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Multiple normalized solutions for Schrödinger equation in RN with shrinking self-focusing core 具有收缩自聚焦核的[公式略]Schrödinger方程的多重归一化解
IF 2.9 2区 数学
Applied Mathematics Letters Pub Date : 2025-07-13 DOI: 10.1016/j.aml.2025.109679
Wenjun Xing, Shoucai Wang, Chunyu Lei
{"title":"Multiple normalized solutions for Schrödinger equation in RN with shrinking self-focusing core","authors":"Wenjun Xing,&nbsp;Shoucai Wang,&nbsp;Chunyu Lei","doi":"10.1016/j.aml.2025.109679","DOIUrl":"10.1016/j.aml.2025.109679","url":null,"abstract":"<div><div>In this paper, we study the multiple normalized solutions for the following Schrödinger equation <span><span><span><math><mfenced><mrow><mtable><mtr><mtd><mo>−</mo><mi>Δ</mi><mi>u</mi><mo>+</mo><mi>λ</mi><mi>u</mi><mo>=</mo><mi>Q</mi><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow><msup><mrow><mrow><mo>|</mo><mi>u</mi><mo>|</mo></mrow></mrow><mrow><mi>p</mi><mo>−</mo><mn>2</mn></mrow></msup><mi>u</mi><mo>,</mo><mspace></mspace><mi>in</mi><mspace></mspace><msup><mrow><mi>R</mi></mrow><mrow><mi>N</mi></mrow></msup><mo>,</mo><mspace></mspace></mtd></mtr><mtr><mtd><msub><mrow><mo>∫</mo></mrow><mrow><msup><mrow><mi>R</mi></mrow><mrow><mi>N</mi></mrow></msup></mrow></msub><msup><mrow><mrow><mo>|</mo><mi>u</mi><mo>|</mo></mrow></mrow><mrow><mn>2</mn></mrow></msup><mi>d</mi><mi>x</mi><mo>=</mo><msup><mrow><mi>a</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>&gt;</mo><mn>0</mn><mo>,</mo><mspace></mspace></mtd></mtr></mtable></mrow></mfenced></math></span></span></span>where <span><math><mrow><mi>N</mi><mo>⩾</mo><mn>3</mn></mrow></math></span>, <span><math><mrow><mi>p</mi><mo>∈</mo><mrow><mo>(</mo><mn>2</mn><mo>,</mo><mn>2</mn><mo>+</mo><mfrac><mrow><mn>4</mn></mrow><mrow><mi>N</mi></mrow></mfrac><mo>)</mo></mrow></mrow></math></span>. After establishing <span><math><msub><mrow><mrow><mo>(</mo><mi>P</mi><mi>S</mi><mo>)</mo></mrow></mrow><mrow><mi>c</mi></mrow></msub></math></span> condition for <span><math><mrow><mi>c</mi><mo>&lt;</mo><mn>0</mn></mrow></math></span> by employing the concentration compactness principle, the multiple normalized solutions are obtained by applying a critical point theorem. In addition, we consider the orbital stability of the ground state solution. Our results generalize some recent results in the literature.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"171 ","pages":"Article 109679"},"PeriodicalIF":2.9,"publicationDate":"2025-07-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144613230","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
Large magnetic field limit for ideal incompressible magnetohydrodynamics 理想不可压缩磁流体力学的大磁场极限
IF 2.9 2区 数学
Applied Mathematics Letters Pub Date : 2025-07-11 DOI: 10.1016/j.aml.2025.109676
Fei Jiang , Jiawei Wang , Xin Xu
{"title":"Large magnetic field limit for ideal incompressible magnetohydrodynamics","authors":"Fei Jiang ,&nbsp;Jiawei Wang ,&nbsp;Xin Xu","doi":"10.1016/j.aml.2025.109676","DOIUrl":"10.1016/j.aml.2025.109676","url":null,"abstract":"<div><div>This paper examines the large magnetic field limit for the ideal incompressible magnetohydrodynamic equations in a three-dimensional periodic domain, where the direction of the background magnetic field satisfies the Diophantine condition. Under distinct assumptions for the initial data, we rigorously justify the convergence of solutions to zero in varying topologies.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"171 ","pages":"Article 109676"},"PeriodicalIF":2.9,"publicationDate":"2025-07-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144613231","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
Initial size sensitivity in Huanglongbing dynamics: How branching processes challenge deterministic outbreak predictions 黄龙冰动力学的初始大小敏感性：分支过程如何挑战确定性爆发预测
IF 2.9 2区 数学
Applied Mathematics Letters Pub Date : 2025-07-10 DOI: 10.1016/j.aml.2025.109674
Jialu Feng, Chunjin Wei
