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Anderson localization for the unitary almost Mathieu operator 几乎是马修单元算子的安德森局部化
IF 1.7 2区 数学
Nonlinearity Pub Date : 2024-07-03 DOI: 10.1088/1361-6544/ad56ec
Fan Yang
{"title":"Anderson localization for the unitary almost Mathieu operator","authors":"Fan Yang","doi":"10.1088/1361-6544/ad56ec","DOIUrl":"https://doi.org/10.1088/1361-6544/ad56ec","url":null,"abstract":"We prove Anderson localization for all Diophantine frequencies and all non-resonant phases for a model that arises from a 2D quantum walk model subject to an external magnetic field, also known as the unitary almost Mathieu operator. Our work provides the first localization results for all Diophantine frequencies in quasi-periodic quantum walk and CMV matrix setting. We also obtain sharp asymptotics of the localized eigenfunctions.","PeriodicalId":54715,"journal":{"name":"Nonlinearity","volume":"24 1","pages":""},"PeriodicalIF":1.7,"publicationDate":"2024-07-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141552777","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
Joint moments of higher order derivatives of CUE characteristic polynomials II: structures, recursive relations, and applications CUE 特征多项式高阶导数的联合矩 II：结构、递推关系与应用
IF 1.7 2区 数学
Nonlinearity Pub Date : 2024-06-26 DOI: 10.1088/1361-6544/ad5948
Jonathan P Keating and Fei Wei
{"title":"Joint moments of higher order derivatives of CUE characteristic polynomials II: structures, recursive relations, and applications","authors":"Jonathan P Keating and Fei Wei","doi":"10.1088/1361-6544/ad5948","DOIUrl":"https://doi.org/10.1088/1361-6544/ad5948","url":null,"abstract":"In a companion paper (Keating and Wei 2023 Int. Math. Res. Not.2024 9607–32), we established asymptotic formulae for the joint moments of higher order derivatives of the characteristic polynomials of CUE random matrices. The leading order coefficients of these asymptotic formulae are expressed as partition sums of derivatives of determinants of Hankel matrices involving I-Bessel functions, with column indices shifted by Young diagrams. In this paper, we continue the study of these joint moments and establish more properties for their leading order coefficients, including structure theorems and recursive relations. We also build a connection to a solution of the σ-Painlevé III equation. In the process, we give recursive formulae for the Taylor coefficients of the Hankel determinants formed from I-Bessel functions that appear at zero and find some differential equations these determinants satisfy. The approach we establish is applicable to determinants of general Hankel matrices whose columns are shifted by Young diagrams.","PeriodicalId":54715,"journal":{"name":"Nonlinearity","volume":"26 1","pages":""},"PeriodicalIF":1.7,"publicationDate":"2024-06-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141504166","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
Integrable operators, ∂― -problems, KP and NLS hierarchy 可积分算子、∂- 问题、KP 和 NLS 层次结构
IF 1.7 2区 数学
Nonlinearity Pub Date : 2024-06-25 DOI: 10.1088/1361-6544/ad4b8e
M Bertola, T Grava and G Orsatti
{"title":"Integrable operators, ∂― -problems, KP and NLS hierarchy","authors":"M Bertola, T Grava and G Orsatti","doi":"10.1088/1361-6544/ad4b8e","DOIUrl":"https://doi.org/10.1088/1361-6544/ad4b8e","url":null,"abstract":"We develop the theory of integrable operators acting on a domain of the complex plane with smooth boundary in analogy with the theory of integrable operators acting on contours of the complex plane. We show how the resolvent operator is obtained from the solution of a -problem in the complex plane. When such a -problem depends on auxiliary parameters we define its Malgrange one form in analogy with the theory of isomonodromic problems. We show that the Malgrange one form is closed and coincides with the exterior logarithmic differential of the Hilbert–Carleman determinant of the operator . With suitable choices of the setup we show that the Hilbert–Carleman determinant is a τ-function of the Kadomtsev–Petviashvili (KP) or nonlinear Schrödinger hierarchies.","PeriodicalId":54715,"journal":{"name":"Nonlinearity","volume":"27 15 1","pages":""},"PeriodicalIF":1.7,"publicationDate":"2024-06-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141504167","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 fuzzy q-closest alignment model 模糊q-最接近配准模型
IF 1.7 2区 数学
Nonlinearity Pub Date : 2024-06-24 DOI: 10.1088/1361-6544/ad5781
Piotr B Mucha and Jan Peszek
