Applied Mathematics Letters最新文献

{"title":"High asymptotic order numerical methods for highly oscillatory ODEs with large initial data","authors":"Zhongli Liu ,&nbsp;Hongjiong Tian","doi":"10.1016/j.aml.2024.109365","DOIUrl":"10.1016/j.aml.2024.109365","url":null,"abstract":"<div><div>In this paper, we propose high asymptotic order numerical methods for solving highly oscillatory second order ODEs with large initial data, where the total energy of the system becomes unbounded as the oscillation frequency grows. The existing asymptotic-numerical solvers are especially designed for the classical energy bounded oscillatory equations, offering no insight into their performance with energy unbounded case. Based on the asymptotic expansion of the solution in the inverse powers of the oscillatory parameter, we propose an asymptotic numerical integrator to solve this class of highly oscillatory ODEs and discuss the computational efficiency for the case of polynomials. One numerical example is given to show the efficiency and accuracy of our proposed asymptotic-numerical solver.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"161 ","pages":"Article 109365"},"PeriodicalIF":2.9,"publicationDate":"2024-11-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142656554","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 L1 discretization error for the Caputo derivative in Hölder spaces","authors":"Félix del Teso ,&nbsp;Łukasz Płociniczak","doi":"10.1016/j.aml.2024.109364","DOIUrl":"10.1016/j.aml.2024.109364","url":null,"abstract":"<div><div>We establish uniform error bounds of the L1 discretization of the Caputo derivative of Hölder continuous functions. The result can be understood as: <em>error = degree of smoothness - order of the derivative.</em> We present an elementary proof and illustrate its optimality with numerical examples.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"161 ","pages":"Article 109364"},"PeriodicalIF":2.9,"publicationDate":"2024-11-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142656783","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":"Double-pole anti-dark solitons for a Lakshmanan-Porsezian-Daniel equation in an optical fiber or a ferromagnetic spin chain","authors":"Xi-Hu Wu ,&nbsp;Yi-Tian Gao","doi":"10.1016/j.aml.2024.109362","DOIUrl":"10.1016/j.aml.2024.109362","url":null,"abstract":"<div><div>Under investigated in this paper is a Lakshmanan-Porsezian-Daniel equation that describes the nonlinear spin excitations in a (1+1)-dimensional isotropic biquadratic Heisenberg ferromagnetic spin chain with the octupole-dipole interaction or the propagation of the ultrashort pulses in a long-distance and high-speed optical fiber transmission system. Under certain parameter conditions, we simultaneously take the multi-pole phenomena and breather-to-soliton transitions into account, then utilize the second-order generalized Darboux transformation to derive the double-pole anti-dark solitons and graphically illustrate them. Asymptotic analysis is conducted to examine the interaction properties of double-pole anti-dark solitons, including their characteristic lines, amplitudes, phase shifts, slopes and position differences. Unlike the double-pole anti-dark solitons found in the Hirota equation, the ones in this study exhibit a distinct feature: Different soliton components share the same amplitude.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"161 ","pages":"Article 109362"},"PeriodicalIF":2.9,"publicationDate":"2024-11-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142705965","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":"Time-periodic mild solutions to the three-dimensional micropolar fluid equations","authors":"Xiaotong Mu,&nbsp;Jinyi Sun","doi":"10.1016/j.aml.2024.109367","DOIUrl":"10.1016/j.aml.2024.109367","url":null,"abstract":"<div><div>The paper is concerned with the three-dimensional micropolar fluid equations. By using the successive approximation and Littlewood–Paley theory, we prove existence and uniqueness of time-periodic mild solutions of the three-dimensional micropolar fluid equations with external forces in Besov spaces.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"161 ","pages":"Article 109367"},"PeriodicalIF":2.9,"publicationDate":"2024-11-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142656551","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":"State transitions for the rational solutions of Kundu equation with non-zero boundary conditions","authors":"Deqin Qiu ,&nbsp;Yongshuai Zhang ,&nbsp;Wei Liu","doi":"10.1016/j.aml.2024.109363","DOIUrl":"10.1016/j.aml.2024.109363","url":null,"abstract":"<div><div>Several novel rational solutions with nonzero boundary condition for the Kundu equation, which is an important physical model, are derived using the technique of generalized Darboux transformation. It is the first time that a systemic analysis has been conducted on such rational solutions for the Kundu equation. For the 1-order rational solutions with nonzero boundary conditions, our findings reveal that three parameters, <span><math><mi>a</mi></math></span>, <span><math><mi>b</mi></math></span>, and <span><math><mi>β</mi></math></span>, which are associated with the effects of self-steepening, self-phase modulation, and quintic nonlinearity in the Kundu equation, can result in four distinct states for case B and five distinct states for case C, all corresponding to rational solutions with nonzero boundary conditions.