Studies in Applied Mathematics最新文献

{"title":"Issue Information-TOC","authors":"","doi":"10.1111/sapm.12585","DOIUrl":"https://doi.org/10.1111/sapm.12585","url":null,"abstract":"","PeriodicalId":51174,"journal":{"name":"Studies in Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":2.7,"publicationDate":"2024-01-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1111/sapm.12585","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139435003","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":"Inversion formula for an integral geometry problem over surfaces of revolution","authors":"Zekeriya Ustaoglu","doi":"10.1111/sapm.12664","DOIUrl":"10.1111/sapm.12664","url":null,"abstract":"<p>An integral geometry problem is considered on a family of <math>\u0000 <semantics>\u0000 <mi>n</mi>\u0000 <annotation>$n$</annotation>\u0000 </semantics></math>-dimensional surfaces of revolution whose vertices lie on a hyperplane and directions of symmetry axes are fixed and orthogonal to this plane, in <math>\u0000 <semantics>\u0000 <msup>\u0000 <mi>R</mi>\u0000 <mrow>\u0000 <mi>n</mi>\u0000 <mo>+</mo>\u0000 <mn>1</mn>\u0000 </mrow>\u0000 </msup>\u0000 <annotation>$mathbb {R} ^{n+1}$</annotation>\u0000 </semantics></math>. More precisely, the reconstruction of a function <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>f</mi>\u0000 <mo>(</mo>\u0000 <mi>x</mi>\u0000 <mo>,</mo>\u0000 <mi>y</mi>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 <annotation>$f(mathbf {x,}y)$</annotation>\u0000 </semantics></math>, <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>x</mi>\u0000 <mo>∈</mo>\u0000 <msup>\u0000 <mi>R</mi>\u0000 <mi>n</mi>\u0000 </msup>\u0000 </mrow>\u0000 <annotation>$mathbf {x}in mathbb {R} ^{n}$</annotation>\u0000 </semantics></math>, <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>y</mi>\u0000 <mo>∈</mo>\u0000 <mi>R</mi>\u0000 </mrow>\u0000 <annotation>$yin mathbb {R}$</annotation>\u0000 </semantics></math>, from the integrals of the form <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>f</mi>\u0000 <mo>(</mo>\u0000 <mi>x</mi>\u0000 <mo>,</mo>\u0000 <mi>y</mi>\u0000 <mo>)</mo>\u0000 <mi>d</mi>\u0000 <mi>x</mi>\u0000 </mrow>\u0000 <annotation>$f(mathbf {x,}y) dmathbf {x}$</annotation>\u0000 </semantics></math> extended over a chosen side of all surfaces of revolution of a given family is investigated. Unlike the usual Radon transform, the integrals considered here are not taken with respect to the surface area element. A Fourier slice identity and a backprojection-type inversion formula are obtained with a method based on the Fourier and Hankel transforms. The reconstruction procedure and some analytical and numerical implementations of the obtained inversion formulas in the cases of <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>n</mi>\u0000 <mo>=</mo>\u0000 <mn>1</mn>\u0000 </mrow>\u0000 <annotation>$n=1$</anno","PeriodicalId":51174,"journal":{"name":"Studies in Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":2.7,"publicationDate":"2024-01-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1111/sapm.12664","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139077660","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":"Resurgent aspects of applied exponential asymptotics","authors":"Samuel Crew,&nbsp;Philippe H. Trinh","doi":"10.1111/sapm.12660","DOIUrl":"10.1111/sapm.12660","url":null,"abstract":"<p>In many physical problems, it is important to capture exponentially small effects that lie beyond-all-orders of an algebraic asymptotic expansion; when collected, the full asymptotic expansion is known as a trans-series. Applied exponential asymptotics has been enormously successful in developing practical tools for studying the leading exponentials of a trans-series expansion, typically for singularly perturbed nonlinear differential or integral equations. Separately to applied exponential asymptotics, there exists a related line of research known as Écalle's theory of resurgence, which, via Borel resummation, describes the connection between trans-series and a certain class of holomorphic functions known as resurgent functions. Most applications and examples of Écalle's resurgence theory focus mainly on nonparametric asymptotic expansions (i.e., differential equations without a parameter). The relationships between these latter areas with applied exponential asymptotics have not been thoroughly examined—largely due to differences in language and emphasis. In this work, we establish these connections as an alternative framework to the factorial-over-power ansatz procedure in applied exponential asymptotics and clarify a number of aspects of applied exponential asymptotic methodology, including Van Dyke's rule and the universality of factorial-over-power ansatzes. We provide a number of useful tools for probing more pathological problems in exponential asymptotics and establish a framework for future applications to nonlinear and multidimensional problems in the physical sciences.