{"title":"A fuzzy q-closest alignment model","authors":"Piotr B Mucha and Jan Peszek","doi":"10.1088/1361-6544/ad5781","DOIUrl":"https://doi.org/10.1088/1361-6544/ad5781","url":null,"abstract":"The paper examines the issue of well-posedness of the Cucker-Smale model with communication restricted to the q-closest neighbors, known also as the Cucker-Dong model. With agents oscillating on the boundary of different clusters, the system becomes difficult to precisely define, which leads to further problems with kinetic limits as the number of agents tends to infinity. We introduce the fuzzy q-closest system, which circumvents the issues with well-posedness. For such a system we prove a stability estimate for measure-valued solutions and perform the kinetic mean-field limit.","PeriodicalId":54715,"journal":{"name":"Nonlinearity","volume":"38 1","pages":""},"PeriodicalIF":1.7,"publicationDate":"2024-06-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141504168","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
The Morse index theorem for mechanical systems with reflections 有反射的机械系统的莫尔斯指数定理
IF 1.7 2区 数学
Nonlinearity Pub Date : 2024-06-23 DOI: 10.1088/1361-6544/ad5636
Jared Wunsch, Mengxuan Yang and Yuzhou Zou
{"title":"The Morse index theorem for mechanical systems with reflections","authors":"Jared Wunsch, Mengxuan Yang and Yuzhou Zou","doi":"10.1088/1361-6544/ad5636","DOIUrl":"https://doi.org/10.1088/1361-6544/ad5636","url":null,"abstract":"We prove a Morse index theorem for action functionals on paths that are allowed to reflect at a hypersurface (either in the interior or at the boundary of a manifold). Both fixed and periodic boundary conditions are treated.","PeriodicalId":54715,"journal":{"name":"Nonlinearity","volume":"17 1","pages":""},"PeriodicalIF":1.7,"publicationDate":"2024-06-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141504169","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
Global transonic solutions of hot-Jupiter model for exoplanetary atmosphere 系外行星大气热木星模型的全球跨音速解法
IF 1.7 2区 数学
Nonlinearity Pub Date : 2024-06-19 DOI: 10.1088/1361-6544/ad506d
Shih-Wei Chou and Bo-Chih Huang
{"title":"Global transonic solutions of hot-Jupiter model for exoplanetary atmosphere","authors":"Shih-Wei Chou and Bo-Chih Huang","doi":"10.1088/1361-6544/ad506d","DOIUrl":"https://doi.org/10.1088/1361-6544/ad506d","url":null,"abstract":"In this paper, we make modifications to the original hot-Jupiter model, which addresses the problem of hydrodynamic escape for the planetary atmosphere. The model involves the Euler equation with gravity, tidal effect, and heat. We employ the generalised Glimm technique to prove the presence of transonic solutions to the problem. By adjusting the dilation of the characteristic fields, we enhance the accuracy of the Glimm–Goodman wave interaction estimates. This allows us to establish a more general admissible condition for stabilizing the generalised Glimm scheme. Additionally, we derive the exact relationship between the lower bound of the gas velocity in the subsonic state and the adiabatic constant of the gas. Under certain constraints on the transonic initial and boundary data, the limit of the approximation solutions represents an entropy transonic solution with bounded variations. Furthermore, we are able to determine the feasible hydrodynamical region directly from the equation itself, without the need for any additional state equation.","PeriodicalId":54715,"journal":{"name":"Nonlinearity","volume":"26 1","pages":""},"PeriodicalIF":1.7,"publicationDate":"2024-06-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141504170","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
Elementary catastrophes underlying bifurcations of vector fields and PDEs 矢量场和 PDE 分岔背后的基本灾变
IF 1.7 2区 数学
Nonlinearity Pub Date : 2024-06-19 DOI: 10.1088/1361-6544/ad5637
Mike R Jeffrey