{"title":"Initial size sensitivity in Huanglongbing dynamics: How branching processes challenge deterministic outbreak predictions","authors":"Jialu Feng,&nbsp;Chunjin Wei","doi":"10.1016/j.aml.2025.109674","DOIUrl":"10.1016/j.aml.2025.109674","url":null,"abstract":"<div><div>Huanglongbing is a serious threat to the citrus industry. In the early stage of Huanglongbing infection, when the number of infected citrus trees and psyllids is sufficiently small, the deterministic system fails to accurately depict the transmission dynamics. However, continuous-time Markov chain (CTMC) can effectively describe these dynamic characteristics through state discretization for small population sizes. To this end, we first study a stochastic system based on CTMC and then estimate the probability of disease extinction and outbreak by applying the Galton–Watson branching process (GWbp). A comparison analysis between the deterministic and stochastic systems of Huanglongbing yields the following insights: <span><math><mrow><mo>(</mo><mn>1</mn><mo>)</mo></mrow></math></span> when <span><math><mrow><msub><mrow><mi>R</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>&gt;</mo><mn>1</mn></mrow></math></span>, the deterministic system predicts Huanglongbing infection outbreak, whereas the stochastic system indicates a nonzero probability of Huanglongbing infection elimination; <span><math><mrow><mo>(</mo><mn>2</mn><mo>)</mo></mrow></math></span> The initial number of infected citrus trees and infected psyllids does not affect the dynamics of the deterministic system, while the stochastic system’s dynamics are highly sensitive to the initial sizes and cannot be ignored. These findings have significant implications for understanding the epidemiological characteristics of Huanglongbing and provide a theoretical foundation for designing more precise and effective control strategies.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"171 ","pages":"Article 109674"},"PeriodicalIF":2.9,"publicationDate":"2025-07-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144596444","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
Solitons, Bäcklund transformation and Lax pair for the (2+1)-dimensional Kaup system （2+1）维Kaup系统的孤子，Bäcklund变换和Lax对
IF 2.9 2区 数学
Applied Mathematics Letters Pub Date : 2025-07-10 DOI: 10.1016/j.aml.2025.109673
Zhong-Zhou Lan
{"title":"Solitons, Bäcklund transformation and Lax pair for the (2+1)-dimensional Kaup system","authors":"Zhong-Zhou Lan","doi":"10.1016/j.aml.2025.109673","DOIUrl":"10.1016/j.aml.2025.109673","url":null,"abstract":"<div><div>In this paper, we investigate the (2+1)-dimensional Kaup system, a nonlinear integrable model arising in water wave dynamics within narrow channels of constant depth. Utilizing the binary Bell polynomials and Hirota’s bilinear method, we derive the bilinear forms of the system and construct one- and two-soliton solutions. The dynamical properties of these solitons, including their stable propagation and interaction behavior, are graphically analyzed, demonstrating typical soliton features such as shape preservation and elastic collision. Furthermore, we establish the Bäcklund transformation and present the associated Lax pair, confirming the integrability of the system. The results enhance the understanding of multidimensional nonlinear wave phenomena within fluid mechanics and provide analytical tools for exploring related integrable models.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"171 ","pages":"Article 109673"},"PeriodicalIF":2.9,"publicationDate":"2025-07-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144604873","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
The defocusing Lakshmanan–Porsezian–Daniel equation with elliptic function backgrounds: N-elliptic-dark solitons and asymptotic behaviors 椭圆函数背景下的散焦Lakshmanan-Porsezian-Daniel方程：n -椭圆暗孤子及其渐近行为
IF 2.9 2区 数学
Applied Mathematics Letters Pub Date : 2025-07-10 DOI: 10.1016/j.aml.2025.109684
Xin Wang , Zhenya Yan , Xiangyu Yang
