Studies in Applied Mathematics最新文献

{"title":"Discrete Infinite-Agent Cucker–Smale Flocking Under Fixed and Switching Digraphs","authors":"Lining Ru,&nbsp;Xiaoyu Li,&nbsp;Jiu-Gang Dong","doi":"10.1111/sapm.70216","DOIUrl":"10.1111/sapm.70216","url":null,"abstract":"<div>\u0000 \u0000 <p>This paper studies the flocking behavior in a discrete-time Cucker–Smale (C-S) model with infinite agents under both fixed and switching directed interaction topologies. For the fixed topology, we analyze the infinite digraph containing a spanning tree with the finite smallest depth under two distinct framework conditions. We then show that unconditional and conditional flocking can occur, consistent with the behavioral patterns of finite-dimensional C-S systems under fixed digraphs. For the switching topologies, we derive analogous sufficient conditions that guarantee the occurrence of flocking. The theoretical results are further illustrated through several examples.</p></div>","PeriodicalId":51174,"journal":{"name":"Studies in Applied Mathematics","volume":"156 4","pages":""},"PeriodicalIF":2.3,"publicationDate":"2026-04-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147668488","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 Negative Flow of the Benjamin–Ono Equation","authors":"Gegenhasi,&nbsp;Xing-Biao Hu,&nbsp;Ya-Jie Liu,&nbsp;Ling-Juan Yan,&nbsp;Ying-Nan Zhang","doi":"10.1111/sapm.70215","DOIUrl":"10.1111/sapm.70215","url":null,"abstract":"<div>\u0000 \u0000 <p>This paper introduces and investigates the negative flow of the Benjamin–Ono (BO) equation, an integrable integrodifferential model that had not previously been studied. We establish its bilinear form and derive both a bilinear Bäcklund transformation and a nonlinear superposition formula. These structures are then combined to develop a unified solution approach, which systematically generates exact solutions in determinant form. The strength of this approach lies not only in its compact algebraic representation but also in its adaptability to rigorous analysis involving the Hilbert transform, thereby revealing deeper structural properties of the system. Within this framework, we obtain a Lax pair and explicitly construct two fundamental classes of solutions—multisoliton solutions and multiphase solutions. This study not only enriches the theory of the BO hierarchy but also provides a theoretical foundation for the investigation of broader classes of integrable integrodifferential equations.</p></div>","PeriodicalId":51174,"journal":{"name":"Studies in Applied Mathematics","volume":"156 4","pages":""},"PeriodicalIF":2.3,"publicationDate":"2026-04-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147668282","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":"Existence and Stability for Traveling Waves of Fourth-Order Semilinear Wave and Schrödinger Equations","authors":"Vishnu Iyer,&nbsp;Ross Parker,&nbsp;Atanas G. Stefanov","doi":"10.1111/sapm.70214","DOIUrl":"10.1111/sapm.70214","url":null,"abstract":"<p>We investigate the existence and spectral stability of traveling wave solutions for a class of fourth-order semilinear wave equations, commonly referred to as beam equations. Using variational methods based on a constrained maximization problem, we establish the existence of smooth, exponentially decaying traveling wave profiles for wavespeeds in the interval <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 <mo>−</mo>\u0000 <msqrt>\u0000 <mn>2</mn>\u0000 </msqrt>\u0000 <mo>,</mo>\u0000 <msqrt>\u0000 <mn>2</mn>\u0000 </msqrt>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 <annotation>$(-sqrt {2}, sqrt {2})$</annotation>\u0000 </semantics></math>. We derive precise spectral properties of the associated linearized operators and prove a Vakhitov–Kolokolov (VK)-type stability criterion that completely characterizes spectral stability. Furthermore, we determine the sharp exponential decay rate of the traveling waves and demonstrate that it matches the decay rate of the Green's function for the linearized operator. Our analysis extends to fourth-order nonlinear Schrödinger equations, for which we establish analogous existence and stability results. The theoretical findings are complemented by numerical computations that verify the stability predictions and reveal the transition from unstable to stable regimes as the wavespeed varies. These results provide a comprehensive mathematical framework for understanding wave propagation phenomena in structural mechanics, particularly suspension bridge models.