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Dilation Theorem Via Schrödingerization, With Applications to the Quantum Simulation of Differential Equations 膨胀定理通过Schrödingerization，应用于微分方程的量子模拟
IF 2.6 2区 数学
Studies in Applied Mathematics Pub Date : 2025-04-07 DOI: 10.1111/sapm.70047
Junpeng Hu, Shi Jin, Nana Liu, Lei Zhang
{"title":"Dilation Theorem Via Schrödingerization, With Applications to the Quantum Simulation of Differential Equations","authors":"Junpeng Hu,&nbsp;Shi Jin,&nbsp;Nana Liu,&nbsp;Lei Zhang","doi":"10.1111/sapm.70047","DOIUrl":"https://doi.org/10.1111/sapm.70047","url":null,"abstract":"<div>\u0000 \u0000 <p>Nagy's unitary dilation theorem in the operator theory asserts the possibility of dilating a contraction into a unitary operator. When used in quantum computing, its practical implementation primarily relies on block-encoding techniques, based on finite-dimensional scenarios. In this study, we delve into the recently devised Schrödingerization approach and demonstrate its viability as an alternative dilation technique. This approach is applicable to operators in the form of <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>V</mi>\u0000 <mo>(</mo>\u0000 <mi>t</mi>\u0000 <mo>)</mo>\u0000 <mo>=</mo>\u0000 <mi>exp</mi>\u0000 <mo>(</mo>\u0000 <mo>−</mo>\u0000 <mi>A</mi>\u0000 <mi>t</mi>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 <annotation>$V(t)=exp (-At)$</annotation>\u0000 </semantics></math>, which arises in wide-ranging applications, particularly in solving linear ordinary and partial differential equations. Importantly, the Schrödingerization approach is adaptable to both finite- and infinite-dimensional cases, in both countable and uncountable domains. For quantum systems lying in infinite-dimensional Hilbert space, the dilation involves adding a single infinite dimensional mode, and this is the continuous-variable version of the Schrödingerization procedure which makes it suitable for analog quantum computing. Furthermore, by discretizing continuous variables, the Schrödingerization method can also be effectively employed in finite-dimensional scenarios suitable for qubit-based quantum computing.</p></div>","PeriodicalId":51174,"journal":{"name":"Studies in Applied Mathematics","volume":"154 4","pages":""},"PeriodicalIF":2.6,"publicationDate":"2025-04-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143786885","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
Evolution of Dispersal in Open Advective Patchy Environments 开放平流斑块环境中扩散的演化
IF 2.6 2区 数学
Studies in Applied Mathematics Pub Date : 2025-04-06 DOI: 10.1111/sapm.70049
Qiang Li, Chen Cheng, Xiaoqian Feng, Peng Zhou
{"title":"Evolution of Dispersal in Open Advective Patchy Environments","authors":"Qiang Li,&nbsp;Chen Cheng,&nbsp;Xiaoqian Feng,&nbsp;Peng Zhou","doi":"10.1111/sapm.70049","DOIUrl":"https://doi.org/10.1111/sapm.70049","url":null,"abstract":"<div>\u0000 \u0000 <p>A Lotka–Volterra competitive patch model in advective homogeneous environments is investigated, where two species are supposed to differ only in their diffusion rates and the environment is assumed to be open so that there may be an inflow (resp. outflow) of individuals at the upstream (resp. downstream) patch. Under certain conditions on the inflow and outflow rates, a complete understanding on the global dynamics is obtained, which, biologically, suggests that in open patchy environments with mild inflow and outflow rates, faster diffusion can evolve, extending two existing results obtained by Chen et al. (Stud. Appl. Math., 149: 762-797, 2022) and (J. Nonlinear Sci., 33: Paper No. 40, 35 pp, 2023) to more general biological situations. Moreover, our main result does not depend on the size relation between the inflow and outflow rates, different from the corresponding space-continuous case treated recently by Wang et al. (SIAM J. Math. Anal., 56: 1643-1671, 2024).</p></div>","PeriodicalId":51174,"journal":{"name":"Studies in Applied Mathematics","volume":"154 4","pages":""},"PeriodicalIF":2.6,"publicationDate":"2025-04-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143787229","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