{"title":"The defocusing Lakshmanan–Porsezian–Daniel equation with elliptic function backgrounds: N-elliptic-dark solitons and asymptotic behaviors","authors":"Xin Wang ,&nbsp;Zhenya Yan ,&nbsp;Xiangyu Yang","doi":"10.1016/j.aml.2025.109684","DOIUrl":"10.1016/j.aml.2025.109684","url":null,"abstract":"<div><div>By using the modified squared wavefunction approach and Darboux transformation, we derive the <span><math><mi>N</mi></math></span>-elliptic-dark soliton solutions for the defocusing Lakshmanan–Porsezian–Daniel equation, which describes the propagation of ultrashort optical pulses with the fourth-order dispersion, self-steepening, self-frequency, and quintic effects. In particular, we exhibit the one-, two- and three-elliptic-dark solitons as well as their asymptotic behaviors as <span><math><mrow><mi>t</mi><mo>→</mo><mo>±</mo><mi>∞</mi></mrow></math></span>, and discuss the compression effects on the spatiotemporal distributions of the elliptic dark solitons produced by the higher-order effects.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"171 ","pages":"Article 109684"},"PeriodicalIF":2.9,"publicationDate":"2025-07-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144611709","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
Stability and asymptotic stability analysis for nonlinear functional differential–algebraic equations 非线性泛函微分-代数方程的稳定性及渐近稳定性分析
IF 2.9 2区 数学
Applied Mathematics Letters Pub Date : 2025-07-10 DOI: 10.1016/j.aml.2025.109682
Haodong Li, Hongliang Liu, Shoufu Li
{"title":"Stability and asymptotic stability analysis for nonlinear functional differential–algebraic equations","authors":"Haodong Li,&nbsp;Hongliang Liu,&nbsp;Shoufu Li","doi":"10.1016/j.aml.2025.109682","DOIUrl":"10.1016/j.aml.2025.109682","url":null,"abstract":"<div><div>This paper is devoted to studying stability and asymptotic stability theories of analytical solutions for nonlinear functional differential–algebraic equations, and the sufficiency conditions of these theories are given, which facilitates the study of the stability and asymptotic stability of their numerical methods.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"171 ","pages":"Article 109682"},"PeriodicalIF":2.9,"publicationDate":"2025-07-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144613204","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
Existence of the nonhomogeneous steady states in a memory-based diffusive model with nonlocal memory and Dirichlet boundary 具有非局部记忆和Dirichlet边界的基于记忆的扩散模型中非齐次稳态的存在性
IF 2.9 2区 数学
Applied Mathematics Letters Pub Date : 2025-07-10 DOI: 10.1016/j.aml.2025.109685
Qingyan Shi
{"title":"Existence of the nonhomogeneous steady states in a memory-based diffusive model with nonlocal memory and Dirichlet boundary","authors":"Qingyan Shi","doi":"10.1016/j.aml.2025.109685","DOIUrl":"10.1016/j.aml.2025.109685","url":null,"abstract":"<div><div>In this paper, the existence of the nonhomogeneous steady states of a nonlocal memory model under Dirichlet boundary condition is investigated. The nonlocal kernel is assumed to be the Green’s function of a diffusion equation. By using the Crandall–Rabinowitz abstract bifurcation theory, the occurrence of a steady-state bifurcation is proved, which guarantees the existence of the nonhomogeneous steady states.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"171 ","pages":"Article 109685"},"PeriodicalIF":2.9,"publicationDate":"2025-07-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144596452","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 fast parameter optimization framework for iterative solvers in linear and nonlinear systems 线性和非线性系统迭代解算器的快速参数优化框架
IF 2.9 2区 数学
Applied Mathematics Letters Pub Date : 2025-07-09 DOI: 10.1016/j.aml.2025.109660
Wei Li , Wenlong Wang , Pingfei Dai , Qingbiao Wu
