Studies in Applied Mathematics最新文献

{"title":"The Riemann Problem for the Flow Pattern in Deviated Pipes Carrying Isentropic Two-Phase Flows","authors":"Sarswati Shah","doi":"10.1111/sapm.70003","DOIUrl":"https://doi.org/10.1111/sapm.70003","url":null,"abstract":"<div>\u0000 \u0000 <p>We study the Riemann problem for the one-dimensional two-phase isentropic flow in deviated pipes. The model under consideration is nonconservative and conditionally strictly hyperbolic. The generalized Rankine–Hugoniot conditions are established for the present system with nonconservative products to define weak solutions. Exact Riemann solutions are presented in fully explicit forms for the nonhomogeneous model, where the elementary waves are discussed along parabolic curves. Moreover, it is demonstrated that a delta shock wave appears in the Riemann solutions under specific conditions when the pressure vanishes.</p></div>","PeriodicalId":51174,"journal":{"name":"Studies in Applied Mathematics","volume":"154 1","pages":""},"PeriodicalIF":2.6,"publicationDate":"2024-12-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143120790","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 Fractional Discrete Nonlinear Schrödinger Equations: Dispersion Relations, Rogue Waves, Fundamental, and Vortex Solitons","authors":"Ming Zhong,&nbsp;Boris A. Malomed,&nbsp;Jin Song,&nbsp;Zhenya Yan","doi":"10.1111/sapm.70001","DOIUrl":"https://doi.org/10.1111/sapm.70001","url":null,"abstract":"<div>\u0000 \u0000 <p>We introduce physically relevant new models of two-dimensional (2D) fractional lattice media accounting for the interplay of fractional intersite coupling and onsite self-focusing. Our approach features novel discrete fractional operators based on an appropriately modified definition of the continuous Riesz fractional derivative. The model of the 2D isotropic lattice employs the discrete fractional Laplacian, whereas the 2D anisotropic system incorporates discrete fractional derivatives acting independently along orthogonal directions with different Lévy indices (LIs). We derive exact linear dispersion relations (DRs), and identify spectral bands that permit linear modes to exist, finding them to be similar to their continuous counterparts, apart from differences in the wavenumber range. Additionally, the modulational instability in the discrete models is studied in detail, and, akin to the linear DRs, it is found to align with the situation in continuous models. This consistency highlights the nature of our newly defined discrete fractional derivatives. Furthermore, using Gaussian inputs, we produce a variety of rogue-wave structures. By means of numerical methods, we systematically construct families of 2D fundamental and vortex solitons, and examine their stability. Fundamental solitons maintain the stability due to the discrete nature of the interactions, preventing the onset of the critical and supercritical collapse. On the other hand, vortex solitons are unstable in the isotropic lattice model. However, the anisotropic one—in particular, its symmetric version with equal LIs acting in both directions—maintains stable vortex solitons with winding numbers <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>S</mi>\u0000 <mo>=</mo>\u0000 <mn>1</mn>\u0000 </mrow>\u0000 <annotation>$S=1$</annotation>\u0000 </semantics></math> and <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>S</mi>\u0000 <mo>=</mo>\u0000 <mn>3</mn>\u0000 </mrow>\u0000 <annotation>$S=3$</annotation>\u0000 </semantics></math>. The detailed results stress the robustness of the newly defined discrete fractional Laplacian in supporting well-defined soliton modes in the 2D lattice media.</p></div>","PeriodicalId":51174,"journal":{"name":"Studies in Applied Mathematics","volume":"154 1","pages":""},"PeriodicalIF":2.6,"publicationDate":"2024-12-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142861651","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":"Variable-Coefficient Evolution Problems via the Fokas Method Part I: Dissipative Case","authors":"Bernard Deconinck,&nbsp;Matthew Farkas","doi":"10.1111/sapm.12800","DOIUrl":"https://doi.org/10.1111/sapm.12800","url":null,"abstract":"<div>\u0000 \u0000 <p>We derive explicit solution representations for linear, dissipative, second-order initial-boundary value problems (IBVPs) with coefficients that are spatially varying, with linear, constant-coefficient, two-point boundary conditions. We accomplish this by considering the variable-coefficient problem as the limit of a constant-coefficient interface problem, previously solved using the unified transform method of Fokas. Our method produces an explicit representation of the solution, allowing us to determine properties of the solution directly. As explicit examples, we demonstrate the solution procedure for different IBVPs of variations of the heat equation, and the linearized complex Ginzburg-Landau (CGL) equation (periodic boundary conditions). We can use this to find the eigenvalues of dissipative second-order linear operators (including non–self-adjoint ones) as roots of a transcendental function, and we can write their eigenfunctions explicitly in terms of the eigenvalues.