Issue Information-TOC 问题Information-TOC
IF 2.6 2区 数学
Studies in Applied Mathematics Pub Date : 2025-04-02 DOI: 10.1111/sapm.70050
{"title":"Issue Information-TOC","authors":"","doi":"10.1111/sapm.70050","DOIUrl":"https://doi.org/10.1111/sapm.70050","url":null,"abstract":"","PeriodicalId":51174,"journal":{"name":"Studies in Applied Mathematics","volume":"154 4","pages":""},"PeriodicalIF":2.6,"publicationDate":"2025-04-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1111/sapm.70050","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143749867","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 Darboux Matrices With a Single Multiple Pole and Their Applications 单多极达布矩阵及其应用
IF 2.6 2区 数学
Studies in Applied Mathematics Pub Date : 2025-04-02 DOI: 10.1111/sapm.70046
Yu-Yue Li, Deng-Shan Wang
{"title":"The Darboux Matrices With a Single Multiple Pole and Their Applications","authors":"Yu-Yue Li,&nbsp;Deng-Shan Wang","doi":"10.1111/sapm.70046","DOIUrl":"https://doi.org/10.1111/sapm.70046","url":null,"abstract":"<div>\u0000 \u0000 <p>Darboux transformation (DT) plays a key role in constructing explicit closed-form solutions of completely integrable systems. This paper provides an algebraic construction of Darboux matrices with a single multiple pole for the <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mn>2</mn>\u0000 <mo>×</mo>\u0000 <mn>2</mn>\u0000 </mrow>\u0000 <annotation>$2times 2$</annotation>\u0000 </semantics></math> Lax pair, in which the coefficient matrices are polynomials of spectral parameter. This special DT can handle the case where the spectral parameter coincides with its conjugate spectral parameter under non-Hermitian reduction. The first-order monic Darboux matrix is constructed explicitly and its classification theorem is presented. Then by using the solutions of the corresponding adjoint Lax pair, the <span></span><math>\u0000 <semantics>\u0000 <mi>n</mi>\u0000 <annotation>$n$</annotation>\u0000 </semantics></math>-order monic Darboux matrix and its inverse, both sharing the same unique pole, are derived explicitly. Further, a theorem is proposed to describe the invariance of Darboux matrix regarding pole distributions in Darboux matrix and its inverse. Finally, a unified theorem is offered to construct formal DT in general form. That is, all Darboux matrices expressible as the product of <span></span><math>\u0000 <semantics>\u0000 <mi>n</mi>\u0000 <annotation>$n$</annotation>\u0000 </semantics></math> first-order monic Darboux matrices can be constructed in this way. The nonlocal focusing NLS equation, the focusing NLS equation, and the Kaup–Boussinesq equation are taken as examples to illustrate the application of these DTs.</p></div>","PeriodicalId":51174,"journal":{"name":"Studies in Applied Mathematics","volume":"154 4","pages":""},"PeriodicalIF":2.6,"publicationDate":"2025-04-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143749863","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
Blow-Up of Radially Symmetric Solutions for a Cubic NLS-Type System in Dimension 4 四维三次nls型系统径向对称解的爆破
IF 2.6 2区 数学
Studies in Applied Mathematics Pub Date : 2025-03-26 DOI: 10.1111/sapm.70044
Maicon Hespanha, Ademir Pastor
