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Studies in Applied Mathematics最新文献

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Stability of bound states for regularized nonlinear Schrödinger equations 正则化非线性薛定谔方程约束状态的稳定性
IF 2.6 2区 数学
Studies in Applied Mathematics Pub Date : 2024-10-23 DOI: 10.1111/sapm.12780
John Albert, Jack Arbunich
{"title":"Stability of bound states for regularized nonlinear Schrödinger equations","authors":"John Albert,&nbsp;Jack Arbunich","doi":"10.1111/sapm.12780","DOIUrl":"https://doi.org/10.1111/sapm.12780","url":null,"abstract":"<p>We consider the stability of bound-state solutions of a family of regularized nonlinear Schrödinger equations which were introduced by Dumas et al. as models for the propagation of laser beams. Among these bound-state solutions are ground states, which are defined as solutions of a variational problem. We give a sufficient condition for existence and orbital stability of ground states, and use it to verify that ground states exist and are stable over a wider range of nonlinearities than for the nonregularized nonlinear Schrödinger equation. We also give another sufficient and almost necessary condition for stability of general bound states, and show that some stable bound states exist which are not ground states.</p>","PeriodicalId":51174,"journal":{"name":"Studies in Applied Mathematics","volume":"153 4","pages":""},"PeriodicalIF":2.6,"publicationDate":"2024-10-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142642033","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}
引用次数: 0
Weak compactons of nonlinearly dispersive KdV and KP equations 非线性色散 KdV 和 KP 方程的弱紧凑子
IF 2.6 2区 数学
Studies in Applied Mathematics Pub Date : 2024-10-22 DOI: 10.1111/sapm.12777
S. C. Anco, M. L. Gandarias
{"title":"Weak compactons of nonlinearly dispersive KdV and KP equations","authors":"S. C. Anco,&nbsp;M. L. Gandarias","doi":"10.1111/sapm.12777","DOIUrl":"https://doi.org/10.1111/sapm.12777","url":null,"abstract":"<p>A weak formulation is devised for the <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>K</mi>\u0000 <mo>(</mo>\u0000 <mi>m</mi>\u0000 <mo>,</mo>\u0000 <mi>n</mi>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 <annotation>$K(m,n)$</annotation>\u0000 </semantics></math> equation, which is a nonlinearly dispersive generalization of the gKdV equation  having compacton solutions. With this formulation, explicit weak compacton solutions are derived, including ones that do not exist as classical (strong) solutions. Similar results are obtained for a nonlinearly dispersive generalization of the gKP equation in two dimensions, which possesses line compacton solutions.</p>","PeriodicalId":51174,"journal":{"name":"Studies in Applied Mathematics","volume":"153 4","pages":""},"PeriodicalIF":2.6,"publicationDate":"2024-10-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1111/sapm.12777","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142642022","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}
引用次数: 0
Singularity formation for the relativistic Euler equations of Chaplygin gases in Schwarzschild spacetime 施瓦兹柴尔德时空中查普利金气体相对论欧拉方程的奇点形成
IF 2.6 2区 数学
Studies in Applied Mathematics Pub Date : 2024-10-18 DOI: 10.1111/sapm.12775
Yanbo Hu, Houbin Guo
{"title":"Singularity formation for the relativistic Euler equations of Chaplygin gases in Schwarzschild spacetime","authors":"Yanbo Hu,&nbsp;Houbin Guo","doi":"10.1111/sapm.12775","DOIUrl":"https://doi.org/10.1111/sapm.12775","url":null,"abstract":"<p>We study the formation of singularities of smooth solutions to the relativistic Euler equations of Chaplygin gases in Schwarzschild spacetime. The system is in the spherically symmetric form, and its coefficients and nonhomogeneous terms contain a parameter reflecting the mass of the black hole, which makes it highly nonlinear and complicated. To overcome the influence of the mass parameter of black hole, we introduce a pair of suitable auxiliary variables related to it and derive their characteristic decompositions to establish the estimates of the smooth solution. We show that, for a kind of initial data, the smooth solution develops singularity in finite time and the mass-energy density itself approaches infinity at the blowup point.</p>","PeriodicalId":51174,"journal":{"name":"Studies in Applied Mathematics","volume":"153 4","pages":""},"PeriodicalIF":2.6,"publicationDate":"2024-10-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142642149","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}
引用次数: 0
A direct approach for solving the cubic Szegö equation 求解三次席格方程的直接方法
IF 2.6 2区 数学
Studies in Applied Mathematics Pub Date : 2024-10-14 DOI: 10.1111/sapm.12770
Yoshimasa Matsuno
