Applied Mathematics Letters最新文献

{"title":"On the representation of energy-preserving quadratic operators with application to Operator Inference","authors":"Leonidas Gkimisis,&nbsp;Igor Pontes Duff,&nbsp;Pawan Goyal,&nbsp;Peter Benner","doi":"10.1016/j.aml.2025.109761","DOIUrl":"10.1016/j.aml.2025.109761","url":null,"abstract":"<div><div>In this work, we investigate a skew-symmetric parameterization for energy-preserving quadratic operators. Earlier, [Goyal et al. (2023)] proposed this parameterization to enforce energy-preservation of quadratic terms in non-intrusive model reduction. We here prove that every energy-preserving quadratic term can be equivalently formulated using a parameterization of the corresponding operator via skew-symmetric matrix blocks. We develop an algorithm to compute an equivalent quadratic operator with skew-symmetric sub-matrices, given an arbitrary energy-preserving operator. Consequently, we employ the skew-symmetric sub-matrix representation in the framework of non-intrusive reduced-order modeling (ROM) via Operator Inference (OpInf) for systems with an energy-preserving nonlinearity. To this end, we propose a sequential, linear least-squares (LS) problems formulation for the inference task, to ensure energy-preservation of the data-driven quadratic operator. The potential of this approach is indicated by the numerical results for a 1D Korteweg–de Vries and a 2D Burgers’ equation benchmark; the inferred system dynamics are accurate, while the corresponding operators are faithful to the underlying physical properties of the system.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"173 ","pages":"Article 109761"},"PeriodicalIF":2.8,"publicationDate":"2025-09-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145097037","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}

{"title":"Global dynamics of a novel viral infection model mediated by pattern recognition receptors","authors":"Wei Wang ,&nbsp;Guoxiao Wu ,&nbsp;Xiaoting Fan","doi":"10.1016/j.aml.2025.109757","DOIUrl":"10.1016/j.aml.2025.109757","url":null,"abstract":"<div><div>Pyroptosis is a primary cause of viral infection of CD4+ T cells. The canonical inflammatory signaling pathway depends on the activation of Pattern Recognition Receptors (PRR). PRR (NLRP3 inflammasome, etc.) activation is a critical step that mediates subsequent Gasdermin D (GSDMD) protein activation and cellular pyroptosis. In this article, we develop a novel model of viral dynamics mediated by PRR. We first prove the existence of equilibria, and define the basic reproduction number <span><math><msub><mrow><mi>R</mi></mrow><mrow><mn>0</mn></mrow></msub></math></span>. Then the global stability of equilibria is investigated by establishing the appropriate Lyapunov functions.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"173 ","pages":"Article 109757"},"PeriodicalIF":2.8,"publicationDate":"2025-09-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145097044","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}

{"title":"Construction and exact solution of the nonlocal Kuralay-II equation via Darboux transformation","authors":"Weiao Yang,&nbsp;Chen Wang,&nbsp;Yue Shi,&nbsp;Xiangpeng Xin","doi":"10.1016/j.aml.2025.109758","DOIUrl":"10.1016/j.aml.2025.109758","url":null,"abstract":"<div><div>The Kuralay-II equation, as a typical form of the well-known Heisenberg ferromagnet equation, is an important integrable model. Here, the nonlocal Kuralay-II equation is constructed for the first time by means of symmetry reduction, resulting in an integrable system of partial differential equations. To solve this equation, Darboux transformation method is employed, which transforms the equation form to eliminate the influence of spectral parameters in the denominator and constructs a suitable gauge transformation matrix. Using trivial solutions as seed solutions, exact solutions of the equation are obtained, and the parameter constraint relationships when spectral parameters take real numbers, conjugate complex numbers, and unrelated complex numbers are analyzed, with specific examples given for the first two cases. This research contributes to solving nonlocal partial differential equations and enriches the construction methods of exact solutions in soliton theory.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"173 ","pages":"Article 109758"},"PeriodicalIF":2.8,"publicationDate":"2025-09-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145061171","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}

