Studies in Applied Mathematics最新文献

{"title":"The Fokas Method to the Modified Camassa–Holm Equation on the Half-Line","authors":"Byungsoo Moon,&nbsp;Guenbo Hwang","doi":"10.1111/sapm.70334","DOIUrl":"https://doi.org/10.1111/sapm.70334","url":null,"abstract":"<div>\u0000 \u0000 <p>We investigate the initial-boundary value problem for the modified Camassa–Holm (mCH) equation  with cubic nonlinearity on the half-line through the unified transform method, also known as the Fokas method. By analyzing the associated Lax pair, we define spectral functions determined by the initial and boundary data, which, in turn, satisfy a global relation coupling all these values. Based on this framework, we construct a matrix Riemann-Hilbert (RH) problem parameterized by appropriately scaled variables, from which the solution of the mCH equation can be represented. The analytic structure of the RH problem depends on the sign of a certain boundary quantity at <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>x</mi>\u0000 <mo>=</mo>\u0000 <mn>0</mn>\u0000 </mrow>\u0000 <annotation>$x=0$</annotation>\u0000 </semantics></math>, leading to distinct forms of the global relation. Finally, it is further shown that the global relation provides both necessary and sufficient conditions for the compatibility of the initial and boundary data.</p></div>","PeriodicalId":51174,"journal":{"name":"Studies in Applied Mathematics","volume":"157 5","pages":""},"PeriodicalIF":2.4,"publicationDate":"2026-11-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149355750","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":"Universal Stability of Multipower Nonlinear Schrödinger Solitary Waves: A Sharp Exponent Threshold","authors":"Hongyu Gu","doi":"10.1111/sapm.70330","DOIUrl":"https://doi.org/10.1111/sapm.70330","url":null,"abstract":"<div>\u0000 \u0000 <p>We study one-dimensional nonlinear Schrödinger equations with finitely many lower defocusing and higher focusing powers. For any fixed exponent lists, we determine when every positive-frequency solitary wave is orbitally stable for all positive choices of the coefficients. Writing <span></span><math>\u0000 <semantics>\u0000 <msub>\u0000 <mi>p</mi>\u0000 <mi>D</mi>\u0000 </msub>\u0000 <annotation>$p_D$</annotation>\u0000 </semantics></math> for the largest defocusing power and <span></span><math>\u0000 <semantics>\u0000 <msub>\u0000 <mi>q</mi>\u0000 <mi>F</mi>\u0000 </msub>\u0000 <annotation>$q_F$</annotation>\u0000 </semantics></math> for the largest focusing power, the sharp condition is <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mn>2</mn>\u0000 <msub>\u0000 <mi>p</mi>\u0000 <mi>D</mi>\u0000 </msub>\u0000 <mo>+</mo>\u0000 <msub>\u0000 <mi>q</mi>\u0000 <mi>F</mi>\u0000 </msub>\u0000 <mo>≤</mo>\u0000 <mn>7</mn>\u0000 </mrow>\u0000 <annotation>$2p_D+q_Fle 7$</annotation>\u0000 </semantics></math>. Under this condition the mass is strictly increasing with frequency, with an explicit positive lower bound on its derivative; equality is included. When the inequality fails, every prescribed exponent list admits an open set of coefficients and frequencies with negative mass slope and unstable waves. The proof decomposes the slope into two-power contributions and controls their integrals through a concavity argument involving a ratio of gamma functions. As an application, we establish the all-frequency triple-power assertion of Morrison and Tsai. We also show that mass provides a global parameter for the stable branch. Numerical calculations quantify the slope bound and illustrate the transition beyond the threshold.</p></div>","PeriodicalId":51174,"journal":{"name":"Studies in Applied Mathematics","volume":"157 5","pages":""},"PeriodicalIF":2.4,"publicationDate":"2026-10-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149312194","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.70335","DOIUrl":"https://doi.org/10.1111/sapm.70335","url":null,"abstract":"","PeriodicalId":51174,"journal":{"name":"Studies in Applied Mathematics","volume":"157 5","pages":""},"PeriodicalIF":2.4,"publicationDate":"2026-10-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1111/sapm.70335","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149312193","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":"Energetic Derivation and Geometric Reduction of Reaction–Diffusion Systems With Holling-Type Functional Responses","authors":"Jan-Eric Sulzbach","doi":"10.1111/sapm.70329","DOIUrl":"https://doi.org/10.1111/sapm.70329","url":null,"abstract":"<div>\u0000 \u0000 <p>We derive and reduce a thermodynamically consistent class of ecological reaction–diffusion models with Holling-type functional responses. Starting from an open reaction network involving water, two