{"title":"A direct approach for solving the cubic Szegö equation","authors":"Yoshimasa Matsuno","doi":"10.1111/sapm.12770","DOIUrl":"https://doi.org/10.1111/sapm.12770","url":null,"abstract":"<p>We study the cubic Szegö equation which is an integrable nonlinear nondispersive and nonlocal evolution equation. In particular, we present a direct approach for obtaining the multiphase and multisoliton solutions as well as a special class of periodic solutions. Our method is substantially different from the existing one which relies mainly on the spectral analysis of the Hankel operator. We show that the cubic Szegö equation can be bilinearized through appropriate dependent variable transformations and then the solutions satisfy a set of bilinear equations. The proof is carried out within the framework of an elementary theory of determinants. Furthermore, we demonstrate that the eigenfunctions associated with the multiphase solutions satisfy the Lax pair for the cubic Szegö equation, providing an alternative proof of the solutions. Last, the eigenvalue problem for a periodic solution is solved exactly to obtain the analytical expressions of the eigenvalues.</p>","PeriodicalId":51174,"journal":{"name":"Studies in Applied Mathematics","volume":"153 4","pages":""},"PeriodicalIF":2.6,"publicationDate":"2024-10-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142642110","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}
引用次数: 0
On a posteriori error estimation for Runge–Kutta discontinuous Galerkin methods for linear hyperbolic problems 论线性双曲问题 Runge-Kutta 非连续 Galerkin 方法的后验误差估计
IF 2.6 2区 数学
Studies in Applied Mathematics Pub Date : 2024-10-11 DOI: 10.1111/sapm.12772
Emmanuil H. Georgoulis, Edward J. C. Hall, Charalambos G. Makridakis
{"title":"On a posteriori error estimation for Runge–Kutta discontinuous Galerkin methods for linear hyperbolic problems","authors":"Emmanuil H. Georgoulis,&nbsp;Edward J. C. Hall,&nbsp;Charalambos G. Makridakis","doi":"10.1111/sapm.12772","DOIUrl":"https://doi.org/10.1111/sapm.12772","url":null,"abstract":"<p>A posteriori bounds for the error measured in various norms for a standard second-order explicit-in-time Runge–Kutta discontinuous Galerkin (RKDG) discretization of a one-dimensional (in space) linear transport problem are derived. The proof is based on a novel space-time polynomial reconstruction, hinging on high-order temporal reconstructions for continuous and discontinuous Galerkin time-stepping methods. Of particular interest is the question of error estimation under dynamic mesh modification. The theoretical findings are tested by numerical experiments.</p>","PeriodicalId":51174,"journal":{"name":"Studies in Applied Mathematics","volume":"153 4","pages":""},"PeriodicalIF":2.6,"publicationDate":"2024-10-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1111/sapm.12772","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142641404","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}
引用次数: 0
The hysteretic Aw–Rascle–Zhang model 滞后的 Aw-Rascle-Zhang 模型
IF 2.6 2区 数学
Studies in Applied Mathematics Pub Date : 2024-10-09 DOI: 10.1111/sapm.12769
Andrea Corli, Haitao Fan
{"title":"The hysteretic Aw–Rascle–Zhang model","authors":"Andrea Corli,&nbsp;Haitao Fan","doi":"10.1111/sapm.12769","DOIUrl":"https://doi.org/10.1111/sapm.12769","url":null,"abstract":"<p>A novel hyperbolic system of partial differential equations is introduced to model traffic flows. This system comprises three equations, with two being linearly degenerate; its main feature is the inclusion of a hysteretic term in a generalized Aw–Rascle–Zhang (ARZ) model. First, a maximum principle for the diffusive version of the model is proven. Then, it is demonstrated that a solution to the Riemann problem exists, which is unique among solutions that are monotone in velocity; all waves exploited in the construction have suitable viscous profiles. Through several examples it is shown how, as a consequence of different driving habits, the system can model the decay, emergence, or persistence of stop-and-go waves (a feature that is missing in the ARZ model), and such behavior is characterized by a simple geometric condition. Furthermore, the model allows the study of traffic flows with a mixture of drivers whose hysteresis loops are either clockwise or counterclockwise. In particular, the presence of sufficiently many of the former dampens speed oscillations.</p>","PeriodicalId":51174,"journal":{"name":"Studies in Applied Mathematics","volume":"153 4","pages":""},"PeriodicalIF":2.6,"publicationDate":"2024-10-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1111/sapm.12769","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142641668","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}
引用次数: 0
Issue Information-TOC 发行信息-TOC
IF 2.6 2区 数学
Studies in Applied Mathematics Pub Date : 2024-10-09 DOI: 10.1111/sapm.12591
{"title":"Issue Information-TOC","authors":"","doi":"10.1111/sapm.12591","DOIUrl":"https://doi.org/10.1111/sapm.12591","url":null,"abstract":"","PeriodicalId":51174,"journal":{"name":"Studies in Applied Mathematics","volume":"153 3","pages":""},"PeriodicalIF":2.6,"publicationDate":"2024-10-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1111/sapm.12591","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142404432","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}
引用次数: 0
Existence of solutions to k-Wave models of nonlinear ultrasound propagation in biological tissue 生物组织中非线性超声波传播 k 波模型解的存在性
IF 2.6 2区 数学
Studies in Applied Mathematics Pub Date : 2024-10-08 DOI: 10.1111/sapm.12771
Ben Cox, Barbara Kaltenbacher, Vanja Nikolić, Felix Lucka