{"title":"Local artificial boundary conditions for the Benjamin–Bona–Mahony–Burgers equation","authors":"Qian Deng,&nbsp;Hongwei Li","doi":"10.1016/j.aml.2025.109747","DOIUrl":"10.1016/j.aml.2025.109747","url":null,"abstract":"<div><div>The Benjamin–Bona–Mahony–Burgers equation models small-amplitude long waves, making the study of its numerical solutions scientifically significant. However, solving it numerically in unbounded domains is challenging due to the unboundedness and nonlinearity. To address this, we combine the artificial boundary method with an operator splitting approach to construct high-order local artificial boundary conditions, reducing the original problem to a truncated bounded domain. The stability of the reduced problem is rigorously analyzed. Numerical results confirm the accuracy of the proposed method, and computational examples reveal the underlying physics.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"173 ","pages":"Article 109747"},"PeriodicalIF":2.8,"publicationDate":"2025-09-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145049624","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}

{"title":"Ultraslow diffusion revisited: Logarithmic scaling in single-term fractional diffusion models for anomalous transport of complex systems","authors":"Jincheng Dong ,&nbsp;Ning Du ,&nbsp;Zhiwei Yang","doi":"10.1016/j.aml.2025.109749","DOIUrl":"10.1016/j.aml.2025.109749","url":null,"abstract":"<div><div>This study establishes rigorous ties between ultraslow diffusion dynamics and single-term Caputo–Hadamard time-fractional diffusion equations via mean square displacement (MSD) analysis. We derive the explicit logarithmic scaling law <span><math><mrow><mi>MSD</mi><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow><mo>∼</mo><msup><mrow><mrow><mo>(</mo><mo>log</mo><mi>t</mi><mo>)</mo></mrow></mrow><mrow><mi>α</mi></mrow></msup></mrow></math></span> for constant-order Hadamard diffusion equations and verify this functional relationship through systematic numerical simulations. The revealed <span><math><msup><mrow><mrow><mo>(</mo><mo>log</mo><mi>t</mi><mo>)</mo></mrow></mrow><mrow><mi>α</mi></mrow></msup></math></span> scaling definitively departs from the classical <span><math><msup><mrow><mi>t</mi></mrow><mrow><mi>α</mi></mrow></msup></math></span> behavior characteristic of Caputo models, establishing a streamlined framework for modeling anomalous transport in mesoscopic complex systems.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"173 ","pages":"Article 109749"},"PeriodicalIF":2.8,"publicationDate":"2025-09-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145049623","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}

{"title":"General propagation lattice Boltzmann model for the variable-coefficient Gardner equation","authors":"Xue-Hui Zhao ,&nbsp;Wen-Qiang Hu ,&nbsp;Guo-Hong Yang ,&nbsp;Xia Yang","doi":"10.1016/j.aml.2025.109728","DOIUrl":"10.1016/j.aml.2025.109728","url":null,"abstract":"<div><div>This study presents a general propagation lattice Boltzmann model for solving the variable-coefficient Gardner equation, a nonlinear evolution equation describing weakly nonlinear long-wave propagation in KdV-type media. The proposed model integrates the Lax–Wendroff technique and fractional propagation methodology within a time-splitting framework, enhancing computational stability through adjustable parameters. By systematically deriving the equilibrium distribution function, compensation terms, and source components, the model accurately recovers the macroscopic equation via the Chapman-Enskog analysis. Numerical simulations validate the model’s accuracy and stability, with optimization methods (the Nelder–Mead algorithm and the Broyden–Fletcher–Goldfarb–Shanno method) employed to determine optimal free parameters. The results demonstrate excellent agreement with analytical solutions, highlighting the model’s potential for handling complex nonlinear systems with variable coefficients.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"173 ","pages":"Article 109728"},"PeriodicalIF":2.8,"publicationDate":"2025-09-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145027456","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}