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"161 ","pages":"Article 109363"},"PeriodicalIF":2.9,"publicationDate":"2024-11-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142656556","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":"Threshold dynamics of a time-delayed dengue virus infection model incorporating vaccination failure and exposed mosquitoes","authors":"Songbai Guo ,&nbsp;Min He ,&nbsp;Fuxiang Li","doi":"10.1016/j.aml.2024.109366","DOIUrl":"10.1016/j.aml.2024.109366","url":null,"abstract":"<div><div>A time-delayed dengue virus transmission model has been developed, which takes into account vaccination failure and the presence of exposed mosquitoes. This model also incorporates the survival probability of infected individuals during the incubation period to provide a clearer understanding of how latency affects the control reproduction number <span><math><msub><mrow><mi>R</mi></mrow><mrow><mi>c</mi></mrow></msub></math></span>. Furthermore, by employing the Lyapunov functional approach, we establish the global asymptotic stability of equilibria in relation to <span><math><msub><mrow><mi>R</mi></mrow><mrow><mi>c</mi></mrow></msub></math></span>. The results indicate that the disease-free equilibrium <span><math><msup><mrow><mi>T</mi></mrow><mrow><mn>0</mn></mrow></msup></math></span> is globally asymptotically stable if and only if <span><math><mrow><msub><mrow><mi>R</mi></mrow><mrow><mi>c</mi></mrow></msub><mo>≤</mo><mn>1</mn></mrow></math></span>, whereas the endemic equilibrium <span><math><msup><mrow><mi>T</mi></mrow><mrow><mo>∗</mo></mrow></msup></math></span> is globally asymptotically stable if and only if <span><math><mrow><msub><mrow><mi>R</mi></mrow><mrow><mi>c</mi></mrow></msub><mo>&gt;</mo><mn>1</mn></mrow></math></span>.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"161 ","pages":"Article 109366"},"PeriodicalIF":2.9,"publicationDate":"2024-11-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142656553","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 the mass concentration of normalized ground state solutions for non-autonomous Kirchhoff equations","authors":"Miao Du ,&nbsp;Xiaohan Gao","doi":"10.1016/j.aml.2024.109371","DOIUrl":"10.1016/j.aml.2024.109371","url":null,"abstract":"<div><div>In this paper, we focus on a class of non-autonomous Kirchhoff equations, that is, <span><math><mrow><mo>−</mo><mrow><mo>(</mo><mi>a</mi><mo>+</mo><mi>b</mi><msub><mrow><mo>∫</mo></mrow><mrow><msup><mrow><mi>R</mi></mrow><mrow><mn>3</mn></mrow></msup></mrow></msub><msup><mrow><mrow><mo>|</mo><mo>∇</mo><mi>u</mi><mo>|</mo></mrow></mrow><mrow><mn>2</mn></mrow></msup><mspace></mspace><mtext>d</mtext><mi>x</mi><mo>)</mo></mrow><mi>Δ</mi><mi>u</mi><mo>−</mo><mi>λ</mi><mi>u</mi><mo>=</mo><mi>K</mi><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow><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></mrow></math></span> in <span><math><msup><mrow><mi>R</mi></mrow><mrow><mn>3</mn></mrow></msup></math></span>, where <span><math><mrow><mi>a</mi><mo>,</mo><mi>b</mi><mo>&gt;</mo><mn>0</mn></mrow></math></span> are constants, <span><math><mrow><mi>λ</mi><mo>∈</mo><mi>R</mi></mrow></math></span> is unknown and appears as a Lagrange multiplier, <span><math><mrow><mn>2</mn><mo>&lt;</mo><mi>p</mi><mo>&lt;</mo><mn>6</mn></mrow></math></span> and <span><math><mrow><mi>K</mi><mo>:</mo><msup><mrow><mi>R</mi></mrow><mrow><mn>3</mn></mrow></msup><mo>→</mo><mi>R</mi></mrow></math></span> is a potential function. Under certain assumptions on the potential <span><math><mi>K</mi></math></span>, the concentration behavior of normalized ground state solutions is analyzed by using variational methods.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"161 ","pages":"Article 109371"},"PeriodicalIF":2.9,"publicationDate":"2024-11-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142656606","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":"Self-interacting CBO: Existence, uniqueness, and long-time convergence","authors":"Hui Huang,&nbsp;Hicham Kouhkouh","doi":"10.1016/j.aml.2024.109372","DOIUrl":"10.1016/j.aml.2024.109372","url":null,"abstract":"<div><div>A self-interacting dynamics that mimics the standard Consensus-Based Optimization (CBO) model is introduced. This single-particle dynamics is shown to converge to a unique invariant measure that approximates the global minimum of a given function. As an application, its connection to CBO with Personal Best introduced by C. Totzeck and M.-T. Wolfram (Math. Biosci. Eng., 2020) has been established.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"161 ","pages":"Article 109372"},"PeriodicalIF":2.9,"publicationDate":"2024-11-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142656607","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":"Absence of dead-core formations in chemotaxis systems with degenerate diffusion","authors":"Tobias Black","doi":"10.1016/j.aml.2024.109361","DOIUrl":"10.1016/j.aml.2024.109361","url":null,"abstract":"&lt;div&gt;&lt;div&gt;In this paper we consider a chemotaxis system with signal consumption and degenerate diffusion of the form &lt;span&gt;&lt;span&gt;&lt;span&gt;&lt;math&gt;&lt;mfenced&gt;&lt;mrow&gt;&lt;mtable&gt;&lt;mtr&gt;&lt;mtd&gt;&lt;/mtd&gt;&lt;mtd&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;u&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;t&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mo&gt;∇&lt;/mo&gt;&lt;mi&gt;⋅&lt;/mi&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;D&lt;/mi&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;u&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;mo&gt;∇&lt;/mo&gt;&lt;mi&gt;u&lt;/mi&gt;&lt;mo&gt;−&lt;/mo&gt;&lt;mi&gt;u&lt;/mi&gt;&lt;mi&gt;S&lt;/mi&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;u&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;mo&gt;∇&lt;/mo&gt;&lt;mi&gt;v&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;mi&gt;f&lt;/mi&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;u&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;v&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mspace&gt;&lt;/mspace&gt;&lt;/mtd&gt;&lt;/mtr&gt;&lt;mtr&gt;&lt;mtd&gt;&lt;/mtd&gt;&lt;mtd&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;v&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;t&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mi&gt;Δ&lt;/mi&gt;&lt;mi&gt;v&lt;/mi&gt;&lt;mo&gt;−&lt;/mo&gt;&lt;mi&gt;u&lt;/mi&gt;&lt;mi&gt;v&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mspace&gt;&lt;/mspace&gt;&lt;/mtd&gt;&lt;/mtr&gt;&lt;mtr&gt;&lt;mtd&gt;&lt;/mtd&gt;&lt;/mtr&gt;&lt;/mtable&gt;&lt;/mrow&gt;&lt;/mfenced&gt;&lt;/math&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;in