent experimental observations of lump solitons in nonlinear optics, this study constructs exact lump solutions and hybrid patterns characterizing the nonlinear interaction between a localized lump and a sine-periodic wave for the (3+1)-dimensional hKP equation. Through rigorous dynamical analysis and visualization, the propagation properties of these localized waves are characterized. The results provide insights into the stability and complexity of high-dimensional nonlinear wave systems.
{"title":"Lump solutions and their dynamics of a (3+1)-dimensional higher-order Kadomtsev–Petviashvili equation","authors":"Zejun Liu, Minxin Jia, Yihao Li","doi":"10.1016/j.aml.2026.109880","DOIUrl":"10.1016/j.aml.2026.109880","url":null,"abstract":"<div><div>This paper investigates a (3+1)-dimensional higher-order Kadomtsev–Petviashvili (hKP) equation within the Hirota bilinear framework. Motivated by recent experimental observations of lump solitons in nonlinear optics, this study constructs exact lump solutions and hybrid patterns characterizing the nonlinear interaction between a localized lump and a sine-periodic wave for the (3+1)-dimensional hKP equation. Through rigorous dynamical analysis and visualization, the propagation properties of these localized waves are characterized. The results provide insights into the stability and complexity of high-dimensional nonlinear wave systems.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"177 ","pages":"Article 109880"},"PeriodicalIF":2.8,"publicationDate":"2026-01-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146072045","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 : 2026-01-27DOI: 10.1016/j.aml.2026.109877
Xiao-Fan Zhang , Tian-Cheng Cao , Zhi-Xue Zhao , Zhong-Jie Han
This paper investigates the dynamic stability of a shear beam system with rotational damping. Using frequency domain methods, we prove that the associated semigroup is polynomially stable with an explicit decay rate of . A detailed spectral analysis of the system operator further proves that this rate is optimal in the sense that it cannot be improved. Numerical simulations are provided to validate the theoretical results.
{"title":"Optimal polynomial decay rate for a damped shear beam model","authors":"Xiao-Fan Zhang , Tian-Cheng Cao , Zhi-Xue Zhao , Zhong-Jie Han","doi":"10.1016/j.aml.2026.109877","DOIUrl":"10.1016/j.aml.2026.109877","url":null,"abstract":"<div><div>This paper investigates the dynamic stability of a shear beam system with rotational damping. Using frequency domain methods, we prove that the associated semigroup is polynomially stable with an explicit decay rate of <span><math><msup><mrow><mi>t</mi></mrow><mrow><mo>−</mo><mn>1</mn><mo>/</mo><mn>2</mn></mrow></msup></math></span>. A detailed spectral analysis of the system operator further proves that this rate is optimal in the sense that it cannot be improved. Numerical simulations are provided to validate the theoretical results.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"177 ","pages":"Article 109877"},"PeriodicalIF":2.8,"publicationDate":"2026-01-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146072050","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 : 2026-01-24DOI: 10.1016/j.aml.2026.109876
Bingwen Liu , Chuangxia Huang
This study investigates a generalized scalar non-autonomous delayed Nicholson’s blowflies model with a Gamma-Ricker-type reproduction rate, covering both linear and sublinear cases. Using newly developed differential inequality techniques and the Schauder’s fixed point theorem, we establish sufficient conditions for the existence of positive periodic solutions and derive corresponding delay-dependent criteria ensuring the global attractivity. For the linear case, our results refine and extend existing sharp conclusions on classical Nicholson’s blowflies equations, while the sublinear case yields entirely new findings. These outcomes provide significant enhancements and extensions to recent research in the field. The validity and feasibility of the theoretical results are verified through two numerical examples.