</p>","PeriodicalId":51174,"journal":{"name":"Studies in Applied Mathematics","volume":"156 4","pages":""},"PeriodicalIF":2.3,"publicationDate":"2026-04-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1111/sapm.70214","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147668192","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":"Non-Relativistic Limit of Dirac Hamiltonians With Aharonov–Bohm Fields","authors":"Matteo Gallone,&nbsp;Alessandro Michelangeli,&nbsp;Diego Noja","doi":"10.1111/sapm.70209","DOIUrl":"10.1111/sapm.70209","url":null,"abstract":"<p>We characterize the families of self-adjoint Dirac and Schrödinger operators with Aharonov–Bohm magnetic field, and we exploit the non-relativistic limit of infinite light speed to connect the former to the latter. The limit consists of the customary removal of the rest energy and of a suitable scaling, with the light speed, of the short-scale boundary condition of self-adjointness. This ensures that the scattering length of the Aharonov–Bohm interaction is preserved along the limit. Noteworthy is the fact that the whole family of Dirac-AB operators is mapped, in the non-relativistic limit, into the physically relevant sub-family of <span></span><math>\u0000 <semantics>\u0000 <mi>s</mi>\u0000 <annotation>$s$</annotation>\u0000 </semantics></math>-wave, angular-momentum-commuting, Schrödinger–AB Hamiltonians with relativistic Dirac approximants.</p>","PeriodicalId":51174,"journal":{"name":"Studies in Applied Mathematics","volume":"156 4","pages":""},"PeriodicalIF":2.3,"publicationDate":"2026-04-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1111/sapm.70209","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147668193","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":"The Two-Component Discrete KP Hierarchy","authors":"Wenqi Cao,&nbsp;Jipeng Cheng,&nbsp;Jinbiao Wang","doi":"10.1111/sapm.70213","DOIUrl":"10.1111/sapm.70213","url":null,"abstract":"&lt;div&gt;\u0000 \u0000 &lt;p&gt;The discrete KP hierarchy is also known as the &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mo&gt;(&lt;/mo&gt;\u0000 &lt;mi&gt;l&lt;/mi&gt;\u0000 &lt;mo&gt;−&lt;/mo&gt;\u0000 &lt;msup&gt;\u0000 &lt;mi&gt;l&lt;/mi&gt;\u0000 &lt;mo&gt;′&lt;/mo&gt;\u0000 &lt;/msup&gt;\u0000 &lt;mo&gt;)&lt;/mo&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$(l-l^{prime })$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;th modified KP hierarchy. In this paper, we consider the corresponding two-component generalization, known as the two-component discrete KP (2dKP) hierarchy. First, starting from the bilinear equation of the 2dKP hierarchy, we derive the corresponding Lax equation by the Shiota method, which uses scalar Lax operators involving two difference operators, &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;msub&gt;\u0000 &lt;mi&gt;Λ&lt;/mi&gt;\u0000 &lt;mn&gt;1&lt;/mn&gt;\u0000 &lt;/msub&gt;\u0000 &lt;annotation&gt;$Lambda _1$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; and &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;msub&gt;\u0000 &lt;mi&gt;Λ&lt;/mi&gt;\u0000 &lt;mn&gt;2&lt;/mn&gt;\u0000 &lt;/msub&gt;\u0000 &lt;annotation&gt;$Lambda _2$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;. Then, starting from the 2dKP Lax equation, we obtain the corresponding bilinear equation, which includes the existence of the tau function. From the above discussions, we can determine which are essential in the 2dKP Lax formulation. Finally, we discuss the reduction of the 2dKP hierarchy corresponding to the loop algebra &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;msub&gt;\u0000 &lt;mover&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;s&lt;/mi&gt;\u0000 &lt;mi&gt;l&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;mo&gt;̂&lt;/mo&gt;\u0000 &lt;/mover&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;M&lt;/mi&gt;\u0000 &lt;mo&gt;+&lt;/mo&gt;\u0000 &lt;mi&gt;N&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/msub&gt;\u0000 &lt;mo&gt;=&lt;/mo&gt;\u0000 &lt;mi&gt;s&lt;/mi&gt;\u0000 &lt;msub&gt;\u0000 &lt;mi&gt;l&lt;/mi&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;M&lt;/mi&gt;\u0000 &lt;mo&gt;+&lt;/mo&gt;\u0000 &lt;mi&gt;N&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/msub&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mo&gt;[&lt;/mo&gt;\u0000 &lt;mi&gt;λ&lt;/mi&gt;\u0000 &lt;mo&gt;,&lt;/mo&gt;\u0000 &lt;msup&gt;\u0000 &lt;mi&gt;λ&lt;/mi&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mo&gt;−&lt;/mo&gt;\u0000 &lt;mn&gt;1&lt;/mn&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/msup&gt;\u0000 &lt;mo&gt;]&lt;/mo&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;mi&gt;⊕&lt;/mi&gt;\u0000 &lt;mi&gt;C&lt;/mi&gt;\u0000 &lt;mi&gt;c&lt;/mi&gt;\u0000 &lt;mspace&gt;&lt;/mspace&gt;\u0000 &lt;mrow","PeriodicalId":51174,"journal":{"name":"Studies in Applied Mathematics","volume":"156 4","pages":""},"PeriodicalIF":2.3,"publicationDate":"2026-04-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147668057","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":"Some Results for a Class of Nonlinear Schrödinger Equations With Derivative Nonlinearities","authors":"Liuyan Huang,&nbsp;Guoqing Zhang","doi":"10.1111/sapm.70211","DOIUrl":"10.1111/sapm.70211","url":null,"abstract":"<div>\u0000 \u0000 <p>In this paper, we consider a class of nonlinear Schrödinger equations with derivative nonlinearities, which is first introduced by Colin and Colin [<i>Differential Integral Equations</i> 17 (2004): 297–330] as a model of laser-plasma interaction. Based on concentration-compactness principle combined with variational methods, we prove some existence and nonexistence results of normalized ground states, respectively. Furthermore, we obtain the global well-posedness in three-dimensional space. By using conservation laws and Virial estimate, we also investigate some blow-up results.