a bounded domain &lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;mi&gt;Ω&lt;/mi&gt;&lt;mo&gt;⊂&lt;/mo&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mi&gt;R&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;N&lt;/mi&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt; with smooth boundary subjected to no-flux and homogeneous Neumann boundary conditions. Herein, the diffusion coefficient &lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;mi&gt;D&lt;/mi&gt;&lt;mo&gt;∈&lt;/mo&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mi&gt;C&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mrow&gt;&lt;mo&gt;[&lt;/mo&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;∞&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;mo&gt;∩&lt;/mo&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mi&gt;C&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;∞&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt; is assumed to satisfy &lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;mi&gt;D&lt;/mi&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt;, &lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;mi&gt;D&lt;/mi&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;s&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;mo&gt;&gt;&lt;/mo&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt; on &lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;∞&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt;, &lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mi&gt;D&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mo&gt;′&lt;/mo&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;s&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;mo&gt;≥&lt;/mo&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt; on &lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;∞&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt; and that there are &lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;s&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;&gt;&lt;/mo&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt;, &lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;mi&gt;p&lt;/mi&gt;&lt;mo&gt;&gt;&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt; and &lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;C&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;D&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;&gt;&lt;/mo&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt; such that &lt;span&gt;&lt;span&gt;&lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;mi&gt;s&lt;/mi&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mi&gt;D&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mo&gt;′&lt;/mo&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;s&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;mo&gt;≤&lt;/mo&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;C&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;D&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mi&gt;D&lt;/mi&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;s&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;mspace&gt;&lt;/mspace&gt;&lt;mtext&gt;and&lt;/mtext&gt;&lt;mspace&gt;&lt;/mspace&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;C&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;D&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mi&gt;s&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;p&lt;/mi&gt;&lt;mo&gt;−&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;mo&gt;≤&lt;/mo&gt;&lt;mi&gt;D&lt;/mi&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;s&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;mspace&gt;&lt;/mspace&gt;&lt;mtext&gt;for&lt;/mtext&gt;&lt;mi&gt;s&lt;","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"161 ","pages":"Article 109361"},"PeriodicalIF":2.9,"publicationDate":"2024-11-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142656552","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":"Peaked Stokes waves as solutions of Babenko’s equation","authors":"Spencer Locke,&nbsp;Dmitry E. Pelinovsky","doi":"10.1016/j.aml.2024.109359","DOIUrl":"10.1016/j.aml.2024.109359","url":null,"abstract":"<div><div>Babenko’s equation describes traveling water waves in holomorphic coordinates. It has been used in the past to obtain properties of Stokes waves with smooth profiles analytically and numerically. We show in the deep-water limit that properties of Stokes waves with peaked profiles can also be recovered from the same Babenko’s equation. In order to develop the local analysis of singularities, we rewrite Babenko’s equation as a fixed-point problem near the maximal elevation level. As a by-product, our results rule out a corner point singularity in the holomorphic coordinates, which has been obtained in a local version of Babenko’s equation.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"161 ","pages":"Article 109359"},"PeriodicalIF":2.9,"publicationDate":"2024-11-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142656782","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}