{"title":"Extinction of intra prey induced by catastrophic shift in a Lesile–Gower intraguild predation model","authors":"Jiaoyan Yao,&nbsp;Sanling Yuan","doi":"10.1016/j.aml.2025.109748","DOIUrl":"10.1016/j.aml.2025.109748","url":null,"abstract":"<div><div>In this letter, we revisit a Lesile–Gower intraguild predation model proposed by Safuan et al. in the paper Safuan et al. (2013). It was shown there as the biotic resource enrichment parameter <span><math><mi>γ</mi></math></span> varies, the model can undergo a transcritical bifurcation which might explain two alternative scenarios: one is the coexistence of three populations, and the other is the extinction of the intra prey. That is, the survival of intra prey population is solely determined by the biotic resource enrichment. In fact, using the same parameter <span><math><mi>γ</mi></math></span> as bifurcation parameter, the model can also undergo a saddle–node bifurcation at some critical value <span><math><msub><mrow><mi>γ</mi></mrow><mrow><mi>S</mi><mi>N</mi></mrow></msub></math></span>, which might explain another two alternative scenarios: one is the bistability between a positive equilibrium and an intra prey extinction one, and the other is the extinction of the intra prey. This means that the intra prey species may undergo a catastrophic shift when <span><math><mi>γ</mi></math></span> increases passing through <span><math><msub><mrow><mi>γ</mi></mrow><mrow><mi>S</mi><mi>N</mi></mrow></msub></math></span>. This is established by proving the existence of positive equilibria and determining their stability, theoretically and numerically.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"173 ","pages":"Article 109748"},"PeriodicalIF":2.8,"publicationDate":"2025-09-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145027459","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}

{"title":"A linearly implicit, mass- and energy-conserving scheme for the Schrödinger-Poisson equation","authors":"Haoyue Jiang ,&nbsp;Dongfang Li ,&nbsp;Hai-wei Sun","doi":"10.1016/j.aml.2025.109746","DOIUrl":"10.1016/j.aml.2025.109746","url":null,"abstract":"<div><div>In this paper, a novel structure-preserving scheme is proposed for numerical solving the Schrödinger-Poisson equation. The scheme is obtained by carefully choosing the intermediate average variable in the leap-frog scheme. It is shown that the scheme is mass- and energy-conserving for the equation. More importantly, the scheme is linearly implicit, while the previous mass- and energy-conserving schemes are generally fully implicit. Numerical experiments are presented to confirm the theoretical results.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"173 ","pages":"Article 109746"},"PeriodicalIF":2.8,"publicationDate":"2025-09-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145019313","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}