biomass states, and reservoir species, we embed the system into a closed reversible network and use the Energetic Variational Approach (EnVarA) to obtain a reaction–diffusion system with entropy structure, detailed-balance equilibria, and mass-action kinetics generated by a logarithmic reaction dissipation. We then pass formally to an open ecological subsystem via a sustained-reservoir limit and identify fast-reaction scalings that lead to Holling type I, II, and III responses. The type I and type III reductions are presented as formal asymptotic limits, together with the estimates needed for rigorous justification. For the Holling type II regime, we apply geometric singular perturbation theory for fast-reaction PDEs. Under normal hyperbolicity, spectral splitting, and bounded-chart assumptions, the singularly perturbed system admits a locally invariant attracting slow manifold near the critical manifold, and the semiflow on this manifold converges to the reduced Holling type II dynamics. The results connect thermodynamic closure, energetic variational modeling, functional-response reductions, and slow-manifold dynamics in multiscale reaction–diffusion systems.</p></div>","PeriodicalId":51174,"journal":{"name":"Studies in Applied Mathematics","volume":"157 4","pages":""},"PeriodicalIF":2.4,"publicationDate":"2026-10-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149259374","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 Behavior of the Basic Reproduction Number and Equilibria for a Partially Degenerate Nonlocal Epidemic Model","authors":"Ming-Zhen Xin","doi":"10.1111/sapm.70331","DOIUrl":"https://doi.org/10.1111/sapm.70331","url":null,"abstract":"<div>\u0000 \u0000 <p>This paper studies a partially degenerate nonlocal epidemic model in a bounded habitat and analyzes the effects of the diffusion coefficient and the diffusion range on 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 the positive steady state. We prove that <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> is strictly decreasing in the diffusion coefficient and determine its limits as the coefficient tends to zero and infinity. For scaled diffusion kernels, we obtain the small- and large-range limits of <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>, including explicit formulas for both limits. We also establish the threshold dynamics, including the critical case. For the parameter-dependent family of positive steady states, we derive the small-diffusion limit, locally uniform convergence to the local positive equilibrium on the strictly favorable region in the small-range regime, and convergence to a local limiting profile in the large-range regime. Numerical simulations illustrate the analytical results.</p></div>","PeriodicalId":51174,"journal":{"name":"Studies in Applied Mathematics","volume":"157 4","pages":""},"PeriodicalIF":2.4,"publicationDate":"2026-10-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149356530","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":"Is Current the Conduction of Charge?","authors":"Robert S. Eisenberg","doi":"10.1111/sapm.70332","DOIUrl":"https://doi.org/10.1111/sapm.70332","url":null,"abstract":"<div>\u0000 \u0000 <p>Most scientists believe that current flow is the conduction of charge. Mathematics and physics imply otherwise. The mathematics of magnetism requires another component, the displacement current that depends on the time derivative of the electric field. Displacement current is an experimental reality. Displacement current is needed for light to propagate in a vacuum devoid of charges. Maxwell himself defined true current to include displacement current. Mathematics and Maxwell both show that displacement current is an essential part of electrodynamics. The success of circuits as the main application of electricity from telegraphs to computers depends on the special properties of displacement current. Those properties allow current flow to be analyzed by Kirchhoff's law (generalized) without dealing with properties of individual charges. Hundreds of equations are needed to specify currents with Kirchhoff law for currents instead of astronomical numbers needed to specify charges with the continuity equation.