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Non-autonomous rational soliton bound states and dynamics in the nonlocal Gross–Pitaevskii equation with a PT-symmetric potential 具有[公式省略]对称势的非局部Gross-Pitaevskii方程中的非自治有理孤子束缚态和动力学
IF 2.9 2区 数学
Applied Mathematics Letters Pub Date : 2025-07-19 DOI: 10.1016/j.aml.2025.109691
Haotian Wang , Fenghua Qi , Wenjun Liu
{"title":"Non-autonomous rational soliton bound states and dynamics in the nonlocal Gross–Pitaevskii equation with a PT-symmetric potential","authors":"Haotian Wang ,&nbsp;Fenghua Qi ,&nbsp;Wenjun Liu","doi":"10.1016/j.aml.2025.109691","DOIUrl":"10.1016/j.aml.2025.109691","url":null,"abstract":"<div><div>This paper investigates an integrable Gross–Pitaevskii equation with nonlocal nonlinear effects, which consists of a nonlocal nonlinear Schrödinger equation adding an external potential function. The generalized Darboux transformation is used to solve this equation directly. We obtain rational solitons that exhibit the coexistence of dark and anti-dark solitons in bound states, and numerical simulations verify the correctness and robustness of these solutions. The influence of nonlocal effects and external potentials on the solutions of rational-type solitons is discussed. Results demonstrated that the dynamical behaviors of these solutions are novel and distinct from those of the local Gross–Pitaevskii equation and nonlocal nonlinear Schrödinger equation, providing some help and guidance for the realization of various soliton bound states in optical experiments.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"171 ","pages":"Article 109691"},"PeriodicalIF":2.9,"publicationDate":"2025-07-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144664997","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
Some discrete solitons and interaction dynamical behaviors for a PT-symmetric discrete nonlocal nonlinear Schrödinger equation pt对称离散非局部非线性Schrödinger方程的离散孤子及其相互作用动力学行为
IF 2.9 2区 数学
Applied Mathematics Letters Pub Date : 2025-07-17 DOI: 10.1016/j.aml.2025.109680
Jingwe Yu, Li Li, Fajunn Yu, Kai Cui
{"title":"Some discrete solitons and interaction dynamical behaviors for a PT-symmetric discrete nonlocal nonlinear Schrödinger equation","authors":"Jingwe Yu,&nbsp;Li Li,&nbsp;Fajunn Yu,&nbsp;Kai Cui","doi":"10.1016/j.aml.2025.109680","DOIUrl":"10.1016/j.aml.2025.109680","url":null,"abstract":"<div><div>At present, there have been many achievements on the study of integrable nonlocal nonlinear Schrödinger (NNLS) equation, which can enrich the mathematical structure of the NNLS equation by adding the discrete conditions. Ablowitz proposed a method to solve the nonlocal discrete Schrödinger equation under decaying boundary conditions by using the inverse scattering transformation. At this stage, there are few work of the discrete nonlocal nonlinear Schrödinger(DNNLS) equation with PT-symmetric. A detailed study of the DNNLS equation with PT-symmetric under fast decaying boundary conditions is carried out by using Darboux transformation method, which obtains the novel formulation of the soliton solution with the 2 × 2 Lax pairs, then some dynamical behaviors of the novel soliton solutions are analyzed by selecting different seed solutions and the wave parameters.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"171 ","pages":"Article 109680"},"PeriodicalIF":2.9,"publicationDate":"2025-07-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144653093","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
Bilinearization, solitons and modulation instability for a variable-coefficient nonlocal Hirota equation 变系数非局域Hirota方程的双线性化、孤子和调制不稳定性
IF 3.7 2区 数学
Applied Mathematics Letters Pub Date : 2025-07-17 DOI: 10.1016/j.aml.2025.109688
Hao-Dong Liu, Bo Tian
{"title":"Bilinearization, solitons and modulation instability for a variable-coefficient nonlocal Hirota equation","authors":"Hao-Dong Liu, Bo Tian","doi":"10.1016/j.aml.2025.109688","DOIUrl":"https://doi.org/10.1016/j.aml.2025.109688","url":null,"abstract":"Hirota equations have been used to model certain nonlinear waves in the nonlinear optical fibers. In this paper, a variable-coefficient nonlocal Hirota equation is investigated: Via the improved Hirota method, we obtain the bilinear forms and soliton solutions; The asymptotic analysis is discussed; We also study the modulation instability.","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"20 1","pages":""},"PeriodicalIF":3.7,"publicationDate":"2025-07-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144665001","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 a sharp mixed Lebesgue upper bound for solutions to the defocusing nonlinear Schrödinger equation in dimension two 二维离焦非线性Schrödinger方程解的尖锐混合勒贝格上界
IF 2.9 2区 数学
Applied Mathematics Letters Pub Date : 2025-07-17 DOI: 10.1016/j.aml.2025.109686
Vo Van Au