{"title":"A note on the positive solutions for critical elliptic problems in exterior domains","authors":"Shubin Yu,&nbsp;Chun-Lei Tang","doi":"10.1016/j.aml.2025.109745","DOIUrl":"10.1016/j.aml.2025.109745","url":null,"abstract":"<div><div>We consider the existence of positive solutions for the elliptic Dirichlet problem <span><math><mfenced><mrow><mtable><mtr><mtd><mo>−</mo><mi>Δ</mi><mi>u</mi><mo>+</mo><mi>u</mi><mo>=</mo><mi>f</mi><mrow><mo>(</mo><mi>u</mi><mo>)</mo></mrow><mspace></mspace></mtd><mtd><mtext>in</mtext><mspace></mspace><mi>Ω</mi><mo>,</mo></mtd></mtr><mtr><mtd><mi>u</mi><mo>=</mo><mn>0</mn><mspace></mspace></mtd><mtd><mtext>on</mtext><mspace></mspace><mi>∂</mi><mi>Ω</mi><mo>,</mo></mtd></mtr></mtable></mrow></mfenced></math></span> where <span><math><mrow><mi>Ω</mi><mo>⊂</mo><msup><mrow><mi>R</mi></mrow><mrow><mi>N</mi></mrow></msup></mrow></math></span> (<span><math><mrow><mi>N</mi><mo>≥</mo><mn>3</mn></mrow></math></span>) is an exterior domain with smooth boundary <span><math><mrow><mi>∂</mi><mi>Ω</mi><mo>≠</mo><mo>0̸</mo></mrow></math></span> such that <span><math><mrow><msup><mrow><mi>R</mi></mrow><mrow><mi>N</mi></mrow></msup><mo>∖</mo><mi>Ω</mi></mrow></math></span> is bounded. If <span><math><mi>f</mi></math></span> involves critical growth, the existing work only covers that <span><math><mrow><mi>f</mi><mrow><mo>(</mo><mi>u</mi><mo>)</mo></mrow><mo>=</mo><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><mi>ɛ</mi><msup><mrow><mrow><mo>|</mo><mi>u</mi><mo>|</mo></mrow></mrow><mrow><msup><mrow><mn>2</mn></mrow><mrow><mo>∗</mo></mrow></msup><mo>−</mo><mn>2</mn></mrow></msup><mi>u</mi></mrow></math></span>, where <span><math><mrow><msup><mrow><mn>2</mn></mrow><mrow><mo>∗</mo></mrow></msup><mo>=</mo><mfrac><mrow><mn>2</mn><mi>N</mi></mrow><mrow><mi>N</mi><mo>−</mo><mn>2</mn></mrow></mfrac></mrow></math></span> is the Sobolev critical exponent and <span><math><mrow><mi>ɛ</mi><mo>&gt;</mo><mn>0</mn></mrow></math></span> is a sufficiently small parameter. In present paper, we remove this parameter, i.e., <span><math><mrow><mi>f</mi><mrow><mo>(</mo><mi>u</mi><mo>)</mo></mrow><mo>=</mo><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><msup><mrow><mrow><mo>|</mo><mi>u</mi><mo>|</mo></mrow></mrow><mrow><msup><mrow><mn>2</mn></mrow><mrow><mo>∗</mo></mrow></msup><mo>−</mo><mn>2</mn></mrow></msup><mi>u</mi></mrow></math></span>, and establish the existence of positive solutions when <span><math><mrow><mn>3</mn><mo>≤</mo><mi>N</mi><mo>≤</mo><mn>6</mn></mrow></math></span> and <span><math><mrow><mfrac><mrow><mi>N</mi><mo>+</mo><mn>2</mn></mrow><mrow><mi>N</mi><mo>−</mo><mn>2</mn></mrow></mfrac><mo>≤</mo><mi>p</mi><mo>&lt;</mo><msup><mrow><mn>2</mn></mrow><mrow><mo>∗</mo></mrow></msup></mrow></math></span> with <span><math><mrow><mi>p</mi><mo>&gt;</mo><mn>2</mn></mrow></math></span>.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"173 ","pages":"Article 109745"},"PeriodicalIF":2.8,"publicationDate":"2025-09-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145097043","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}

{"title":"On an integrable discrete coupled nonlinear Schrödinger equation with branched dispersion: Discrete N-fold Darboux transformation and exact solutions","authors":"Tong Zhou,&nbsp;Hai-qiong Zhao","doi":"10.1016/j.aml.2025.109744","DOIUrl":"10.1016/j.aml.2025.109744","url":null,"abstract":"<div><div>In this letter, we introduced an integrable discrete coupled nonlinear Schrödinger equation with branched dispersion (dcNLSBD) and constructed its discrete <span><math><mi>N</mi></math></span>-fold Darboux transformation (DT). We studied several types of exact solutions for this equation with the aid of DT and investigated dynamics of the exact solutions.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"173 ","pages":"Article 109744"},"PeriodicalIF":2.8,"publicationDate":"2025-09-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145010813","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}