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Bilinear Bäcklund transformation method to the quasi-periodic wave solutions of the associated Camassa–Holm equation 相关Camassa-Holm方程拟周期波解的双线性Bäcklund变换方法
IF 2.9 2区 数学
Applied Mathematics Letters Pub Date : 2025-06-30 DOI: 10.1016/j.aml.2025.109671
Wanting Tang , Hui Wang , Yunhu Wang
{"title":"Bilinear Bäcklund transformation method to the quasi-periodic wave solutions of the associated Camassa–Holm equation","authors":"Wanting Tang ,&nbsp;Hui Wang ,&nbsp;Yunhu Wang","doi":"10.1016/j.aml.2025.109671","DOIUrl":"10.1016/j.aml.2025.109671","url":null,"abstract":"<div><div>In this paper, we construct the quasi-periodic wave solutions of the associated Camassa–Holm equation based on the bilinear Bäcklund transformation and Riemann theta function. We demonstrate that the dynamic characteristics of the one- and two-periodic waves under different parameter conditions. The relations between the periodic wave solutions and the corresponding soliton solutions are established through the asymptotic properties.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"171 ","pages":"Article 109671"},"PeriodicalIF":2.9,"publicationDate":"2025-06-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144523672","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}
引用次数: 0
Well-posedness of second-order uniformly elliptic PDEs with Neumann conditions 具有Neumann条件的二阶一致椭圆偏微分方程的适定性
IF 2.9 2区 数学
Applied Mathematics Letters Pub Date : 2025-06-30 DOI: 10.1016/j.aml.2025.109670
Haruki Kono
{"title":"Well-posedness of second-order uniformly elliptic PDEs with Neumann conditions","authors":"Haruki Kono","doi":"10.1016/j.aml.2025.109670","DOIUrl":"10.1016/j.aml.2025.109670","url":null,"abstract":"<div><div>Extending the results of Nardi and Giacomo (2015), this note establishes an existence and uniqueness result for second-order uniformly elliptic PDEs in divergence form with Neumann boundary conditions. A Schauder estimate and a stability result are also derived.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"171 ","pages":"Article 109670"},"PeriodicalIF":2.9,"publicationDate":"2025-06-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144523673","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}
引用次数: 0
Further results on zeros distribution for second order nonlinear neutral delay differential equations 二阶非线性中立型时滞微分方程零分布的进一步结果
IF 2.9 2区 数学
Applied Mathematics Letters Pub Date : 2025-06-26 DOI: 10.1016/j.aml.2025.109666
Hui Li , Yupin Wang , Nana Jin
{"title":"Further results on zeros distribution for second order nonlinear neutral delay differential equations","authors":"Hui Li ,&nbsp;Yupin Wang ,&nbsp;Nana Jin","doi":"10.1016/j.aml.2025.109666","DOIUrl":"10.1016/j.aml.2025.109666","url":null,"abstract":"<div><div>This paper investigates the distribution of zeros of oscillatory solutions for a certain class of second order nonlinear neutral differential equations. By constructing some new function sequences and the properties of solutions for the corresponding first order differential inequality, several further results for the distance between adjacent zeros and sufficient conditions for oscillation are given, which generalize and extend some known results.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"171 ","pages":"Article 109666"},"PeriodicalIF":2.9,"publicationDate":"2025-06-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144510982","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}
引用次数: 0
On the unconditional long-time L2 stability of the SAV-BDF2 time-stepping schemes for the forced Navier–Stokes equations with nonsmooth initial data 具有非光滑初始数据的强迫Navier-Stokes方程的SAV-BDF2时间步进格式的无条件长[公式略]稳定性
IF 2.9 2区 数学
Applied Mathematics Letters Pub Date : 2025-06-26 DOI: 10.1016/j.aml.2025.109665
Quen-Yi Lin, Ming-Cheng Shiue