</p></div>","PeriodicalId":51174,"journal":{"name":"Studies in Applied Mathematics","volume":"154 1","pages":""},"PeriodicalIF":2.6,"publicationDate":"2024-12-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142861440","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":"Concentric-Ring Patterns of Higher-Order Lumps in the Kadomtsev–Petviashvili I Equation","authors":"Bo Yang,&nbsp;Jianke Yang","doi":"10.1111/sapm.70000","DOIUrl":"https://doi.org/10.1111/sapm.70000","url":null,"abstract":"<p>Large-time patterns of general higher-order lump solutions in the Kadomtsev–Petviashvili I (KP-I) equation are investigated. It is shown that when the index vector of the general lump solution is a sequence of consecutive odd integers starting from one, the large-time pattern in the spatial <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 <mi>x</mi>\u0000 <mo>,</mo>\u0000 <mi>y</mi>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 <annotation>$(x, y)$</annotation>\u0000 </semantics></math>-plane generically would comprise fundamental lumps uniformly distributed on concentric rings. For other index vectors, the large-time pattern would comprise fundamental lumps in the outer region as described analytically by the nonzero-root structure of the associated Wronskian–Hermite polynomial, together with possible fundamental lumps in the inner region that are uniformly distributed on concentric rings generically. Leading-order predictions of fundamental lumps in these solution patterns are also derived. The predicted patterns at large times are compared to true solutions, and good agreement is observed.</p>","PeriodicalId":51174,"journal":{"name":"Studies in Applied Mathematics","volume":"154 1","pages":""},"PeriodicalIF":2.6,"publicationDate":"2024-12-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1111/sapm.70000","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142861441","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":"On Global and Decay Solution of Viscous Compressible MHD Equations","authors":"Rachid Benabidallah,&nbsp;François Ebobisse,&nbsp;Mohamed Azouz","doi":"10.1111/sapm.12794","DOIUrl":"https://doi.org/10.1111/sapm.12794","url":null,"abstract":"<p>We consider in an infinite horizontal layer, the equations of the viscous compressible magnetohydrodynamic flows subject to the gravitational force. On the upper and lower planes of the layer, we consider homogeneous Dirichlet conditions on the velocity while a large constant vector field is prescribed on the magnetic field. The existence of the global strong solution with small initial data and its asymptotic behavior as time goes to infinity are established.</p>","PeriodicalId":51174,"journal":{"name":"Studies in Applied Mathematics","volume":"154 1","pages":""},"PeriodicalIF":2.6,"publicationDate":"2024-12-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1111/sapm.12794","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142860887","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":"Stability Analysis of Nondifferentiable Systems","authors":"Jiwoon Sim,&nbsp;Tianxu Wang,&nbsp;Hao Wang","doi":"10.1111/sapm.12801","DOIUrl":"https://doi.org/10.1111/sapm.12801","url":null,"abstract":"<p>Differential equations with right-hand side functions that are not everywhere differentiable are referred to as nondifferentiable systems. This paper introduces three novel methods to address stability issues in nondifferentiable systems. The first method extends the linearization method as it fails when the equilibrium is in a nondifferentiable region. We find that the stability of a piecewise differentiable system aligns with the behavior of its subsystems as long as the “distance” between these subsystems is sufficiently small. The second method is to examine the eigenvalues of the symmetric part of the Jacobian matrix in the vicinity of the equilibrium. This method applies to functions with even weaker regularity conditions, and does not require the eigenvalues to have a negative upper bound (or positive lower bound) over the domain. The third method establishes a connection between nondifferentiable systems and their approximate counterparts, revealing that their stability can be consistent under certain conditions. Additionally, we reaffirm the first two results via the approximation method. Examples are provided to illustrate the applications of our main results, including piecewise differentiable systems, general nondifferentiable systems, and realistic scenarios.</p>","PeriodicalId":51174,"journal":{"name":"Studies in Applied Mathematics","volume":"154 1","pages":""},"PeriodicalIF":2.6,"publicationDate":"2024-12-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1111/sapm.12801","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142860816","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":"A Numerical and Bi-directional Study of the Blackstock and Diaz–Solovchuk–Sheu Models for Approximating the Euler System","authors":"Anzhelika Vasilyeva,&nbsp;James V. Lambers","doi":"10.1111/sapm.12802","DOIUrl":"https://doi.org/10.1111/sapm.12802","url":null,"abstract":"<div>\u0000 \u0000 <p>This paper is a revisitation of a prior analytical and numerical study of two competing finite-amplitude models of one-dimensional acoustic propagation in perfect gases, due to Blackstock and Diaz et al., through comparison with the Euler system specialized to this case. In this study, we consider alternative time-stepping approaches, to validate the findings of the prior numerical study, and refined numerical boundary conditions. We also investigate whether the approximate models can be described as nearly equivalent to the Euler system with modified parameters, and the behavior of reflected waves produced by all three models.