Studies in Applied Mathematics最新文献

{"title":"Well-Posedness and Pattern Formation in a Two-Species Reaction–Diffusion System with Nonlocal Perception","authors":"Yaqi Chen,&nbsp;Ben Niu,&nbsp;Hao Wang","doi":"10.1111/sapm.70186","DOIUrl":"https://doi.org/10.1111/sapm.70186","url":null,"abstract":"<p>Nonlocal perceptual cues, such as visual, auditory, and olfactory signals, profoundly influence animal movement and the emergence of ecological patterns. To capture these effects, we introduce a two-species reaction–diffusion system with mutual nonlocal perception on a two-dimensional periodic domain. We establish global well-posedness of the model through a generalized entropy framework that accommodates nonlinear reaction kinetics and convolution-based perception fields. Specializing to a predator–prey interaction, we carry out linear stability and bifurcation analyses with perceptual diffusion coefficients as bifurcation parameters. Explicit criteria are derived for the onset of Turing and Turing–Hopf instabilities, showing how perception radius and behavioral response jointly drive spatial self-organization. Numerical simulations with a Holling Type II response illustrate both stationary and oscillatory heterogeneous patterns. Our results reveal complementary mechanisms linking perceptual range and movement tendencies within and across species, offering new theoretical insight into the role of nonlocal perception in ecological pattern formation.</p>","PeriodicalId":51174,"journal":{"name":"Studies in Applied Mathematics","volume":"156 2","pages":""},"PeriodicalIF":2.3,"publicationDate":"2026-02-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1111/sapm.70186","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147280950","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Adiabatic Perturbation Theory for the Soliton of the Nonlinear Dirac Equation in 1D","authors":"Taras I. Lakoba","doi":"10.1111/sapm.70185","DOIUrl":"https://doi.org/10.1111/sapm.70185","url":null,"abstract":"<div>\u0000 \u0000 <p>We derive equations for the slow changes of parameters of the soliton of the 1D nonlinear Dirac, or Gross–Neveu, equation under the action of a small perturbation. Our perturbation theory uses the neutral modes of the linearized operator of the nonlinear Dirac equation. In addition to the conventional soliton parameters such as its frequency (related to the amplitude and width), velocity, and shifts of the center and phase, we also account for an additional parameter, related the so-called Bogoliubov symmetry of the Dirac equation, which was first pointed out almost half a century ago and rediscovered in the last decade. This aspect of our theory allows one to explain both asymmetric changes of the soliton profile and large growth of the soliton amplitude, which was observed in previous studies via numerical simulations.</p></div>","PeriodicalId":51174,"journal":{"name":"Studies in Applied Mathematics","volume":"156 2","pages":""},"PeriodicalIF":2.3,"publicationDate":"2026-02-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147280918","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":"Issue Information-TOC","authors":"","doi":"10.1111/sapm.70187","DOIUrl":"https://doi.org/10.1111/sapm.70187","url":null,"abstract":"","PeriodicalId":51174,"journal":{"name":"Studies in Applied Mathematics","volume":"156 2","pages":""},"PeriodicalIF":2.3,"publicationDate":"2026-02-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1111/sapm.70187","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146162426","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Partial Mass Dynamics of the Defocusing Nonlinear Schrödinger Equation","authors":"Jiaqi Liu,&nbsp;Xixi Xu","doi":"10.1111/sapm.70183","DOIUrl":"https://doi.org/10.1111/sapm.70183","url":null,"abstract":"<div>\u0000 \u0000 <p>We study the long-time dynamics of the defocusing nonlinear Schrödinger (NLS) equation. Compared with previous literature, we revisit the direct and inverse scattering map to obtain asymptotics in some weighted energy space that requires less restrictive decay and regularity assumptions. The main result is derived from an application of uniform resolvent bound and an approximation argument in the spirit of <i>Riemann–Lebesgue</i> lemma. As a consequence, our result demonstrates that zeros of the solution to the defocusing NLS equation cannot lie in bounded sets as <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>t</mi>\u0000 <mo>→</mo>\u0000 <mi>∞</mi>\u0000 </mrow>\u0000 <annotation>$trightarrow infty$</annotation>\u0000 </semantics></math>.</p></div>","PeriodicalId":51174,"journal":{"name":"Studies in Applied Mathematics","volume":"156 2","pages":""},"PeriodicalIF":2.3,"publicationDate":"2026-02-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146176088","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 Two-Species Competition Reaction–Diffusion Systems in a Time-Varying Domain","authors":"Shiheng Fan,&nbsp;Xiao-Qiang Zhao","doi":"10.1111/sapm.70179","DOIUrl":"https://doi.org/10.1111/sapm.70179","url":null,"abstract":"<div>\u0000 \u0000 <p>In this paper, we investigate the global dynamics of a two-species competition reaction–diffusion model in a time-varying domain under the homogeneous Dirichlet and Neumann boundary conditions. Under appropriate conditions, we establish the competitive exclusion principle for asymptotically bounded and periodic domains, respectively. By the method of upper and lower solutions and comparison arguments, we prove that one species will exclude the other in an asymptotically unbounded domain. We further apply the analytic results to a Lotka–Volterra competition model for its global dynamics and conduct numerical simulations to illustrate our findings.