</p>\u0000 </div>","PeriodicalId":51174,"journal":{"name":"Studies in Applied Mathematics","volume":"157 4","pages":""},"PeriodicalIF":2.4,"publicationDate":"2026-10-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149259373","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":"Long-Wave Instability of Periodic Shear Flows With Constant Magnetic Field for the 2D Resistive MHD Equations","authors":"Roberto Feola,&nbsp;Luca Franzoi,&nbsp;Riccardo Montalto,&nbsp;Claudia Peña","doi":"10.1111/sapm.70325","DOIUrl":"https://doi.org/10.1111/sapm.70325","url":null,"abstract":"&lt;div&gt;\u0000 \u0000 &lt;p&gt;We investigate the long-wave linear stability and instability of the two-dimensional viscous, resistive Magnetohydrodynamic (MHD) equations, in vorticity-current formulation, on the periodic domain &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;msub&gt;\u0000 &lt;mi&gt;T&lt;/mi&gt;\u0000 &lt;mi&gt;α&lt;/mi&gt;\u0000 &lt;/msub&gt;\u0000 &lt;mo&gt;×&lt;/mo&gt;\u0000 &lt;mi&gt;T&lt;/mi&gt;\u0000 &lt;mo&gt;=&lt;/mo&gt;\u0000 &lt;mfenced&gt;\u0000 &lt;mi&gt;R&lt;/mi&gt;\u0000 &lt;mo&gt;/&lt;/mo&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mo&gt;(&lt;/mo&gt;\u0000 &lt;mfrac&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mn&gt;2&lt;/mn&gt;\u0000 &lt;mi&gt;π&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;mi&gt;α&lt;/mi&gt;\u0000 &lt;/mfrac&gt;\u0000 &lt;mi&gt;Z&lt;/mi&gt;\u0000 &lt;mo&gt;)&lt;/mo&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;mo&gt;×&lt;/mo&gt;\u0000 &lt;mi&gt;R&lt;/mi&gt;\u0000 &lt;mo&gt;/&lt;/mo&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mo&gt;(&lt;/mo&gt;\u0000 &lt;mn&gt;2&lt;/mn&gt;\u0000 &lt;mi&gt;π&lt;/mi&gt;\u0000 &lt;mi&gt;Z&lt;/mi&gt;\u0000 &lt;mo&gt;)&lt;/mo&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/mfenced&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;${mathbb {T}}_alpha times {mathbb {T}}= left({mathbb {R}}/(frac{2 pi }{alpha } {mathbb {Z}}) times {mathbb {R}}/(2 pi {mathbb {Z}}) right)$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;, around a periodic shear flow &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;U&lt;/mi&gt;\u0000 &lt;mo&gt;(&lt;/mo&gt;\u0000 &lt;mi&gt;y&lt;/mi&gt;\u0000 &lt;mo&gt;)&lt;/mo&gt;\u0000 &lt;mo&gt;,&lt;/mo&gt;\u0000 &lt;mn&gt;0&lt;/mn&gt;\u0000 &lt;mo&gt;)&lt;/mo&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$(U(y),0)$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; coupled with a constant background magnetic field &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;b&lt;/mi&gt;\u0000 &lt;mo&gt;=&lt;/mo&gt;\u0000 &lt;mo&gt;(&lt;/mo&gt;\u0000 &lt;msub&gt;\u0000 &lt;mi&gt;b&lt;/mi&gt;\u0000 &lt;mn&gt;1&lt;/mn&gt;\u0000 &lt;/msub&gt;\u0000 &lt;mo&gt;,&lt;/mo&gt;\u0000 &lt;msub&gt;\u0000 &lt;mi&gt;b&lt;/mi&gt;\u0000 &lt;mn&gt;2&lt;/mn&gt;\u0000 &lt;/msub&gt;\u0000 &lt;mo&gt;)&lt;/mo&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;${bf b}=({rm b}_1,{rm b}_2)$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;. It is a nontrivial extension of a recent paper for the Navier–Stokes equations by Colombo, Dolce, Montalto, and Ventura to the MHD setting in the spirit of the classical works of Kolmogorov, Meshalkin, Sinai, and Yudovich. We establish explicit conditions on the shear flow profile &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 ","PeriodicalId":51174,"journal":{"name":"Studies in Applied Mathematics","volume":"157 4","pages":""},"PeriodicalIF":2.4,"publicationDate":"2026-10-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149259332","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":"Interaction-Phase Dynamics and Spectral Organization in Damped Higher-Order Nonlinear Schrödinger Models","authors":"C. M. Schober","doi":"10.1111/sapm.70328","DOIUrl":"https://doi.org/10.1111/sapm.70328","url":null,"abstract":"<div>\u0000 \u0000 <p>We investigate the dynamical mechanisms underlying the contrasting nonlinear Floquet spectral evolutions observed in viscously damped and in nonlinear mean-flow damped higher-order nonlinear Schrödinger models. A reduced five-mode carrier–sideband truncation is derived and reformulated in amplitude–phase variables to isolate the principal interaction phases associated with the dominant four-wave interaction products. Within this framework, viscous damping acts modewise and does not contribute explicitly to the leading interaction-phase equations, whereas nonlinear mean-flow damping acts through the coupled mean-flow interactions and, in the carrier–sideband regime, generates terms of the form <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mo>−</mo>\u0000 <msub>\u0000 <mi>κ</mi>\u0000 <mi>j</mi>\u0000 </msub>\u0000 <mi>sin</mi>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 <msub>\u0000 <mi>ψ</mi>\u0000 <mi>j</mi>\u0000 </msub>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 </mrow>\u0000 <annotation>$-kappa _j sin (psi _j)$</annotation>\u0000 </semantics></math>. The reduced system is used as a mechanism-identification model rather than as a quantitatively accurate approximation of the full PDE. To interpret the resulting interaction-phase evolution, we examine recurrent nonlinear Schrödinger (NLS) benchmark solutions whose modulation dynamics and Floquet