Studies in Applied Mathematics最新文献

{"title":"A New Integrable N-Particle McMillan Map and Its Exact Solutions","authors":"Ruguang Zhou,&nbsp;Zilong Yu,&nbsp;Baoqiang Xia","doi":"10.1111/sapm.70318","DOIUrl":"https://doi.org/10.1111/sapm.70318","url":null,"abstract":"<div>\u0000 \u0000 <p>An integrable <span></span><math>\u0000 <semantics>\u0000 <mi>N</mi>\u0000 <annotation>$N$</annotation>\u0000 </semantics></math>-particle generalization of the classical McMillan map with distinct particle-dependent parameters is introduced. Its Liouville integrability is established through a discrete Lax representation and the associated classical <span></span><math>\u0000 <semantics>\u0000 <mi>r</mi>\u0000 <annotation>$r$</annotation>\u0000 </semantics></math>-matrix structure. The map is further shown to provide a discrete auto-Bäcklund transformation for the restricted Kaup–Newell flows and to arise from the nonlinearization of a Darboux transformation for the Kaup–Newell spectral problem. Using the associated hyperelliptic spectral curve and Baker–Akhiezer functions, explicit algebro-geometric solutions for the multi-particle orbits are derived in terms of Riemann theta functions. These results provide an exact solution framework for multi-particle McMillan dynamics with particle-dependent parameters and clarify its connection with the continuous Kaup–Newell hierarchy.</p></div>","PeriodicalId":51174,"journal":{"name":"Studies in Applied Mathematics","volume":"157 4","pages":""},"PeriodicalIF":2.4,"publicationDate":"2026-10-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149099944","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":"Two-Dimensional Incompressible Rotational Impinging Jets Issuing From a Finite Nozzle","authors":"Xin Wang","doi":"10.1111/sapm.70310","DOIUrl":"https://doi.org/10.1111/sapm.70310","url":null,"abstract":"<div>\u0000 \u0000 <p>This study is devoted to the well-posedness of a two-dimensional incompressible rotational impinging jet issuing from a finite nozzle. More precisely, for a given vertical velocity and a constant vorticity at the nozzle entrance, it is shown that there exists a unique incompressible rotational impinging jet with the free boundary joining smoothly to the endpoint of the nozzle. The crucial difficulty in our analysis is to overcome the smoothness loss of the solution at the corners of the nozzle entrance. Furthermore, we establish the negativity of the vertical velocity and the asymptotic behavior of the flow far downstream.</p></div>","PeriodicalId":51174,"journal":{"name":"Studies in Applied Mathematics","volume":"157 3","pages":""},"PeriodicalIF":2.4,"publicationDate":"2026-09-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149048076","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":"Modeling Cholera Transmission Dynamics With Antibiotic Resistance and Mutation: A PDE Perspective","authors":"Wei Wang,&nbsp;Shuang Liu,&nbsp;Yuan Lou,&nbsp;Xiunan Wang","doi":"10.1111/sapm.70308","DOIUrl":"https://doi.org/10.1111/sapm.70308","url":null,"abstract":"<div>\u0000 \u0000 <p>Cholera originated in the Ganges Delta of India in 1817 and then spread globally through several overlapping waves of epidemics. Its prevalence has since been reported to vary widely across different regions. Spatial heterogeneity plays a crucial role in shaping cholera transmission through the interplay of environment, population, and infrastructure. In this paper, we propose a new reaction-advection-diffusion equation model in a closed advective environment, which extends the ODE model introduced in Wang et al. (Wang W., Y. Lou, X. Wang, “Modeling Cholera Transmission Dynamics with Antibiotic Resistance and Mutation: A Case Study in Zimbabwe,” Mathematical Biosciences 390 (2025): 109545). We establish three critical thresholds and analyze the dependence of the basic reproduction number on model parameters by studying the principal eigenvalue of a series of cooperative elliptic systems with weight and potential. We further derive threshold-type results for the global dynamics, and investigate the asymptotic profiles of the coexistence endemic steady state when the diffusion rate of the susceptible individuals is small. Interestingly, for a spatially homogeneous case, we numerically find the spatially inhomogeneous steady state. We also observe that bacterial advection exhibits antibiotic-resistance-dependent effects on cholera outbreaks, and this dependence can be modified by environmental mutation of <i>Vibrio cholerae</i>. These results underscore the critical roles of antibiotic resistance and bacterial mutation in shaping spatial cholera transmission dynamics with geographical heterogeneity and population mobility.