{"title":"Existence of solutions to k-Wave models of nonlinear ultrasound propagation in biological tissue","authors":"Ben Cox,&nbsp;Barbara Kaltenbacher,&nbsp;Vanja Nikolić,&nbsp;Felix Lucka","doi":"10.1111/sapm.12771","DOIUrl":"https://doi.org/10.1111/sapm.12771","url":null,"abstract":"<p>We investigate models for nonlinear ultrasound propagation in soft biological tissue based on the one that serves as the core for the software package k-Wave. The systems are solved for the acoustic particle velocity, mass density, and acoustic pressure and involve a fractional absorption operator. We first consider a system that incorporates additional viscosity in the equation for momentum conservation. By constructing a Galerkin approximation procedure, we prove the local existence of its solutions. In view of inverse problems arising from imaging tasks, the theory allows for the variable background mass density, speed of sound, and the nonlinearity parameter in the systems. Second, under stronger conditions on the data, we take the vanishing viscosity limit of the problem, thereby rigorously establishing the existence of solutions for the limiting system as well.</p>","PeriodicalId":51174,"journal":{"name":"Studies in Applied Mathematics","volume":"153 4","pages":""},"PeriodicalIF":2.6,"publicationDate":"2024-10-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1111/sapm.12771","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142641614","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}
引用次数: 0
Exponentially localized interface eigenmodes in finite chains of resonators 有限谐振器链中的指数局部界面特征模式
IF 2.6 2区 数学
Studies in Applied Mathematics Pub Date : 2024-09-19 DOI: 10.1111/sapm.12765
Habib Ammari, Silvio Barandun, Bryn Davies, Erik Orvehed Hiltunen, Thea Kosche, Ping Liu
{"title":"Exponentially localized interface eigenmodes in finite chains of resonators","authors":"Habib Ammari,&nbsp;Silvio Barandun,&nbsp;Bryn Davies,&nbsp;Erik Orvehed Hiltunen,&nbsp;Thea Kosche,&nbsp;Ping Liu","doi":"10.1111/sapm.12765","DOIUrl":"10.1111/sapm.12765","url":null,"abstract":"<p>This paper studies wave localization in chains of finitely many resonators. There is an extensive theory predicting the existence of localized modes induced by defects in infinitely periodic systems. This work extends these principles to finite-sized systems. We consider one-dimensional, finite systems of subwavelength resonators arranged in dimers that have a geometric defect in the structure. This is a classical wave analog of the Su–Schrieffer–Heeger model. We prove the existence of a spectral gap for defectless finite dimer structures and find a direct relationship between eigenvalues being within the spectral gap and the localization of their associated eigenmode. Then, for sufficiently large-size systems, we show the existence and uniqueness of an eigenvalue in the gap in the defect structure, proving the existence of a unique localized interface mode. To the best of our knowledge, our method, based on Chebyshev polynomials, is the first to characterize quantitatively the localized interface modes in systems of finitely many resonators.</p>","PeriodicalId":51174,"journal":{"name":"Studies in Applied Mathematics","volume":"153 4","pages":""},"PeriodicalIF":2.6,"publicationDate":"2024-09-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142261639","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}
引用次数: 0
Inverse scattering transform for continuous and discrete space-time-shifted integrable equations 连续和离散时移可积分方程的反散射变换
IF 2.6 2区 数学
Studies in Applied Mathematics Pub Date : 2024-09-17 DOI: 10.1111/sapm.12764
Mark J. Ablowitz, Ziad H. Musslimani, Nicholas J. Ossi
{"title":"Inverse scattering transform for continuous and discrete space-time-shifted integrable equations","authors":"Mark J. Ablowitz,&nbsp;Ziad H. Musslimani,&nbsp;Nicholas J. Ossi","doi":"10.1111/sapm.12764","DOIUrl":"10.1111/sapm.12764","url":null,"abstract":"<p>Nonlocal integrable partial differential equations possessing a spatial or temporal reflection have constituted an active research area for the past decade. Recently, more general classes of these nonlocal equations have been proposed, wherein the nonlocality appears as a combination of a shift (by a real or a complex parameter) and a reflection. This new shifting parameter manifests itself in the inverse scattering transform (IST) as an additional phase factor in an analogous way to the classical Fourier transform. In this paper, the IST is analyzed in detail for several examples of such systems. Particularly, time, space, and space-time-shifted nonlinear Schrödinger (NLS) and space-time-shifted modified Korteweg-de Vries equations are studied. Additionally, the semidiscrete IST is developed for the time, space, and space-time-shifted variants of the Ablowitz–Ladik integrable discretization of the NLS. One-soliton solutions are constructed for all continuous and discrete cases.</p>","PeriodicalId":51174,"journal":{"name":"Studies in Applied Mathematics","volume":"153 4","pages":""},"PeriodicalIF":2.6,"publicationDate":"2024-09-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142261604","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}
引用次数: 0
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