spectrum are independently characterized. These benchmarks show that substantial interaction-phase evolution may coexist with recurrent modulation and invariant Floquet-band structure. Full-PDE diagnostics are then used to compare the phase dynamics within the spectral regimes previously identified for the two damped systems. Under nonlinear mean-flow damping, the interaction phases develop a persistent large-scale evolution, with the larger phase changes remaining tied to recurrent focusing events while the Floquet-band configuration persists. Under viscous damping, the large-scale phase trends change repeatedly without a systematic association with recurrent focusing, while the Floquet spectrum undergoes repeated critical-point crossings and band reconfiguration. A Fourier-energy assessment further shows that this contrast cannot be attributed simply to broader excitation of Fourier modes in the viscous system. Instead, the results are consistent with a structural distinction in how the two dissipative mechanisms act on the dominant carrier–sideband interactions.</p></div>","PeriodicalId":51174,"journal":{"name":"Studies in Applied Mathematics","volume":"157 4","pages":""},"PeriodicalIF":2.4,"publicationDate":"2026-10-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149259169","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":"Homoclinic Quasiperiodic Orbits and Emergence of Strange Nonchaotic Attractors in a Discontinuous Piecewise Smooth Map","authors":"Jicheng Duan,&nbsp;Laura Gardini,&nbsp;Zhouchao Wei,&nbsp;Iryna Sushko,&nbsp;Yiwen Chen","doi":"10.1111/sapm.70326","DOIUrl":"https://doi.org/10.1111/sapm.70326","url":null,"abstract":"<div>\u0000 \u0000 <p>This paper investigates the formation and evolution of strange nonchaotic attractors (SNAs) in a discontinuous noninvertible piecewise-smooth map subjected to quasiperiodic forcing. The system is formulated as a two-dimensional skew-product, combining a piecewise-smooth one-dimensional base map with an irrational rotation. The notion of quasiperiodic homoclinic and heteroclinic orbits is introduced, and their potential relevance to the transition from smooth tori to SNAs is explored. Forward images of critical lines are shown to reflect key changes in the attractor and its basin, including disconnected components and the formation of holes. Discontinuities in the attractor are found to result from direct contact with the discontinuity line of the map. Through a set of representative examples, we identify three main routes to SNA formation: (i) contact between the attractor and its basin boundary leading to homoclinic orbits, (ii) contact between the attractor and a repeller, leading to homoclinic orbits, and (iii) contact between the attractor and the discontinuity set. These results clarify how different types of critical curves shape the dynamics, and contribute to the understanding of attractor evolution in discontinuous noninvertible quasiperiodically forced systems.</p></div>","PeriodicalId":51174,"journal":{"name":"Studies in Applied Mathematics","volume":"157 4","pages":""},"PeriodicalIF":2.4,"publicationDate":"2026-10-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149205420","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":"Gibbons–Tsarev Type Systems and Eventual Identities","authors":"Alessandro Arsie,&nbsp;Paolo Lorenzoni,&nbsp;Sara Perletti,&nbsp;Karoline van Gemst","doi":"10.1111/sapm.70321","DOIUrl":"https://doi.org/10.1111/sapm.70321","url":null,"abstract":"<p>We show that non-diagonalizable reductions of the dKP equation associated with regular non-semisimple <span></span><math>\u0000 <semantics>\u0000 <mi>F</mi>\u0000 <annotation>$F$</annotation>\u0000 </semantics></math>-manifolds cannot exist. The proof is based on the derivation and study of a generalized Gibbons–Tsarev system (gGT system) in the non-semisimple/non-diagonalizable setting. Remarkably, a class of solutions of the gGT system is defined by eventual identities of the underlying regular <span></span><math>\u0000 <semantics>\u0000 <mi>F</mi>\u0000 <annotation>$F$</annotation>\u0000 </semantics></math>-manifold structure. Furthermore, we use these vector fields to construct integrable reductions of Pavlov's hydrodynamic chain. In this case, the corresponding solutions are defined for any choice of Jordan block structure of the operator of multiplication by an eventual identity.</p>","PeriodicalId":51174,"journal":{"name":"Studies in Applied Mathematics","volume":"157 4","pages":""},"PeriodicalIF":2.4,"publicationDate":"2026-10-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1111/sapm.70321","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149205421","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}