</p></div>","PeriodicalId":51174,"journal":{"name":"Studies in Applied Mathematics","volume":"157 3","pages":""},"PeriodicalIF":2.4,"publicationDate":"2026-09-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149047962","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":"Unified Ray and Amplitude Tracing ODE Systems for the Eikonal and Transport Equations via Contact Geometry","authors":"Ahmet Beyaz,&nbsp;Çağrı Diner,&nbsp;Mustafa Tevfik Aktar","doi":"10.1111/sapm.70309","DOIUrl":"https://doi.org/10.1111/sapm.70309","url":null,"abstract":"<p>High-frequency seismic wave descriptions are essential for fundamental geophysical applications, including earthquake hypocenter location, magnitude estimation, and traveltime–amplitude tomography. These descriptions rely on two coupled PDEs: the eikonal equation (governing traveltimes) and the transport equation (governing amplitudes). Solving both equations together provides sharper subsurface images and more reliable magnitude/location estimates. Although the transport equation has been transformed into an ODE in the classical literature, this reduction relies crucially on the isotropy assumption (i.e., the wavefront normal is parallel to the ray direction). An explicit, characteristic-based ODE formulation analogous to the one used for the eikonal equation—and valid without imposing isotropy—has been lacking. This study addresses that limitation by deriving a unified first-order ODE framework, using the principles of contact geometry, that simultaneously transforms both the eikonal and transport equations into coupled ODE systems. This formulation allows ray paths, traveltimes, and amplitudes to be solved together and explicitly as functions of ray time. In addition, we introduce a general methodology for computing the traveltime Laplacian—a key quantity in the amplitude equation—without assuming isotropy. We first apply the chain rule to the ray-coordinate mappings to derive an exact analytical expression for the Laplacian. We then provide a geometric interpretation that links this analytical expression to the local structure of the ray tubes in both the physical and momentum spaces, offering a robust way to compute amplitude evolution in anisotropic media. To validate the framework, we solve the coupled ray-tracing and amplitude-tracing ODEs analytically for benchmark models. For a homogeneous medium, our method analytically derives the classical amplitude decay proportional to <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mn>1</mn>\u0000 <mo>/</mo>\u0000 <mi>t</mi>\u0000 </mrow>\u0000 <annotation>$1/t$</annotation>\u0000 </semantics></math> in three-dimensional space and <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mn>1</mn>\u0000 <mo>/</mo>\u0000 <msqrt>\u0000 <mi>t</mi>\u0000 </msqrt>\u0000 </mrow>\u0000 <annotation>$1/sqrt {t}$</annotation>\u0000 </semantics></math> in two-dimensional space, explicitly linking our formulation to the physical principle of geometric spreading and energy conservation. For a linearly inhomogeneous and isotropic medium, we derive a new closed-form analytical solution for amplitude evolution along the ray. These analytical solutions demonstrate the accuracy and computational power of our unified framework.</p>","PeriodicalId":51174,"journal":{"name":"Studies in Applied Mathematics","volume":"157 3","pages":""},"PeriodicalIF":2.4,"publicationDate":"2026-09-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1111/sapm.70309","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149047961","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 Solvability of the Cauchy Problem for a Fully Parabolic System Modeling Biological Transport Networks","authors":"Bin Li,&nbsp;Li Xie","doi":"10.1111/sapm.70312","DOIUrl":"https://doi.org/10.1111/sapm.70312","url":null,"abstract":"<div>\u0000 \u0000 <p>We investigate the Cauchy problem for a fully parabolic system modeling biological transport networks. The key results of this work demonstrate that: global-in-time strong solutions exist in both two-dimensional and three-dimensional settings; in the two-dimensional case, the uniqueness of such global strong solutions is further proven, and their classical regularity is verified under an additional assumption on the metabolic parameter. These findings extend recent relevant studies on the elliptic-parabolic counterpart of the model to the fully parabolic framework, thereby overcoming the additional analytical challenges arising from the time-dependence in all equations.