{"title":"A fast parameter optimization framework for iterative solvers in linear and nonlinear systems","authors":"Wei Li ,&nbsp;Wenlong Wang ,&nbsp;Pingfei Dai ,&nbsp;Qingbiao Wu","doi":"10.1016/j.aml.2025.109660","DOIUrl":"10.1016/j.aml.2025.109660","url":null,"abstract":"<div><div>To solve the equation using the matrix-splitting iterative method, it is essential to determine the optimal parameters so as to minimize the number of iterations. In this paper, a search paradigm based on Bayesian optimization is used to find the optimal parameters of linear and nonlinear iterative methods, and a large number of numerical experiments are provided to assess and contrast the search performance of the method against that of the traditional interval traversal. The numerical results show that compared with interval traversal in the iterative methods of matrix splitting for linear and nonlinear systems, the optimal parameters searched by Bayesian optimization can not only have the least number of iterations but also be more efficient.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"171 ","pages":"Article 109660"},"PeriodicalIF":2.9,"publicationDate":"2025-07-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144613237","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
Alternating direction implicit iterative method for solving indefinite least squares problem 求解不定最小二乘问题的交替方向隐式迭代法
IF 2.9 2区 数学
Applied Mathematics Letters Pub Date : 2025-07-09 DOI: 10.1016/j.aml.2025.109677
Lingsheng Meng, Peizhe Li, Kailiang Xin
{"title":"Alternating direction implicit iterative method for solving indefinite least squares problem","authors":"Lingsheng Meng,&nbsp;Peizhe Li,&nbsp;Kailiang Xin","doi":"10.1016/j.aml.2025.109677","DOIUrl":"10.1016/j.aml.2025.109677","url":null,"abstract":"<div><div>To solve the indefinite least squares problem, first we propose the generalized splitting iterative method, which is unconditionally convergent. Further, to accelerate the generalized splitting iterative method, we propose the alternating direction implicit iterative method, which needs to satisfy condition to guarantee convergence. Numerical experiments show that the alternating direction implicit iterative method outperforms the current methods in terms of CPU time and number of iteration steps.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"171 ","pages":"Article 109677"},"PeriodicalIF":2.9,"publicationDate":"2025-07-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144596472","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 modified CMRH method for solving large nonsymmetric linear systems 求解大型非对称线性系统的改进CMRH方法
IF 2.9 2区 数学
Applied Mathematics Letters Pub Date : 2025-07-08 DOI: 10.1016/j.aml.2025.109672
Qianqian Xue, Wenli Zeng, Xiaoqi Xu, Xian-Ming Gu
{"title":"A modified CMRH method for solving large nonsymmetric linear systems","authors":"Qianqian Xue,&nbsp;Wenli Zeng,&nbsp;Xiaoqi Xu,&nbsp;Xian-Ming Gu","doi":"10.1016/j.aml.2025.109672","DOIUrl":"10.1016/j.aml.2025.109672","url":null,"abstract":"<div><div>This paper presents a modified CMRH method for solving large nonsymmetric linear systems. Based on the Hessenberg process, the proposed method requires less computation and storage compared to GMRES and QMR methods. The improvement involves utilizing the <span><math><mrow><mo>(</mo><mi>m</mi><mo>+</mo><mn>1</mn><mo>)</mo></mrow></math></span>-th vector generated during the Hessenberg process to optimize the approximate solution through a linear combination, thereby reducing the number of matrix–vector multiplications and inner products. Theoretical analysis demonstrates that the improved CMRH method is more cost-effective than the original <span><math><mrow><mo>(</mo><mi>m</mi><mo>+</mo><mn>1</mn><mo>)</mo></mrow></math></span>-step method. Numerical experiments validate the efficiency of the modified CMRH method across various test problems, showing fewer iterations and less computation time, particularly in large-scale problems.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"171 ","pages":"Article 109672"},"PeriodicalIF":2.9,"publicationDate":"2025-07-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144613238","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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