</p></div>","PeriodicalId":51174,"journal":{"name":"Studies in Applied Mathematics","volume":"156 4","pages":""},"PeriodicalIF":2.3,"publicationDate":"2026-04-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147668056","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 Linearized Korteweg–de Vries Equation on the Line With Metric Graph Defects","authors":"D. A. Smith","doi":"10.1111/sapm.70208","DOIUrl":"10.1111/sapm.70208","url":null,"abstract":"<p>We study the small-amplitude linearization of the Korteweg–de Vries equation on the line with a local defect scattering waves represented by a metric graph domain adjoined at one point. For a representative collection of examples, we derive explicit solution formulas expressed as contour integrals and obtain existence and unicity results for piecewise absolutely continuous data. In so doing, we implement the unified transform method on metric graphs comprising both bonds and leads for a third-order differential operator.</p>","PeriodicalId":51174,"journal":{"name":"Studies in Applied Mathematics","volume":"156 4","pages":""},"PeriodicalIF":2.3,"publicationDate":"2026-04-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1111/sapm.70208","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147668058","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":"Existence and Spectral Stability Analysis of Viscous-Dispersive Shock Profiles for Isentropic Compressible Fluids of Korteweg Type","authors":"Raffaele Folino,&nbsp;Corrado Lattanzio,&nbsp;Ramón G. Plaza","doi":"10.1111/sapm.70210","DOIUrl":"10.1111/sapm.70210","url":null,"abstract":"<p>The system describing the dynamics of a compressible isentropic fluid exhibiting viscosity and internal capillarity in one space dimension and in Lagrangian coordinates, is considered. It is assumed that the viscosity and the capillarity coefficients are nonlinear smooth, positive functions of the specific volume, making the system the most general case possible. It is shown, under very general circumstances, that the system admits traveling wave solutions connecting two constant states and traveling with a certain speed that satisfy the classical Rankine–Hugoniot and Lax entropy conditions, and hence called viscous-dispersive shock profiles. These traveling wave solutions are unique up to translations and have arbitrary amplitude. The spectral stability of such viscous-dispersive profiles is also considered. It is shown that the essential spectrum of the linearized operator around the profile (posed on an appropriate energy space) is stable, independently of the shock strength. With the aid of energy estimates, it is also proved that the point spectrum is also stable, provided that the shock amplitude is sufficiently small and a structural condition on the inviscid shock is fulfilled.</p>","PeriodicalId":51174,"journal":{"name":"Studies in Applied Mathematics","volume":"156 4","pages":""},"PeriodicalIF":2.3,"publicationDate":"2026-04-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1111/sapm.70210","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147668055","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":"Issue Information-TOC","authors":"","doi":"10.1111/sapm.70212","DOIUrl":"10.1111/sapm.70212","url":null,"abstract":"","PeriodicalId":51174,"journal":{"name":"Studies in Applied Mathematics","volume":"156 4","pages":""},"PeriodicalIF":2.3,"publicationDate":"2026-03-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1111/sapm.70212","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147668848","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":"Traveling Wavefronts to the Precursor and Differentiated Cell Model: The Critical Degenerate Nonlinearity","authors":"Yuanxi Yue,&nbsp;Chunhua Ou","doi":"10.1111/sapm.70206","DOIUrl":"10.1111/sapm.70206","url":null,"abstract":"<div>\u0000 \u0000 <p>In this paper, we develop new ideas to establish the existence of traveling waves to a precursor and differentiated cell model with degenerate nonlinearity and non-isolated equilibria. Our new approach is based on continuation argument and the abstract implicit function theorem coupled with the upper–lower solution method, which seems to be able to widely apply to many other systems with degenerate nonlinearity and/or non-isolated equilibria. We prove that the traveling wave with the minimal speed decays exponentially to zero at positive infinity, while for all other speeds, the decay is algebraic. Furthermore, due to the significance of the minimal speed (usually regarded as the spreading speed), we provide an estimate of it. In particular, when the parameter <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>k</mi>\u0000 <mo>=</mo>\u0000 <mn>1</mn>\u0000 </mrow>\u0000 <annotation>$k=1$</annotation>\u0000 </semantics></math>, we derive an exact value of the minimal wave speed and the expression of the traveling wave solution with the minimal-speed.</p></div>","PeriodicalId":51174,"journal":{"name":"Studies in Applied Mathematics","volume":"156 4","pages":""},"PeriodicalIF":2.3,"publicationDate":"2026-03-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147668860","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}