{"title":"On the unconditional long-time L2 stability of the SAV-BDF2 time-stepping schemes for the forced Navier–Stokes equations with nonsmooth initial data","authors":"Quen-Yi Lin,&nbsp;Ming-Cheng Shiue","doi":"10.1016/j.aml.2025.109665","DOIUrl":"10.1016/j.aml.2025.109665","url":null,"abstract":"<div><div>In this work, the long-time <span><math><msup><mrow><mi>L</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span> stability of the SAV-BDF2 time-stepping scheme for the forced Navier–Stokes equations under a regularization of the initial data <span><math><mrow><msub><mrow><mi>u</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>∈</mo><mi>H</mi></mrow></math></span> using a method that lifts the solution to the space <span><math><msup><mrow><mi>H</mi></mrow><mrow><mn>1</mn></mrow></msup></math></span> while preserving control over the <span><math><msup><mrow><mi>L</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span> norm is investigated. In this paper, the unconditional long-time <span><math><msup><mrow><mi>L</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span> stability of the scheme is established by utilizing a refined estimate of the <span><math><mi>G</mi></math></span>-norm introduced in Shiue (2025), together with recent results from Han and Wang (2024). Moreover, the uniform-in-time bound on the energy norm of the solution is derived independent on the time step size, which allows for larger time steps to speed up simulations, especially for long-term problem. This also improves the result in Han and Wang (2024) where a uniform-in-time bound on the energy norm was obtained under a condition involving the time step size and assuming the initial data is in <span><math><msup><mrow><mi>H</mi></mrow><mrow><mn>1</mn></mrow></msup></math></span> directly.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"171 ","pages":"Article 109665"},"PeriodicalIF":2.9,"publicationDate":"2025-06-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144516130","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}
引用次数: 0
Preconditioned linearized Bregman method with Golub-Kahan bidiagonalization for frame-based image deblurring 基于帧图像去模糊的Golub-Kahan双对角化预处理线性Bregman方法
IF 3.7 2区 数学
Applied Mathematics Letters Pub Date : 2025-06-26 DOI: 10.1016/j.aml.2025.109667
Ze Wang, Jun-Feng Yin, Shao-Liang Zhang, Ning Zheng
{"title":"Preconditioned linearized Bregman method with Golub-Kahan bidiagonalization for frame-based image deblurring","authors":"Ze Wang, Jun-Feng Yin, Shao-Liang Zhang, Ning Zheng","doi":"10.1016/j.aml.2025.109667","DOIUrl":"https://doi.org/10.1016/j.aml.2025.109667","url":null,"abstract":"A preconditioned linearized Bregman method with Golub-Kahan bidiagonalization is proposed for solving frame-based image deblurring problems suffering from ill-posedness, where the constructed preconditioner is general and independent of the specific structure of the coefficient matrix. The convergence theorem of the proposed method is established based on its connection with the gradient descent method through the dual objective function. Numerical experiments further demonstrate the computational efficiency of the proposed method in terms of the iteration steps and the elapsed time.","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"27 1","pages":""},"PeriodicalIF":3.7,"publicationDate":"2025-06-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144516012","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}
引用次数: 0
Time domain dimension reduction for discrete-time systems via low-rank approximate Gramians 基于低秩近似格拉姆的离散系统时域降维
IF 2.9 2区 数学
Applied Mathematics Letters Pub Date : 2025-06-25 DOI: 10.1016/j.aml.2025.109662
Zhen-Zhong Qi , Jia-Chao Zhao , Yao-Lin Jiang , Zhi-Hua Xiao