{"title":"Blow-Up of Radially Symmetric Solutions for a Cubic NLS-Type System in Dimension 4","authors":"Maicon Hespanha,&nbsp;Ademir Pastor","doi":"10.1111/sapm.70044","DOIUrl":"https://doi.org/10.1111/sapm.70044","url":null,"abstract":"<p>This paper is concerned with a cubic nonlinear Schrödinger system modeling the interaction between an optical beam and its third harmonic in a material with Kerr-type nonlinear response. We are mainly interested in the so-called energy-critical case, that is, in dimension four. Our main result states that radially symmetric solutions with initial energy below that of the ground states but with kinetic energy above that of the ground states must blow up in finite time. The proof of this result is based on the convexity method. As an independent interest we also establish the existence of ground state solutions, that is, solutions that minimize some action functional. In order to obtain our existence results, we use the concentration–compactness method combined with variational arguments. As a byproduct, we also obtain the best constant in a vector-critical Sobolev-type inequality.</p>","PeriodicalId":51174,"journal":{"name":"Studies in Applied Mathematics","volume":"154 3","pages":""},"PeriodicalIF":2.6,"publicationDate":"2025-03-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143699025","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 Frobenius-Type Theory for Discrete Systems 离散系统的frobenius型理论
IF 2.6 2区 数学
Studies in Applied Mathematics Pub Date : 2025-03-26 DOI: 10.1111/sapm.70037
Daniel Reyes, Miguel A. Rodríguez, Piergiulio Tempesta
{"title":"A Frobenius-Type Theory for Discrete Systems","authors":"Daniel Reyes,&nbsp;Miguel A. Rodríguez,&nbsp;Piergiulio Tempesta","doi":"10.1111/sapm.70037","DOIUrl":"https://doi.org/10.1111/sapm.70037","url":null,"abstract":"<div>\u0000 \u0000 <p>We develop an approach analogous to the classical Frobenius theory for the analysis of singularities of ODEs in the case of discrete dynamical systems. Our methodology is based on the Roman–Rota theory of finite operators and relies crucially on the idea of preserving the Leibniz rule on a lattice of points by means of the notion of Rota algebras. The relevant cases of the Bessel, Hermite, and Airy equations are discussed.</p></div>","PeriodicalId":51174,"journal":{"name":"Studies in Applied Mathematics","volume":"154 3","pages":""},"PeriodicalIF":2.6,"publicationDate":"2025-03-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143707488","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
An Integrable Two-Component Degasperis–Procesi Equation 可积分双分量德加斯佩里斯-普罗塞西方程
IF 2.6 2区 数学
Studies in Applied Mathematics Pub Date : 2025-03-25 DOI: 10.1111/sapm.70045
Nianhua Li, Bao-Feng Feng
{"title":"An Integrable Two-Component Degasperis–Procesi Equation","authors":"Nianhua Li,&nbsp;Bao-Feng Feng","doi":"10.1111/sapm.70045","DOIUrl":"https://doi.org/10.1111/sapm.70045","url":null,"abstract":"<div>\u0000 \u0000 <p>We propose a new two-component Degasperis–Procesi (2-DP) equation, which is shown to be integrable. First of all, we derive an integrable three-component system from the Witten–Dijkgraaf–Verlinde–Verlinde (WDVV) associativity equation and construct its Lax pair and bi-Hamiltonian structure. Next, a 2-DP equation is proposed as further reduction of this three-component system, along with its Lax pair and associated bi-Hamiltonian structure. A reciprocal transformation is found to connect the 2-DP equation with a negative flow in a coupled KdV hierarchy, the associated system has the property of Painlevé. Finally, infinitely many conserved quantities, simple periodic and soliton solutions for the newly integrable 2-DP equation are provided.</p></div>","PeriodicalId":51174,"journal":{"name":"Studies in Applied Mathematics","volume":"154 3","pages":""},"PeriodicalIF":2.6,"publicationDate":"2025-03-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143689777","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
In Search of Rogue Waves: A Novel Proposal Distribution for Parallelized Rejection Sampling of the Truncated KdV Gibbs Measure 寻找异常波：截断KdV吉布斯测度的并行拒绝抽样的一种新的建议分布
IF 2.6 2区 数学
Studies in Applied Mathematics Pub Date : 2025-03-19 DOI: 10.1111/sapm.70043
Nicholas J. Moore, Brendan Foerster