{"title":"On a sharp mixed Lebesgue upper bound for solutions to the defocusing nonlinear Schrödinger equation in dimension two","authors":"Vo Van Au","doi":"10.1016/j.aml.2025.109686","DOIUrl":"10.1016/j.aml.2025.109686","url":null,"abstract":"<div><div>In the unbounded two-dimensional domain, we study a class of nonlinear Schrödinger equations with a smooth power-type nonlinearity. We establish a novel global-in-time estimate that yields a sharp upper bound in the mixed Lebesgue space <span><math><mrow><msubsup><mrow><mi>L</mi></mrow><mrow><mi>t</mi></mrow><mrow><mn>4</mn></mrow></msubsup><msubsup><mrow><mi>L</mi></mrow><mrow><mi>x</mi></mrow><mrow><mn>8</mn></mrow></msubsup></mrow></math></span>. This work is motivated by the author’s previous results on the nonlinear Schrödinger equation, as well as by the influential work of Killip, Tao, and Visan (2009).</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"171 ","pages":"Article 109686"},"PeriodicalIF":2.9,"publicationDate":"2025-07-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144663219","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
Determining Turing instability of the periodic solution of a predator–prey model 捕食者-猎物模型周期解的图灵不稳定性
IF 2.9 2区 数学
Applied Mathematics Letters Pub Date : 2025-07-17 DOI: 10.1016/j.aml.2025.109689
Mengxin Chen , Xue-Zhi Li , Canrong Tian
{"title":"Determining Turing instability of the periodic solution of a predator–prey model","authors":"Mengxin Chen ,&nbsp;Xue-Zhi Li ,&nbsp;Canrong Tian","doi":"10.1016/j.aml.2025.109689","DOIUrl":"10.1016/j.aml.2025.109689","url":null,"abstract":"<div><div>This paper investigates the instability of the periodic solution of a predator–prey model which involves the Beddington–Deangelis functional response. We first show that there is a stable periodic solution resulting from the Hopf bifurcation for the diffusion-free model. Thereafter, we establish a simple sufficient condition to guarantee this stable periodic solution will become unstable in the sense of Turing by virtue of the regular perturbation theory and Poincar<span><math><mover><mrow><mtext>e</mtext></mrow><mrow><mo>́</mo></mrow></mover></math></span>-Andronov–Hopf bifurcation theory.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"171 ","pages":"Article 109689"},"PeriodicalIF":2.9,"publicationDate":"2025-07-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144663217","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
Stabilization to a positive equilibrium for a class of diffusive SIS epidemic model with linear source 一类具有线性源的扩散sis流行病模型的正平衡点镇定
IF 2.9 2区 数学
Applied Mathematics Letters Pub Date : 2025-07-17 DOI: 10.1016/j.aml.2025.109683
Yujie Zhu , Liang Zhang , Ruiwen Wu
{"title":"Stabilization to a positive equilibrium for a class of diffusive SIS epidemic model with linear source","authors":"Yujie Zhu ,&nbsp;Liang Zhang ,&nbsp;Ruiwen Wu","doi":"10.1016/j.aml.2025.109683","DOIUrl":"10.1016/j.aml.2025.109683","url":null,"abstract":"<div><div>This work is devoted to the asymptotic behavior of solutions for a reaction–diffusion SIS epidemic model with distinct dispersal rates. In the case of a bounded spatial domain, we establish the global stability of the unique positive constant steady state, which provides a supplement to Li et al. (2017). In the case of an unbounded spatial domain, we explore the local uniform convergence of solutions to the endemic steady state in the final zone, which gives an affirmative answer to the open problem in Zhang and Wang (2025).</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"171 ","pages":"Article 109683"},"PeriodicalIF":2.9,"publicationDate":"2025-07-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144665003","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 modified stochastic theta scheme for McKean–Vlasov stochastic differential equations under local one-sided Lipschitz conditions 局部单侧Lipschitz条件下McKean-Vlasov随机微分方程的改进随机theta格式
IF 2.9 2区 数学
Applied Mathematics Letters Pub Date : 2025-07-17 DOI: 10.1016/j.aml.2025.109681
Hongxia Chu , Haiyan Yuan , Hongjiong Tian
{"title":"The modified stochastic theta scheme for McKean–Vlasov stochastic differential equations under local one-sided Lipschitz conditions","authors":"Hongxia Chu ,&nbsp;Haiyan Yuan ,&nbsp;Hongjiong Tian","doi":"10.1016/j.aml.2025.109681","DOIUrl":"10.1016/j.aml.2025.109681","url":null,"abstract":"<div><div>This paper focuses on analytic and numerical solutions of McKean–Vlasov stochastic differential equations under local one-sided Lipschitz conditions. We first introduce the stochastic interacting particle system and the propagation of chaos. Then we propose a modified stochastic theta scheme to approximate the interacting particle system and then obtain the strong convergence of the continuous-time modified stochastic theta scheme to the non-interacting particle system. Finally, we give a numerical example to verify our theoretical results.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"171 ","pages":"Article 109681"},"PeriodicalIF":2.9,"publicationDate":"2025-07-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144653092","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