{"title":"Time domain dimension reduction for discrete-time systems via low-rank approximate Gramians","authors":"Zhen-Zhong Qi ,&nbsp;Jia-Chao Zhao ,&nbsp;Yao-Lin Jiang ,&nbsp;Zhi-Hua Xiao","doi":"10.1016/j.aml.2025.109662","DOIUrl":"10.1016/j.aml.2025.109662","url":null,"abstract":"<div><div>This paper considers the topic on model order reduction (MOR) based on approximate Gramians for discrete-time systems (DTSs), appearing in integrated circuits (ICs) and other engineering fields. The proposed approach is implemented by a balanced truncation framework, where the time domain controllability and observability Gramians are approximated by a low-rank decomposition, whose factors are constructed of Charlier polynomial expansion coefficients from linear equations instead of Lyapunov equations, which makes it more efficient and flexible. In avoid of the drawback that may lead to an unstable reduced-order model (ROM), a modified version of dominant subspace projection is employed to calculate a stability-preserving ROM. Finally, a numerical simulation on IC chips model is provided, where the results demonstrate the effectiveness of our algorithms in the views of time cost and accuracy.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"171 ","pages":"Article 109662"},"PeriodicalIF":2.9,"publicationDate":"2025-06-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144516013","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}
引用次数: 0
Breather solutions and higher-order rogue wave solutions to the modified complex short pulse equation 修正复短脉冲方程的呼吸解和高阶异常波解
IF 2.9 2区 数学
Applied Mathematics Letters Pub Date : 2025-06-25 DOI: 10.1016/j.aml.2025.109664
Cong Lv , Deqin Qiu , Yongshuai Zhang
{"title":"Breather solutions and higher-order rogue wave solutions to the modified complex short pulse equation","authors":"Cong Lv ,&nbsp;Deqin Qiu ,&nbsp;Yongshuai Zhang","doi":"10.1016/j.aml.2025.109664","DOIUrl":"10.1016/j.aml.2025.109664","url":null,"abstract":"<div><div>Breather solutions and higher-order rogue wave solutions with two arbitrary parameters <span><math><mi>a</mi></math></span> and <span><math><mi>c</mi></math></span> of the modified complex short pulse (mcSP) equation are generated based on the reciprocal transformation and the Darboux transformation. We construct the <span><math><mi>n</mi></math></span>th-order Darboux transformation in terms of determinants whose entries are represented by initial eigenfunctions and seed solutions. Furthermore, the formulae for the higher-order rogue wave solutions of the mcSP equation are obtained by using the Taylor expansion with the help of degenerate eigenvalues <span><math><mrow><msub><mrow><mi>λ</mi></mrow><mrow><mi>j</mi></mrow></msub><mo>→</mo><msup><mrow><mi>a</mi></mrow><mrow><mn>2</mn></mrow></msup><mi>c</mi><mo>−</mo><mfrac><mrow><mi>i</mi><mi>a</mi><msqrt><mrow><mn>1</mn><mo>−</mo><mn>4</mn><msup><mrow><mi>a</mi></mrow><mrow><mn>2</mn></mrow></msup><msup><mrow><mi>c</mi></mrow><mrow><mn>2</mn></mrow></msup></mrow></msqrt></mrow><mrow><mn>2</mn></mrow></mfrac><mo>,</mo><mi>j</mi><mo>=</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo>,</mo><mo>…</mo><mo>,</mo><mi>n</mi></mrow></math></span>. The analyticity of first-order rogue wave solution is studied. Some figures illustrate dynamic structures of the rogue waves from the first to the third order. The effect of the choice of parameters on the rogue waves are specifically discussed.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"171 ","pages":"Article 109664"},"PeriodicalIF":2.9,"publicationDate":"2025-06-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144511080","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}
引用次数: 0
An exact periodic solution of the semi-discrete ‘long wave-short wave’ resonance equation 半离散“长波-短波”共振方程的精确周期解
IF 2.9 2区 数学
Applied Mathematics Letters Pub Date : 2025-06-24 DOI: 10.1016/j.aml.2025.109656
H.M. Yin, K.W. Chow