{"title":"In Search of Rogue Waves: A Novel Proposal Distribution for Parallelized Rejection Sampling of the Truncated KdV Gibbs Measure","authors":"Nicholas J. Moore,&nbsp;Brendan Foerster","doi":"10.1111/sapm.70043","DOIUrl":"https://doi.org/10.1111/sapm.70043","url":null,"abstract":"<div>\u0000 \u0000 <p>The Gibbs ensemble of the truncated KdV (TKdV) equation has been shown to accurately describe the anomalous wave statistics observed in laboratory experiments, in particular the emergence of extreme events. Here, we introduce a novel proposal distribution that facilitates efficient rejection sampling of the TKdV Gibbs measure. Within parameter regimes accessible to laboratory experiments and capable of producing extreme events, the proposal distribution generates 1–6 orders of magnitude more accepted samples than does a naive, uniform distribution. When equipped with the new proposal distribution, a simple rejection algorithm enjoys key advantages over a Markov chain Monte Carlo algorithm, include better parallelization properties and generation of uncorrelated samples.</p></div>","PeriodicalId":51174,"journal":{"name":"Studies in Applied Mathematics","volume":"154 3","pages":""},"PeriodicalIF":2.6,"publicationDate":"2025-03-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143645856","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
Nonlinear Subwavelength Resonances in Three Dimensions 三维非线性亚波长共振
IF 2.6 2区 数学
Studies in Applied Mathematics Pub Date : 2025-03-16 DOI: 10.1111/sapm.70036
Habib Ammari, Thea Kosche
{"title":"Nonlinear Subwavelength Resonances in Three Dimensions","authors":"Habib Ammari,&nbsp;Thea Kosche","doi":"10.1111/sapm.70036","DOIUrl":"https://doi.org/10.1111/sapm.70036","url":null,"abstract":"<div>\u0000 \u0000 <p>In this paper, we consider the resonance problem for the cubic nonlinear Helmholtz equation in the subwavelength regime. We derive a discrete model for approximating the subwavelength resonances of finite systems of high-contrast resonators with Kerr-type nonlinearities. Our discrete formulation is valid in both weak and strong nonlinear regimes. Compared to the linear formulation, it characterizes the extra experimentally observed eigenmodes that are induced by the nonlinearities.</p></div>","PeriodicalId":51174,"journal":{"name":"Studies in Applied Mathematics","volume":"154 3","pages":""},"PeriodicalIF":2.6,"publicationDate":"2025-03-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143633043","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
Classical Multiple Orthogonal Polynomials for Arbitrary Number of Weights and Their Explicit Representation 任意数权值的经典多重正交多项式及其显式表示
IF 2.6 2区 数学
Studies in Applied Mathematics Pub Date : 2025-03-10 DOI: 10.1111/sapm.70033
Amílcar Branquinho, Juan E. F. Díaz, Ana Foulquié-Moreno, Manuel Mañas
{"title":"Classical Multiple Orthogonal Polynomials for Arbitrary Number of Weights and Their Explicit Representation","authors":"Amílcar Branquinho,&nbsp;Juan E. F. Díaz,&nbsp;Ana Foulquié-Moreno,&nbsp;Manuel Mañas","doi":"10.1111/sapm.70033","DOIUrl":"https://doi.org/10.1111/sapm.70033","url":null,"abstract":"<div>\u0000 \u0000 <p>This paper delves into classical multiple orthogonal polynomials with an arbitrary number of weights, including Jacobi–Piñeiro, Laguerre of both first and second kinds, as well as multiple orthogonal Hermite polynomials. Novel explicit expressions for general recurrence coefficients, as well as the stepline case, are provided for all these polynomial families. Furthermore, new explicit expressions for type I multiple orthogonal polynomials are derived for Laguerre of the second kind and also for multiple Hermite polynomials.</p></div>","PeriodicalId":51174,"journal":{"name":"Studies in Applied Mathematics","volume":"154 3","pages":""},"PeriodicalIF":2.6,"publicationDate":"2025-03-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143595050","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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