Pub Date : 2026-06-01Epub 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":"2026-06-01","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 : 2026-06-01Epub 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":"2026-06-01","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 : 2026-06-01Epub 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":"2026-06-01","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 : 2026-06-01Epub Date: 2026-02-02DOI: 10.1016/j.aml.2026.109884
Runjie Han, Shaojie Yang
In this paper, we investigate wave breaking in the unidirectional non-local wave model describing the motion of a collision-free plasma in a magnetic field. By analyzing the blow-up behavior of a Riccati-type inequality involving a linear function of time , a new wave breaking criterion is presented. Our result shows that wave breaking can occur even with small slope of the initial data.
{"title":"New wave breaking in the unidirectional non-local wave model","authors":"Runjie Han, Shaojie Yang","doi":"10.1016/j.aml.2026.109884","DOIUrl":"10.1016/j.aml.2026.109884","url":null,"abstract":"<div><div>In this paper, we investigate wave breaking in the unidirectional non-local wave model describing the motion of a collision-free plasma in a magnetic field. By analyzing the blow-up behavior of a Riccati-type inequality involving a linear function of time <span><math><mi>t</mi></math></span>, a new wave breaking criterion is presented. Our result shows that wave breaking can occur even with small slope of the initial data.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"177 ","pages":"Article 109884"},"PeriodicalIF":2.8,"publicationDate":"2026-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146110515","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 : 2026-06-01Epub Date: 2026-02-03DOI: 10.1016/j.aml.2026.109881
Jishan Fan , Fucai Li
In this note, we prove some new -type estimates of strong solutions to the incompressible magnetohydrodynamic equations in by the energy method.
本文用Lp能量法证明了Rn（n≥3）中不可压缩磁流体动力学方程强解的一些新的Lp型估计。
{"title":"A note on Lp estimates of the n-dimensional incompressible magnetohydrodynamic equations","authors":"Jishan Fan , Fucai Li","doi":"10.1016/j.aml.2026.109881","DOIUrl":"10.1016/j.aml.2026.109881","url":null,"abstract":"<div><div>In this note, we prove some new <span><math><msup><mrow><mi>L</mi></mrow><mrow><mi>p</mi></mrow></msup></math></span>-type estimates of strong solutions to the incompressible magnetohydrodynamic equations in <span><math><mrow><msup><mrow><mi>R</mi></mrow><mrow><mi>n</mi></mrow></msup><mrow><mo>(</mo><mi>n</mi><mo>≥</mo><mn>3</mn><mo>)</mo></mrow></mrow></math></span> by the <span><math><msup><mrow><mi>L</mi></mrow><mrow><mi>p</mi></mrow></msup></math></span> energy method.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"177 ","pages":"Article 109881"},"PeriodicalIF":2.8,"publicationDate":"2026-06-01","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 : 2026-06-01Epub Date: 2026-01-29DOI: 10.1016/j.aml.2026.109878
Fei Sun, Hongxing Rui
In this paper, a novel nonlinear hybrid-dimensional fracture porous media flow model is proposed, where the aperture of the fracture is varying and related to the fluid pressure in the fracture. This model is first proposed and more consistent with the real scenarios. Mixed finite element method (MFEM) is applied to solve this nonlinear coupled system. Finally, some numerical experiments are carried out to demonstrate the correctness of the approximation scheme and the capability of the proposed model.
{"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":"10.1016/j.aml.2026.109878","url":null,"abstract":"<div><div>In this paper, a novel nonlinear hybrid-dimensional fracture porous media flow model is proposed, where the aperture of the fracture is varying and related to the fluid pressure in the fracture. This model is first proposed and more consistent with the real scenarios. Mixed finite element method (MFEM) is applied to solve this nonlinear coupled system. Finally, some numerical experiments are carried out to demonstrate the correctness of the approximation scheme and the capability of the proposed model.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"177 ","pages":"Article 109878"},"PeriodicalIF":2.8,"publicationDate":"2026-06-01","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 : 2026-06-01Epub Date: 2026-02-04DOI: 10.1016/j.aml.2026.109879
Chunxue Zhao , Xingjie Yan , Xiubin Wang
-symmetric systems have attracted significant interest in quantum theory, optics and other physical fields in recent years. In this work, we rigorously derive the -order vector rogue wave solutions for the coupled reverse-time nonlocal -symmetric nonlinear Schrödinger equations in the focusing regime. Then the expressions of -order vector rogue wave solutions can be expressed in a separation of variable form. Furthermore, the dynamic patterns of these solutions are discussed with some graphics. Our observations reveal that vector rogue waves exhibit two distinct regimes: global boundedness or collapse into singularity formation. In particular, we find that these solutions in coupled nonlocal equations exhibit novel patterns, most of which lack direct analogs in the corresponding local equation.
{"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":"10.1016/j.aml.2026.109879","url":null,"abstract":"<div><div><span><math><mrow><mi>P</mi><mi>T</mi></mrow></math></span>-symmetric systems have attracted significant interest in quantum theory, optics and other physical fields in recent years. In this work, we rigorously derive the <span><math><mrow><mo>(</mo><mi>N</mi><mo>,</mo><mi>M</mi><mo>)</mo></mrow></math></span>-order vector rogue wave solutions for the coupled reverse-time nonlocal <span><math><mrow><mi>P</mi><mi>T</mi></mrow></math></span>-symmetric nonlinear Schrödinger equations in the focusing regime. Then the expressions of <span><math><mrow><mo>(</mo><mi>N</mi><mo>,</mo><mi>M</mi><mo>)</mo></mrow></math></span>-order vector rogue wave solutions can be expressed in a separation of variable form. Furthermore, the dynamic patterns of these solutions are discussed with some graphics. Our observations reveal that vector rogue waves exhibit two distinct regimes: global boundedness or collapse into singularity formation. In particular, we find that these solutions in coupled nonlocal equations exhibit novel patterns, most of which lack direct analogs in the corresponding local equation.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"177 ","pages":"Article 109879"},"PeriodicalIF":2.8,"publicationDate":"2026-06-01","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 : 2026-06-01Epub 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":"2026-06-01","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 : 2026-06-01Epub 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":"2026-06-01","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 : 2026-06-01Epub Date: 2026-02-10DOI: 10.1016/j.aml.2026.109893
Yu-Han Li , Ze Wang , Yu-Xin Ye , Jun-Feng Yin
A residual-based randomized Kaczmarz method is proposed for solving linear feasibility problems by adaptively selecting active row index with the probability criterion defined by the negative part of the residual. The convergence theory of the proposed method is established and the upper bound of the convergence rate in expectation is derived by making use of the Hoffman’s lemma. Numerical experiments are presented to further demonstrate the efficiency of the proposed method in terms of the number of iteration steps and computation time.
{"title":"A residual-based randomized Kaczmarz method for solving linear feasibility problems","authors":"Yu-Han Li , Ze Wang , Yu-Xin Ye , Jun-Feng Yin","doi":"10.1016/j.aml.2026.109893","DOIUrl":"10.1016/j.aml.2026.109893","url":null,"abstract":"<div><div>A residual-based randomized Kaczmarz method is proposed for solving linear feasibility problems by adaptively selecting active row index with the probability criterion defined by the negative part of the residual. The convergence theory of the proposed method is established and the upper bound of the convergence rate in expectation is derived by making use of the Hoffman’s lemma. Numerical experiments are presented to further demonstrate the efficiency of the proposed method in terms of the number of iteration steps and computation time.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"177 ","pages":"Article 109893"},"PeriodicalIF":2.8,"publicationDate":"2026-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146152826","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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