Asymptotic behavior of the N-soliton solution for the compound WKI-SP equation 复合WKI-SP方程n -孤子解的渐近性质
IF 2.9 2区 数学
Applied Mathematics Letters Pub Date : 2025-07-15 DOI: 10.1016/j.aml.2025.109678
Gaizhu Qu , Xiaorui Hu , Xiazhi Hao
{"title":"Asymptotic behavior of the N-soliton solution for the compound WKI-SP equation","authors":"Gaizhu Qu ,&nbsp;Xiaorui Hu ,&nbsp;Xiazhi Hao","doi":"10.1016/j.aml.2025.109678","DOIUrl":"10.1016/j.aml.2025.109678","url":null,"abstract":"<div><div>In this letter, we investigate the asymptotic behavior of the general <span><math><mi>N</mi></math></span>-soliton solution for an integrable compound equation which is a mix of the Wadati-Konno-Ichikawa (WKI) equation and the short-pulse (SP) equation. It is shown that the <span><math><mi>N</mi></math></span>-soliton solution is decomposed exactly into <span><math><mi>N</mi></math></span> separate soliton elements at <span><math><mrow><mi>t</mi><mo>→</mo><mo>±</mo><mi>∞</mi></mrow></math></span>. The <span><math><mi>N</mi></math></span>-soliton solution of the WKI-SP equation would include <span><math><mi>m</mi></math></span> loop solitons and <span><math><mrow><mi>N</mi><mo>−</mo><mi>m</mi></mrow></math></span> antiloop solitons. Most of references only consider the asymptotic behavior for <span><math><mi>N</mi></math></span>-loop soliton. Here, the asymptotic behavior of <span><math><mi>N</mi></math></span>-soliton including both loops and antiloops for large time is firstly studied. The phase shift of each soliton caused by its interaction with the other ones is also calculated.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"171 ","pages":"Article 109678"},"PeriodicalIF":2.9,"publicationDate":"2025-07-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144663218","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
Unconditionally energy-stable decoupled schemes for binary phase field crystal models using staggered temporal grids 交错时间网格二元相场晶体模型的无条件能量稳定解耦方案
IF 2.9 2区 数学
Applied Mathematics Letters Pub Date : 2025-07-15 DOI: 10.1016/j.aml.2025.109687
Xuewei Zhang , Maosheng Jiang , Jia Zhao
{"title":"Unconditionally energy-stable decoupled schemes for binary phase field crystal models using staggered temporal grids","authors":"Xuewei Zhang ,&nbsp;Maosheng Jiang ,&nbsp;Jia Zhao","doi":"10.1016/j.aml.2025.109687","DOIUrl":"10.1016/j.aml.2025.109687","url":null,"abstract":"<div><div>The binary phase field crystal (BPFC) model has been widely used to study alloy systems and material mixtures. However, most existing energy-stable numerical schemes for the BPFC model require solving coupled nonlinear systems at every time step, which are computationally expensive and often face convergence issues. Moreover, the existence and uniqueness of solutions to these numerical schemes often have strict restrictions on the time step size. To address these issues, we propose a novel, fully decoupled, unconditionally energy-stable time integration scheme for the BPFC model. The key idea is to discretize the two phase field variables on staggered temporal grids, with one on an integer mesh and the other on a half-integer (staggered) mesh. We rigorously prove its unconditional energy stability and verify its second-order accuracy through numerical convergence tests. Numerical simulations demonstrate the robustness and efficiency of the proposed scheme.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"171 ","pages":"Article 109687"},"PeriodicalIF":2.9,"publicationDate":"2025-07-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144665022","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
Analysis of a meshless boundary integral equation method for acoustic problems 声学问题的无网格边界积分方程法分析
IF 2.9 2区 数学
Applied Mathematics Letters Pub Date : 2025-07-15 DOI: 10.1016/j.aml.2025.109690
Linchong Chen , Xiaolin Li
{"title":"Analysis of a meshless boundary integral equation method for acoustic problems","authors":"Linchong Chen ,&nbsp;Xiaolin Li","doi":"10.1016/j.aml.2025.109690","DOIUrl":"10.1016/j.aml.2025.109690","url":null,"abstract":"<div><div>In this paper, a meshless boundary integral equation method, the Galerkin boundary element-free method, is proposed to solve acoustic problems. The existence, uniqueness, and optimal asymptotic error estimate of the solution are analyzed theoretically. In the method, the system matrix is symmetric and positive definite, boundary conditions are satisfied directly and exactly, approximation and discretization only use boundary nodes, and computational formulas are suitable for both interior and exterior acoustic problems. Numerical results verify the effectiveness of the method and the theoretical analysis.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"171 ","pages":"Article 109690"},"PeriodicalIF":2.9,"publicationDate":"2025-07-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144653094","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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