</p></div>","PeriodicalId":51174,"journal":{"name":"Studies in Applied Mathematics","volume":"157 3","pages":""},"PeriodicalIF":2.4,"publicationDate":"2026-09-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148994439","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":"Sharp Upper Bound for Amplitudes of Finite-Gap Solutions of the Modified Korteweg-de Vries Equation","authors":"Otis C. Wright III","doi":"10.1111/sapm.70307","DOIUrl":"https://doi.org/10.1111/sapm.70307","url":null,"abstract":"<p>A sharp upper bound is established for the amplitudes of finite-gap solutions of the focusing modified Korteweg–de Vries equation. The proof shows that the optimization can be carried out entirely within the finite-dimensional hierarchy, without explicit integration of the finite-gap solution. The maximal amplitude is expressed in terms of the roots of the invariant polynomial associated with the finite-gap solution. An analogous formula is established for a bounded class of solutions of the defocusing modified Korteweg–de Vries equation. Both upper bounds are sharp and are attained by explicit initial data.</p>","PeriodicalId":51174,"journal":{"name":"Studies in Applied Mathematics","volume":"157 3","pages":""},"PeriodicalIF":2.4,"publicationDate":"2026-09-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1111/sapm.70307","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148994564","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":"Growth Rate Estimates for the Maximizer Sequence in an Adaptive Score-Based Secretary Problem","authors":"Zeke Espinoza,&nbsp;Xin Yang Lu,&nbsp;Xiang Xu","doi":"10.1111/sapm.70306","DOIUrl":"https://doi.org/10.1111/sapm.70306","url":null,"abstract":"<div>\u0000 \u0000 <p>In [<i>Journal of Mathematical Study</i>, 57 (2024): 476–485], the authors studied a sequence of expected score functions arising from an adaptive algorithm motivated by the classical score-based secretary problem. More specifically, they proved that, for each <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>n</mi>\u0000 <mo>∈</mo>\u0000 <mi>N</mi>\u0000 </mrow>\u0000 <annotation>$nin mathbb {N}$</annotation>\u0000 </semantics></math>, the corresponding expected score function admits a unique maximizer, and that the resulting sequence of maximizers is monotonically increasing and diverges to infinity as <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>n</mi>\u0000 <mo>→</mo>\u0000 <mi>∞</mi>\u0000 </mrow>\u0000 <annotation>$nrightarrow infty$</annotation>\u0000 </semantics></math>. In the present paper, we further investigate the asymptotic behavior of this maximizer sequence by establishing both upper and lower bounds for its growth rate.</p></div>","PeriodicalId":51174,"journal":{"name":"Studies in Applied Mathematics","volume":"157 3","pages":""},"PeriodicalIF":2.4,"publicationDate":"2026-09-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148994117","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":"Perturbation Theory for Kinks of the Defocusing Modified Korteweg–de Vries Equation","authors":"Nicholas J. Ossi,&nbsp;Barbara Prinari,&nbsp;Theodoros P. Horikis,&nbsp;Dimitrios J. Frantzeskakis","doi":"10.1111/sapm.70302","DOIUrl":"https://doi.org/10.1111/sapm.70302","url":null,"abstract":"<div>\u0000 \u0000 <p>In this work, we develop an integrable perturbation theory for the defocusing modified Korteweg–de Vries kink solution based on the squared eigenfunction expansion associated with the underlying Zakharov–Shabat scattering problem. We derive the completeness relation for the squared eigenfunctions appropriate to the kink background, establish the adjoint structure needed to handle perturbations of both the continuous and discrete spectral components, and obtain explicit evolution equations for the perturbed kink parameters at leading order. The study of the first-order correction shows that perturbations generically produce a radiative shelf in front of the kink. We also apply our results to certain physically relevant perturbations and show that the predictions are consistent with direct numerical simulations.