{"title":"An exact periodic solution of the semi-discrete ‘long wave-short wave’ resonance equation","authors":"H.M. Yin,&nbsp;K.W. Chow","doi":"10.1016/j.aml.2025.109656","DOIUrl":"10.1016/j.aml.2025.109656","url":null,"abstract":"<div><div>One resonance in a dispersive wave system is governed by a set of coupled partial differential equations, relating the complex-valued short wave envelope and a real-valued long wave component. A semi-discrete form proposed recently, continuous in time but discrete in space, possesses soliton solutions. Extension to the periodic case is accomplished here by employing theta function identities and the Hirota bilinear method.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"171 ","pages":"Article 109656"},"PeriodicalIF":2.9,"publicationDate":"2025-06-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144516131","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}
引用次数: 0
Dynamics of a non-autonomous Kawasaki disease model with endothelial cell injury and general functional responses 内皮细胞损伤和一般功能反应的非自主川崎病模型动力学
IF 2.9 2区 数学
Applied Mathematics Letters Pub Date : 2025-06-23 DOI: 10.1016/j.aml.2025.109659
Ke Guo , Wanbiao Ma , Conghui Xu , Fuxiang Li
{"title":"Dynamics of a non-autonomous Kawasaki disease model with endothelial cell injury and general functional responses","authors":"Ke Guo ,&nbsp;Wanbiao Ma ,&nbsp;Conghui Xu ,&nbsp;Fuxiang Li","doi":"10.1016/j.aml.2025.109659","DOIUrl":"10.1016/j.aml.2025.109659","url":null,"abstract":"<div><div>Patients with Kawasaki disease (KD) are exposed to various environmental factors during the onset and treatment of the disease, which result in the parameters of the KD model not remaining constant but fluctuating over time. Consequently, this paper constructs and studies a non-autonomous KD model with endothelial cell injury and general functional responses. We first obtain some explicit estimates of the ultimate lower bounds of any positive solution of the model through some elaborate mathematical analytical approaches, from which we deduce the model is permanent if <span><math><mrow><msup><mrow><mi>R</mi></mrow><mrow><mi>p</mi></mrow></msup><mo>&gt;</mo><mn>1</mn></mrow></math></span>. If the model is transformed into the autonomous case, then <span><math><msup><mrow><mi>R</mi></mrow><mrow><mi>p</mi></mrow></msup></math></span> is the basic reproduction number of the model. In addition, some sufficient conditions for inflammatory cytokines to be cleared are obtained.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"171 ","pages":"Article 109659"},"PeriodicalIF":2.9,"publicationDate":"2025-06-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144480512","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}
引用次数: 0
A two-grid characteristic finite element method for incompressible flow 不可压缩流动的双网格特征有限元法
IF 2.9 2区 数学
Applied Mathematics Letters Pub Date : 2025-06-21 DOI: 10.1016/j.aml.2025.109663
Yu Jiang , Junchang Qin , Xiaoming He
{"title":"A two-grid characteristic finite element method for incompressible flow","authors":"Yu Jiang ,&nbsp;Junchang Qin ,&nbsp;Xiaoming He","doi":"10.1016/j.aml.2025.109663","DOIUrl":"10.1016/j.aml.2025.109663","url":null,"abstract":"<div><div>This study proposes and briefly analyzes a two-grid characteristic finite element method based on a residual technique, with the low order pair of mixed finite element such as <span><math><mrow><msub><mrow><mi>P</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>−</mo><msub><mrow><mi>P</mi></mrow><mrow><mn>1</mn></mrow></msub></mrow></math></span>, for the incompressible time-dependent Navier–Stokes equations. A characteristic finite element calculation of nonlinear Navier–Stokes problem is first presented on a coarse grid, followed by the residual correction on a fine grid utilizing the difference between the coarse and fine grids. The characteristic method is transported by divergence-free velocity field, free of the Newton iterations, unconditionally stable, and free of stabilization for large Reynolds numbers of incompressible flow. The numerical results show high accuracy and efficiency.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"171 ","pages":"Article 109663"},"PeriodicalIF":2.9,"publicationDate":"2025-06-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144337701","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}
引用次数: 0
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