</p>","PeriodicalId":51174,"journal":{"name":"Studies in Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":2.7,"publicationDate":"2023-12-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1111/sapm.12660","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139052079","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":"Long-time asymptotics and the radiation condition with time-periodic boundary conditions for linear evolution equations on the half-line and experiment","authors":"Yifeng Mao,&nbsp;Dionyssios Mantzavinos,&nbsp;Mark A. Hoefer","doi":"10.1111/sapm.12665","DOIUrl":"10.1111/sapm.12665","url":null,"abstract":"<p>The asymptotic Dirichlet-to-Neumann (D-N) map is constructed for a class of scalar, constant coefficient, linear, third-order, dispersive equations with asymptotically time/periodic Dirichlet boundary data and zero initial data on the half-line, modeling a wavemaker acting upon an initially quiescent medium. The large time <math>\u0000 <semantics>\u0000 <mi>t</mi>\u0000 <annotation>$t$</annotation>\u0000 </semantics></math> asymptotics for the special cases of the linear Korteweg-de Vries and linear Benjamin–Bona–Mahony (BBM) equations are obtained. The D-N map is proven to be unique if and only if the radiation condition that selects the unique wave number branch of the dispersion relation for a sinusoidal, time-dependent boundary condition holds: (i) for frequencies in a finite interval, the wave number is real and corresponds to positive group velocity, and (ii) for frequencies outside the interval, the wave number is complex with positive imaginary part. For fixed spatial location <math>\u0000 <semantics>\u0000 <mi>x</mi>\u0000 <annotation>$x$</annotation>\u0000 </semantics></math>, the corresponding asymptotic solution is (i) a traveling wave or (ii) a spatially decaying, time-periodic wave. The linearized BBM asymptotics are found to quantitatively agree with viscous core-annular fluid experiments.</p>","PeriodicalId":51174,"journal":{"name":"Studies in Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":2.7,"publicationDate":"2023-12-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138946027","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":"Predator–prey model with sigmoid functional response","authors":"Wei Su,&nbsp;Xiang Zhang","doi":"10.1111/sapm.12667","DOIUrl":"10.1111/sapm.12667","url":null,"abstract":"<p>The sigmoid functional response in the predator–prey model was posed in 1977. But its dynamics has not been completely characterized. This paper completes the classification of the global dynamics for the classical predator–prey model with the sigmoid functional response, whose denominator has two different zeros. The dynamical phenomena we obtain here include global stability, the existence of the heteroclinic and homoclinic loops, the consecutive canard explosions via relaxation oscillation, and the canard explosion to a homoclinic loop among others. As we know, the last one is a new dynamical phenomenon, which has never been reported previously. In addition, with the help of geometric singular perturbation theory, we solve the problem of connection between stable and unstable manifolds from different singularities, which has not been well settled in the published literature.</p>","PeriodicalId":51174,"journal":{"name":"Studies in Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":2.7,"publicationDate":"2023-12-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138826166","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":"Instability of near-extreme solutions to the Whitham equation","authors":"John D. Carter","doi":"10.1111/sapm.12668","DOIUrl":"10.1111/sapm.12668","url":null,"abstract":"<p>The Whitham equation is a model for the evolution of small-amplitude, unidirectional waves of all wavelengths in shallow water. It has been shown to accurately model the evolution of waves in laboratory experiments. We compute <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mn>2</mn>\u0000 <mi>π</mi>\u0000 </mrow>\u0000 <annotation>$2pi$</annotation>\u0000 </semantics></math>-periodic traveling wave solutions of the Whitham equation and numerically study their stability with a focus on solutions with large steepness.</p><p>We show that the Hamiltonian oscillates at least twice as a function of wave steepness when the solutions are sufficiently steep. We show that a superharmonic instability is created at each extremum of the Hamiltonian and that between each extremum the stability spectra undergo similar bifurcations. Finally, we compare these results with those from the Euler equations.</p>","PeriodicalId":51174,"journal":{"name":"Studies in Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":2.7,"publicationDate":"2023-12-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138826814","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":"Rigorous estimates on mechanical balance laws in the Boussinesq–Peregrine equations","authors":"Bashar Khorbatly,&nbsp;Henrik Kalisch","doi":"10.1111/sapm.12666","DOIUrl":"10.1111/sapm.12666","url":null,"abstract":"<p>It is shown that the Boussinesq–Peregrine system, which describes long waves of small amplitude at the surface of an inviscid fluid with variable depth, admits a number of approximate conservation equations. Notably, this paper provides accurate estimations for the approximate conservation of the mechanical balance laws associated with mass, momentum, and energy. These precise estimates offer valuable insights into the behavior and dynamics of the system, shedding light on the conservation principles governing the wave motion.