{"title":"Global periodic attractivity for a generalized Nicholson’s blowflies equation with delays","authors":"Bingwen Liu , Chuangxia Huang","doi":"10.1016/j.aml.2026.109876","DOIUrl":"10.1016/j.aml.2026.109876","url":null,"abstract":"<div><div>This study investigates a generalized scalar non-autonomous delayed Nicholson’s blowflies model with a Gamma-Ricker-type reproduction rate, covering both linear and sublinear cases. Using newly developed differential inequality techniques and the Schauder’s fixed point theorem, we establish sufficient conditions for the existence of positive periodic solutions and derive corresponding delay-dependent criteria ensuring the global attractivity. For the linear case, our results refine and extend existing sharp conclusions on classical Nicholson’s blowflies equations, while the sublinear case yields entirely new findings. These outcomes provide significant enhancements and extensions to recent research in the field. The validity and feasibility of the theoretical results are verified through two numerical examples.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"177 ","pages":"Article 109876"},"PeriodicalIF":2.8,"publicationDate":"2026-01-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146047910","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 : 2026-01-20DOI: 10.1016/j.aml.2026.109875
Wenbin Sun , Haodong Ma , Yan Gu , Bo Yu
The boundary element method (BEM) has long been recognized as an efficient numerical technique for the analysis of three-dimensional (3D) elasticity problems due to its intrinsic advantage of dimensionality reduction. However, for inhomogeneous materials or elasticity formulations involving body forces, domain integrals arise, compromising the boundary-only nature of the method. This work proposes a novel scaled-coordinate transformation BEM (SCT-BEM) for 3D elasticity, which inherits the SCT framework recently developed for potential and heat transfer problems. The proposed SCT-BEM transforms the elasticity domain integrals into low-dimensional boundary integrals without invoking particular solutions or volume discretization. Further, a unified treatment is provided for weakly- and strongly-integrals using an SCT-based coordinate translation. Numerical examples demonstrate that the proposed framework significantly improves the applicability of BEM to complex elasticity problems while preserving its fundamental advantages.
{"title":"Scaled-coordinate BEM for 3D elasticity problems with efficient domain integral treatment","authors":"Wenbin Sun , Haodong Ma , Yan Gu , Bo Yu","doi":"10.1016/j.aml.2026.109875","DOIUrl":"10.1016/j.aml.2026.109875","url":null,"abstract":"<div><div>The boundary element method (BEM) has long been recognized as an efficient numerical technique for the analysis of three-dimensional (3D) elasticity problems due to its intrinsic advantage of dimensionality reduction. However, for inhomogeneous materials or elasticity formulations involving body forces, domain integrals arise, compromising the boundary-only nature of the method. This work proposes a novel scaled-coordinate transformation BEM (SCT-BEM) for 3D elasticity, which inherits the SCT framework recently developed for potential and heat transfer problems. The proposed SCT-BEM transforms the elasticity domain integrals into low-dimensional boundary integrals without invoking particular solutions or volume discretization. Further, a unified treatment is provided for weakly- and strongly-integrals using an SCT-based coordinate translation. Numerical examples demonstrate that the proposed framework significantly improves the applicability of BEM to complex elasticity problems while preserving its fundamental advantages.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"177 ","pages":"Article 109875"},"PeriodicalIF":2.8,"publicationDate":"2026-01-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146014828","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 : 2026-01-12DOI: 10.1016/j.aml.2026.109874
Chenyu Zhang , Junying Cao , Shuying Zhai
We present a fast and effective method for image inpainting based on a modified viscous Cahn–Hilliard equation. By employing the second-order operator time-splitting method, the original problem is discretized into two subproblems based on the distinct properties of each part of the model, where the linear subproblem is handled by a Crank–Nicolson (CN) finite difference scheme, and the nonlinear subproblem is treated explicitly with the second-order strong stability preserving Runge–Kutta (SSP-RK) method. Theoretical analysis indicates that the stability of the algorithm depends on the viscosity coefficient , and it is progressively strengthened as increases. Numerical experiments are presented to verify the robustness and accuracy of the proposed method.
{"title":"A fast explicit hybrid numerical method for image inpainting using the viscous Cahn–Hilliard model","authors":"Chenyu Zhang , Junying Cao , Shuying Zhai","doi":"10.1016/j.aml.2026.109874","DOIUrl":"10.1016/j.aml.2026.109874","url":null,"abstract":"<div><div>We present a fast and effective method for image inpainting based on a modified viscous Cahn–Hilliard equation. By employing the second-order operator time-splitting method, the original problem is discretized into two subproblems based on the distinct properties of each part of the model, where the linear subproblem is handled by a Crank–Nicolson (CN) finite difference scheme, and the nonlinear subproblem is treated explicitly with the second-order strong stability preserving Runge–Kutta (SSP-RK) method. Theoretical analysis indicates that the stability of the algorithm depends on the viscosity coefficient <span><math><mi>α</mi></math></span>, and it is progressively strengthened as <span><math><mi>α</mi></math></span> increases. Numerical experiments are presented to verify the robustness and accuracy of the proposed method.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"176 ","pages":"Article 109874"},"PeriodicalIF":2.8,"publicationDate":"2026-01-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145956602","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}
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