</p>\u0000 </div>","PeriodicalId":51174,"journal":{"name":"Studies in Applied Mathematics","volume":"156 1","pages":""},"PeriodicalIF":2.3,"publicationDate":"2026-01-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146140105","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":"Asymptotic Profiles and Disease Prevalence at the Steady State for an SIS Patch Model","authors":"Daozhou Gao,&nbsp;Xin Li","doi":"10.1111/sapm.70180","DOIUrl":"https://doi.org/10.1111/sapm.70180","url":null,"abstract":"<p>Infected individuals often display mobility patterns that differ significantly from those of healthy individuals—traveling less frequently, covering shorter distances, visiting fewer destinations, and altering their timing and modes of movement. In this paper, to explore the influence of changes in travel frequency and destination on the spatial spread of infectious diseases, we propose a susceptible–infectious–susceptible patch model in which susceptible and infected populations have different dispersal rates and connectivity matrices. We first establish the threshold dynamics in terms of the basic reproduction number <span></span><math>\u0000 <semantics>\u0000 <msub>\u0000 <mi>R</mi>\u0000 <mn>0</mn>\u0000 </msub>\u0000 <annotation>$mathcal {R}_0$</annotation>\u0000 </semantics></math> and show the existence and uniqueness of endemic equilibrium (EE) when <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <msub>\u0000 <mi>R</mi>\u0000 <mn>0</mn>\u0000 </msub>\u0000 <mo>&gt;</mo>\u0000 <mn>1</mn>\u0000 </mrow>\u0000 <annotation>$mathcal {R}_0&gt;1$</annotation>\u0000 </semantics></math>. Then we examine the asymptotic profiles of the EE under small dispersal rate of the susceptible or infected population. In particular, we prove that as susceptible mobility tends to zero, the EE converges a disease-free equilibrium in the most general case. We find that asymmetric dispersal provides a new approach to eliminate infections than small susceptible mobility. Furthermore, we analyze both local and global disease prevalence to identify strategies for lowering endemic level. Variations in connectivity matrix can lead to high prevalence in low-risk patch, a failure of the order-preserving property on local prevalence. Numerical simulations are conducted to further reveal the role of heterogeneous mobility patterns. Overall, this study offers new insights into how human movement shapes the distribution of disease and generalizes many results in the literature.</p>","PeriodicalId":51174,"journal":{"name":"Studies in Applied Mathematics","volume":"156 1","pages":""},"PeriodicalIF":2.3,"publicationDate":"2026-01-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1111/sapm.70180","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146140106","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Global Solutions for Supersonic Flow of a Chaplygin Gas Past a Conical Wing With a Shock Wave Detached From the Leading Edges","authors":"Bingsong Long","doi":"10.1111/sapm.70181","DOIUrl":"https://doi.org/10.1111/sapm.70181","url":null,"abstract":"<div>\u0000 \u0000 <p>In this paper, we first investigate the mathematical aspects of supersonic flow of a Chaplygin gas past a conical wing with diamond-shaped cross sections in the case of a shock wave detached from the leading edges. The flow under consideration is governed by the three-dimensional steady compressible Euler equations. For the Chaplygin gas, all characteristics are linearly degenerate, and shocks are reversible and characteristic. Using these properties, we can determine the location of the shock in advance and reformulate our problem as an oblique derivative problem for a nonlinear degenerate elliptic equation in conical coordinates. By establishing a Lipschitz estimate, we show that the equation is uniformly elliptic in any subdomain strictly away from the degenerate boundary, and then further prove the existence of a solution to the problem via the continuity method and vanishing viscosity method.</p></div>","PeriodicalId":51174,"journal":{"name":"Studies in Applied Mathematics","volume":"156 1","pages":""},"PeriodicalIF":2.3,"publicationDate":"2026-01-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146091394","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":"Alexseev–Gröbner Formula and Asymptotic Phase-Locking of Kuramoto Ensembles With Inertia and Frustration","authors":"Hangjun Cho,&nbsp;Jiu-Gang Dong,&nbsp;Seung-Yeal Ha","doi":"10.1111/sapm.70177","DOIUrl":"https://doi.org/10.1111/sapm.70177","url":null,"abstract":"<p>We study asymptotic dynamics of Kuramoto oscillators with inertia and frustration using the classical perturbation theory of ordinary differential equation systems. Frustration also known as the phase-lag poses challenges for the mathematical analysis of asymptotic dynamics due to the breakdown of total phase conservation and the gradient structure. The effect of frustration, represented by an additive angular constant in the sinusoidal interaction term, transforms the Kuramoto model into a perturbed one relative to the nonfrustration regime. We apply the Alekseev–Gröbner formula to explicitly characterize the relationship between perturbed and unperturbed systems, and we demonstrate the emergence of phase-locking in the perturbed system from the unperturbed one. Finally, we provide a sufficient framework for asymptotic phase-locking in terms of system parameters and initial data. In particular, we explicitly compute the rotation numbers of the Kuramoto oscillators.