</p>","PeriodicalId":51174,"journal":{"name":"Studies in Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":2.7,"publicationDate":"2023-12-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1111/sapm.12666","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138826426","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":"Dynamics of 2D fluid in bounded domain via conformal variables","authors":"Alexander Chernyavsky,&nbsp;Sergey Dyachenko","doi":"10.1111/sapm.12663","DOIUrl":"10.1111/sapm.12663","url":null,"abstract":"<p>In the present work, we compute numerical solutions of an integro-differential equation for traveling waves on the boundary of a 2D blob of an ideal fluid in the presence of surface tension. We find that solutions with multiple lobes tend to approach Crapper capillary waves in the limit of many lobes. Solutions with a few lobes become elongated as they become more nonlinear. It is unclear whether there is a limiting solution for small number of lobes, and what are its properties. Solutions are found from solving a nonlinear pseudodifferential equation by means of the Newton conjugate-residual method. We use Fourier basis to approximate the solution with the number of Fourier modes up to <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>N</mi>\u0000 <mo>=</mo>\u0000 <mn>65536</mn>\u0000 </mrow>\u0000 <annotation>$N = 65536$</annotation>\u0000 </semantics></math>.</p>","PeriodicalId":51174,"journal":{"name":"Studies in Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":2.7,"publicationDate":"2023-12-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138575723","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":"Multisoliton interactions approximating the dynamics of breather solutions","authors":"Dmitry Agafontsev,&nbsp;Andrey Gelash,&nbsp;Stephane Randoux,&nbsp;Pierre Suret","doi":"10.1111/sapm.12662","DOIUrl":"10.1111/sapm.12662","url":null,"abstract":"<p>Nowadays, breather solutions are generally accepted models of rogue waves. However, breathers exist on a finite background and therefore are not localized, while wavefields in nature can generally be considered as localized due to the limited sizes of physical domain. Hence, the theory of rogue waves needs to be supplemented with localized solutions, which evolve locally as breathers. In this paper, we present a universal method for constructing such solutions from exact multisoliton solutions, which consists in replacing the plane wave in the dressing construction of the breathers with a specific exact <i>N</i>-soliton solution converging asymptotically to the plane wave at large number of solitons <i>N</i>. On the example of the Peregrine, Akhmediev, Kuznetsov–Ma, and Tajiri–Watanabe breathers, we show that constructed with our method multisoliton solutions, being localized in space with characteristic width proportional to <i>N</i>, are practically indistinguishable from the breathers in a wide region of space and time at large <i>N</i>. Our method makes it possible to build solitonic models with the same dynamical properties for the higher order rational and super-regular breathers, and can be applied to general multibreather solutions, breathers on a nontrivial background (e.g., cnoidal waves), and other integrable systems. The constructed multisoliton solutions can also be generalized to capture the spontaneous emergence of rogue waves through the spontaneous synchronization of soliton norming constants, though finding these synchronization conditions represents a challenging problem for future studies.</p>","PeriodicalId":51174,"journal":{"name":"Studies in Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":2.7,"publicationDate":"2023-12-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138575534","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":"Matrix exceptional Laguerre polynomials","authors":"E. Koelink,&nbsp;L. Morey,&nbsp;P. Román","doi":"10.1111/sapm.12661","DOIUrl":"10.1111/sapm.12661","url":null,"abstract":"<p>We give an analog of exceptional polynomials in the matrix-valued setting by considering suitable factorizations of a given second-order differential operator and performing Darboux transformations. Orthogonality and density of the exceptional sequence are discussed in detail. We give an example of matrix-valued exceptional Laguerre polynomials of arbitrary size.</p>","PeriodicalId":51174,"journal":{"name":"Studies in Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":2.7,"publicationDate":"2023-12-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138555852","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}