</p></div>","PeriodicalId":51174,"journal":{"name":"Studies in Applied Mathematics","volume":"154 1","pages":""},"PeriodicalIF":2.6,"publicationDate":"2024-12-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142860976","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 Approaches in Nonlinear Fourier Transform-Based Signal Processing for Telecommunications","authors":"Egor Sedov,&nbsp;Igor Chekhovskoy,&nbsp;Mikhail Fedoruk,&nbsp;Sergey Turitsyn","doi":"10.1111/sapm.12795","DOIUrl":"https://doi.org/10.1111/sapm.12795","url":null,"abstract":"<p>We discuss applications of the inverse scattering transform, also known as the nonlinear Fourier transform (NFT) in telecommunications, both for nonlinear optical fiber communication channel equalization and time-domain signal processing techniques. Our main focus is on the challenges and recent progress in the development of efficient numerical algorithms and approaches to NFT implementation.</p>","PeriodicalId":51174,"journal":{"name":"Studies in Applied Mathematics","volume":"154 1","pages":""},"PeriodicalIF":2.6,"publicationDate":"2024-12-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1111/sapm.12795","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142860195","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":"Invariant Manifolds in a Class-Structured Model From Adaptive Dynamics","authors":"Nikola Popović","doi":"10.1111/sapm.12797","DOIUrl":"https://doi.org/10.1111/sapm.12797","url":null,"abstract":"<p>We consider a family of structured population models from adaptive dynamics in which cells transition through a number of growth states, or classes, before division. We prove the existence and global asymptotic stability of invariant (‘resident') manifolds in that family; furthermore, we re-derive conditions under which scarce mutants can invade established resident populations, and we show the existence of corresponding ‘invasion’ manifolds that are obtained as critical manifolds under the additional assumption that resident has attained quasi-steady state, which induces a separation of scales. Our analysis is based on standard phase space techniques for ordinary differential equations, in combination with the geometric singular perturbation theory due to Fenichel.</p>","PeriodicalId":51174,"journal":{"name":"Studies in Applied Mathematics","volume":"154 1","pages":""},"PeriodicalIF":2.6,"publicationDate":"2024-11-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1111/sapm.12797","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142749275","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":"Thermal Convection in a Linearly Viscous Fluid Overlying a Bidisperse Porous Medium","authors":"P. Dondl,&nbsp;B. Straughan","doi":"10.1111/sapm.12799","DOIUrl":"https://doi.org/10.1111/sapm.12799","url":null,"abstract":"<p>A bidisperse porous medium is one with two porosity scales. There are the usual pores known as macropores but also cracks or fissures in the skeleton which give rise to micropores. In this article, we develop and analyze a model for thermal convection where a layer of viscous incompressible fluid overlies a layer of bidisperse porous medium. Care has to be taken with the boundary conditions at the interface of the fluid and the porous material, and this aspect is investigated. We propose two Beavers–Joseph conditions at the interface and we argue that the parameters in these relations should be different since they depend on the macro or micro permeability, and these parameters are estimated from the original experiments of Beavers and Joseph. The situation is one in a layer which is heated from below and under appropriate conditions bimodal neutral curves are found. These can depend on the relative permeability between the macro and micropores, the Beavers–Joseph conditions appropriate to the macro or micropores, the ratio <span></span><math>\u0000 <semantics>\u0000 <mover>\u0000 <mi>d</mi>\u0000 <mo>̂</mo>\u0000 </mover>\u0000 <annotation>${hat{d}}$</annotation>\u0000 </semantics></math> of the depth <span></span><math>\u0000 <semantics>\u0000 <mi>d</mi>\u0000 <annotation>$d$</annotation>\u0000 </semantics></math> of the fluid layer to the depth <span></span><math>\u0000 <semantics>\u0000 <msub>\u0000 <mi>d</mi>\u0000 <mi>m</mi>\u0000 </msub>\u0000 <annotation>$d_m$</annotation>\u0000 </semantics></math> of the porous layer, or generally the nature of the bidisperse medium.</p>","PeriodicalId":51174,"journal":{"name":"Studies in Applied Mathematics","volume":"154 1","pages":""},"PeriodicalIF":2.6,"publicationDate":"2024-11-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1111/sapm.12799","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142749274","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}