</p>","PeriodicalId":51174,"journal":{"name":"Studies in Applied Mathematics","volume":"156 1","pages":""},"PeriodicalIF":2.3,"publicationDate":"2026-01-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1111/sapm.70177","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146099347","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"On the N-Elliptic Localized Wave Solutions to the Derivative Nonlinear Schrödinger Equation and Their Asymptotic Analysis","authors":"Liming Ling,&nbsp;Wang Tang","doi":"10.1111/sapm.70176","DOIUrl":"https://doi.org/10.1111/sapm.70176","url":null,"abstract":"<div>\u0000 \u0000 <p>We parameterize elliptic function solutions to the derivative nonlinear Schrödinger (DNLS) equation with four independent parameters and generate two equivalent forms of <span></span><math>\u0000 <semantics>\u0000 <mi>N</mi>\u0000 <annotation>$N$</annotation>\u0000 </semantics></math>-elliptic localized wave solutions to the DNLS equation through the Darboux–Bäcklund transformation. The <span></span><math>\u0000 <semantics>\u0000 <mi>N</mi>\u0000 <annotation>$N$</annotation>\u0000 </semantics></math>-elliptic localized wave solutions are expressed as (the derivative of) the ratios of determinants with entries in terms of Weierstrass sigma functions. Moreover, the asymptotic behaviors of both forms of the <span></span><math>\u0000 <semantics>\u0000 <mi>N</mi>\u0000 <annotation>$N$</annotation>\u0000 </semantics></math>-elliptic localized wave solutions are analyzed both along and between the propagation directions as <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>t</mi>\u0000 <mo>→</mo>\u0000 <mo>±</mo>\u0000 <mi>∞</mi>\u0000 </mrow>\u0000 <annotation>$trightarrow pm infty$</annotation>\u0000 </semantics></math>, which verifies that the collisions between elliptic-solutions are elastic. We prove that the solution tends to a simple elliptic localized wave solution along each propagation direction. Between the propagation directions, the solution asymptotically approaches a shifted background. Furthermore, we establish sufficient conditions for strictly elastic collisions. The dynamic behaviors of the solutions are systematically investigated, with analytical results visualized through graphical illustrations. The asymptotic analysis of these solutions confirms that they exhibit the behaviors predicted by the generalized soliton resolution conjecture on the elliptic function background.</p></div>","PeriodicalId":51174,"journal":{"name":"Studies in Applied Mathematics","volume":"156 1","pages":""},"PeriodicalIF":2.3,"publicationDate":"2026-01-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146099348","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":"The Periodic Wave Solution and Riemann Problem for the Modified Benjamin–Bona–Mahony Equation","authors":"Jing Chen,&nbsp;Yushan Xue,&nbsp;Ao Zhou","doi":"10.1111/sapm.70166","DOIUrl":"https://doi.org/10.1111/sapm.70166","url":null,"abstract":"<div>\u0000 \u0000 <p>In this paper, we investigate periodic wave solution and the complete classifications of solutions for the modified Benjamin–Bona–Mahony (mBBM) equation, also commonly referred to as the modified regularized long wave (mRLW) equation with initial discontinuous Riemann problem. The nonlinear dispersive mBBM equation serves as an alternative model to the modified Korteweg–de Vries (mKdV) equation in physical phenomena such as long-crested waves in near-shore regions and unidirectional wave propagation in water channels. By employing hyperbolic theory, asymptotic analysis, Whitham modulation theory, and the dispersive shock wave (DSW) fitting method, along with direct numerical simulations, we systematically analyze the fundamental wave structures in the Riemann problem. These basic waves include linear wavetrains composed of one-phase and two-phase solutions, RWs, DSWs, and the two-phase modulation structures for DSW implosion. Due to the non-integrability of the mBBM equation and the non-convexity of its linear dispersion relation, its Riemann problem exhibits a richer variety of solutions compared to the mKdV equation. The most notable differences include the emergence of two-phase linear wavetrains and DSW implosion. Finally, based on the differences in wave structures, we classify the initial parameter space into 10 distinct regions.</p></div>","PeriodicalId":51174,"journal":{"name":"Studies in Applied Mathematics","volume":"156 1","pages":""},"PeriodicalIF":2.3,"publicationDate":"2026-01-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146096462","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}