</p></div>","PeriodicalId":51174,"journal":{"name":"Studies in Applied Mathematics","volume":"157 3","pages":""},"PeriodicalIF":2.4,"publicationDate":"2026-09-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148942887","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":"One-Dimensional Wave Propagation in Transversely Isotropic Viscoelastic Materials","authors":"Marco Coco,&nbsp;Giuseppe Saccomandi,&nbsp;Luigi Vergori","doi":"10.1111/sapm.70305","DOIUrl":"https://doi.org/10.1111/sapm.70305","url":null,"abstract":"<div>\u0000 \u0000 <p>The propagation of transverse waves in an anisotropic elastic solid is investigated both in the presence and absence of viscous effects. After discussing in detail the appropriate mathematical models for transversely isotropic viscoelastic materials, we have studied the propagation of bulk shear waves. In particular, we have investigated the break of simple waves and the admissibility of shocks when dissipative effects are negligible, and have provided conditions on the existence of kinks waves (also known as viscous shocks) when dissipation has to be taken into account. Particular attention has been paid also to the propagation of small but finite amplitude waves within the fourth-order weakly nonlinear theory of viscoelasticity.</p></div>","PeriodicalId":51174,"journal":{"name":"Studies in Applied Mathematics","volume":"157 3","pages":""},"PeriodicalIF":2.4,"publicationDate":"2026-09-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148942920","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":"Numerical Identification of Stationary States and Their Stability in a Model of Quantum Droplets","authors":"Sun Lee,&nbsp;Panayotis G. Kevrekidis,&nbsp;Wenrui Hao","doi":"10.1111/sapm.70299","DOIUrl":"https://doi.org/10.1111/sapm.70299","url":null,"abstract":"<p>In this work, we are motivated by a recent variant of the nonlinear Schrödinger (NLS) equation describing cold, dilute atomic condensates with quantum fluctuation effects. Our goal is to develop robust numerical methods capable of uncovering diverse stationary solutions in such NLS models. Specifically, and in line with recent theoretical and experimental interest, we focus on ultracold quantum droplets in Bose mixtures influenced by the Lee–Huang–Yang quantum fluctuation correction and study these systems in one- and two-dimensional settings. To this end, we deploy several numerical techniques. The homotopy grid method allows systematic refinement from coarse to fine spatial discretizations in one dimension, while the dimension-by-dimension homotopy approach extends one-dimensional solutions to two-dimensional domains. These methods effectively detect broad families of stationary states, many of which have not been previously reported, to the best of our knowledge. Furthermore, they enable the monitoring of solution continuation and bifurcation phenomena. During our investigation, we encounter unusual bifurcation events, including nonstandard pitchforks and saddle-center bifurcations, which exhibit novel stability transitions. For example, we identify continuous pathways connecting vortex and dark soliton stripe branches, absent in the standard cubic defocusing model. Overall, the presence of competing mean-field and quantum fluctuation interactions leads to a richer bifurcation structure than in traditional cubic NLS systems. These findings suggest that similar complex bifurcation and stability phenomena may appear in other settings, including higher dimensional systems or models with competing nonlinearities such as cubic–quintic interactions, highlighting the importance of further theoretical and numerical exploration.</p>","PeriodicalId":51174,"journal":{"name":"Studies in Applied Mathematics","volume":"157 3","pages":""},"PeriodicalIF":2.4,"publicationDate":"2026-09-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1111/sapm.70299","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148942918","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}