{"title":"Elementary catastrophes underlying bifurcations of vector fields and PDEs","authors":"Mike R Jeffrey","doi":"10.1088/1361-6544/ad5637","DOIUrl":"https://doi.org/10.1088/1361-6544/ad5637","url":null,"abstract":"A practical method was proposed recently for finding local bifurcation points in an n-dimensional vector field F by seeking their ‘underlying catastrophes’. Here we apply the idea to the homogeneous steady states of a partial differential equation as an example of the role that catastrophes can play in reaction diffusion. What are these ‘underlying’ catastrophes? We then show they essentially define a restricted class of ‘solvable’ rather than ‘all classifiable’ singularities, by identifying degenerate zeros of a vector field F without taking into account its vectorial character. As a result they are defined by a minimal set of r analytic conditions that provide a practical means to solve for them, and a huge reduction from the calculations needed to classify a singularity, which we will also enumerate here. In this way, underlying catastrophes seem to allow us apply Thom’s elementary catastrophes in much broader contexts.","PeriodicalId":54715,"journal":{"name":"Nonlinearity","volume":"192 1","pages":""},"PeriodicalIF":1.7,"publicationDate":"2024-06-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141516156","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
Scattering of solutions with group invariance for the fourth-order nonlinear Schrödinger equation 四阶非线性薛定谔方程具有群不变性的解的散射
IF 1.7 2区 数学
Nonlinearity Pub Date : 2024-06-18 DOI: 10.1088/1361-6544/ad5639
Koichi Komada and Satoshi Masaki
{"title":"Scattering of solutions with group invariance for the fourth-order nonlinear Schrödinger equation","authors":"Koichi Komada and Satoshi Masaki","doi":"10.1088/1361-6544/ad5639","DOIUrl":"https://doi.org/10.1088/1361-6544/ad5639","url":null,"abstract":"In this paper, we consider the focusing, L2-supercritical and -subcritical fourth-order nonlinear Schrödinger equations. We show the scattering of group-invariant solutions below the ground state threshold, under the hypothesis that the threshold for group-invariant solutions is less than a certain value.","PeriodicalId":54715,"journal":{"name":"Nonlinearity","volume":"1 1","pages":""},"PeriodicalIF":1.7,"publicationDate":"2024-06-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141516158","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
Well-posedness of the periodic dispersion-generalized Benjamin–Ono equation in the weakly dispersive regime 弱弥散机制下周期弥散广义本杰明-奥诺方程的良好拟合
IF 1.7 2区 数学
Nonlinearity Pub Date : 2024-06-18 DOI: 10.1088/1361-6544/ad52e2
Niklas Jöckel
{"title":"Well-posedness of the periodic dispersion-generalized Benjamin–Ono equation in the weakly dispersive regime","authors":"Niklas Jöckel","doi":"10.1088/1361-6544/ad52e2","DOIUrl":"https://doi.org/10.1088/1361-6544/ad52e2","url":null,"abstract":"We study the dispersion-generalized Benjamin–Ono equation in the periodic setting. This equation interpolates between the Benjamin–Ono equation ( ) and the inviscid Burgers’ equation ( ). We obtain local well-posedness in for and by using the short-time Fourier restriction method.","PeriodicalId":54715,"journal":{"name":"Nonlinearity","volume":"42 1","pages":""},"PeriodicalIF":1.7,"publicationDate":"2024-06-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141516157","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
Dynamics of a two-patch logistic model with diffusion and time delay 具有扩散和时间延迟的双片段逻辑模型的动态变化
IF 1.7 2区 数学
Nonlinearity Pub Date : 2024-06-17 DOI: 10.1088/1361-6544/ad55a0
Yukihiro Sawada, Yasuhiro Takeuchi and Yueping Dong
{"title":"Dynamics of a two-patch logistic model with diffusion and time delay","authors":"Yukihiro Sawada, Yasuhiro Takeuchi and Yueping Dong","doi":"10.1088/1361-6544/ad55a0","DOIUrl":"https://doi.org/10.1088/1361-6544/ad55a0","url":null,"abstract":"In this paper, we proposed a two-patch logistic model connected by diffusion, where one patch includes the Gamma type distribution time delay while the other patch does not include the time delay. In general, Routh–Hurwitz criterion is applied to the derivation for the conditions of Hopf bifurcation, but the more the order of the time delay increases the more the difficulty rises. Hence we adopt the polar form method for the characteristic equation to study the stability of coexistence equilibrium. Our findings show that the diffusion prevents the instabilization of the coexistence equilibrium. Besides, we found that the coexistence equilibrium is stable when time delay is small, and becomes unstable as the delay increases. But it can be restabilized for further increasing of time delay and continues to be stable afterwards. In other words, the diffusion and the time delay are beneficial to the stability of the coexistence equilibrium.","PeriodicalId":54715,"journal":{"name":"Nonlinearity","volume":"2 1","pages":""},"PeriodicalIF":1.7,"publicationDate":"2024-06-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141504171","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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