Nonlinearity最新文献_第4页

Equilibrium states for hyperbolic potentials via inducing schemes * 通过诱导方案实现双曲势的平衡态 *

IF 1.7 2区数学

Nonlinearity Pub Date : 2024-08-13 DOI: 10.1088/1361-6544/ad6b6e

José F Alves, Krerley Oliveira, Eduardo Santana

引用次数: 0

An inverse problem for the minimal surface equation in the presence of a riemannian metric 存在里曼度量时最小曲面方程的逆问题

IF 1.7 2区数学

Nonlinearity Pub Date : 2024-08-11 DOI: 10.1088/1361-6544/ad6949

Janne Nurminen

引用次数: 0

Lorentzian distance on the Lobachevsky plane * 洛巴切夫斯基平面上的洛伦兹距离 *

IF 1.7 2区数学

Nonlinearity Pub Date : 2024-08-07 DOI: 10.1088/1361-6544/ad67a0

Yu L Sachkov

引用次数: 0

A family of integrable maps associated with the Volterra lattice 与伏特拉网格相关的可积分映射族

IF 1.7 2区数学

Nonlinearity Pub Date : 2024-08-07 DOI: 10.1088/1361-6544/ad68ba

A N W Hone, J A G Roberts and P Vanhaecke

{"title":"A family of integrable maps associated with the Volterra lattice","authors":"A N W Hone, J A G Roberts and P Vanhaecke","doi":"10.1088/1361-6544/ad68ba","DOIUrl":"https://doi.org/10.1088/1361-6544/ad68ba","url":null,"abstract":"Recently Gubbiotti, Joshi, Tran and Viallet classified birational maps in four dimensions admitting two invariants (first integrals) with a particular degree structure, by considering recurrences of fourth order with a certain symmetry. The last three of the maps so obtained were shown to be Liouville integrable, in the sense of admitting a non-degenerate Poisson bracket with two first integrals in involution. Here we show how the first of these three Liouville integrable maps corresponds to genus 2 solutions of the infinite Volterra lattice, being the g = 2 case of a family of maps associated with the Stieltjes continued fraction expansion of a certain function on a hyperelliptic curve of genus . The continued fraction method provides explicit Hankel determinant formulae for tau functions of the solutions, together with an algebro-geometric description via a Lax representation for each member of the family, associating it with an algebraic completely integrable system. In particular, in the elliptic case (g = 1), as a byproduct we obtain Hankel determinant expressions for the solutions of the Somos-5 recurrence, but different to those previously derived by Chang, Hu and Xin. By applying contraction to the Stieltjes fraction, we recover integrable maps associated with Jacobi continued fractions on hyperelliptic curves, that one of us considered previously, as well as the Miura-type transformation between the Volterra and Toda lattices.","PeriodicalId":54715,"journal":{"name":"Nonlinearity","volume":"23 1","pages":""},"PeriodicalIF":1.7,"publicationDate":"2024-08-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141944171","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 Euler non-mixing made easy 欧拉非混频变得简单

IF 1.7 2区数学

Nonlinearity Pub Date : 2024-08-07 DOI: 10.1088/1361-6544/ad694c

Boris Khesin

引用次数: 0

Remarks on the separation of Navier–Stokes flows 关于纳维-斯托克斯流分离的评论

IF 1.7 2区数学

Nonlinearity Pub Date : 2024-08-06 DOI: 10.1088/1361-6544/ad68b9

Zachary Bradshaw

{"title":"Remarks on the separation of Navier–Stokes flows","authors":"Zachary Bradshaw","doi":"10.1088/1361-6544/ad68b9","DOIUrl":"https://doi.org/10.1088/1361-6544/ad68b9","url":null,"abstract":"Recently, strong evidence has accumulated that some solutions to the Navier–Stokes equations in physically meaningful classes are not unique. The primary purpose of this paper is to establish necessary properties for the error of hypothetical non-unique Navier–Stokes flows under conditions motivated by the scaling of the equations. Our first set of results show that some scales are necessarily active—comparable in norm to the full error—as solutions separate. ‘Scale’ is interpreted in several ways, namely via algebraic bounds, the Fourier transform and discrete volume elements. These results include a new type of uniqueness criteria which is stated in terms of the error. The second result is a conditional predictability criteria for the separation of small perturbations. An implication is that the error necessarily activates at larger scales as flows de-correlate. The last result says that the error of the hypothetical non-unique Leray–Hopf solutions of Jia and Šverák locally grows in a self-similar fashion. Consequently, within the Leray–Hopf class, energy can hypothetically de-correlate at a rate which is faster than linear. This contrasts numerical work on predictability which identifies a linear rate. Our results suggest that this discrepancy may be explained by the fact that non-uniqueness might arise from perturbation around a singular flow.","PeriodicalId":54715,"journal":{"name":"Nonlinearity","volume":"12 1","pages":""},"PeriodicalIF":1.7,"publicationDate":"2024-08-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141944173","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 Lorenz system as a gradient-like system 作为梯度系统的洛伦兹系统

IF 1.7 2区数学

Nonlinearity Pub Date : 2024-08-06 DOI: 10.1088/1361-6544/ad68bb

Jeremy P Parker

引用次数: 0

Completely degenerate equilibria of the Kuramoto model on networks 网络上仓本模型的完全退化均衡状态

IF 1.7 2区数学

Nonlinearity Pub Date : 2024-08-06 DOI: 10.1088/1361-6544/ad694a

Davide Sclosa

{"title":"Completely degenerate equilibria of the Kuramoto model on networks","authors":"Davide Sclosa","doi":"10.1088/1361-6544/ad694a","DOIUrl":"https://doi.org/10.1088/1361-6544/ad694a","url":null,"abstract":"Kuramoto Networks contain non-hyperbolic equilibria whose stability is sometimes difficult to determine. We consider the extreme case in which all Jacobian eigenvalues are zero. In this case linearizing the system at the equilibrium leads to a Jacobian matrix which is zero in every entry. We call these equilibria completely degenerate. We prove that they exist for certain intrinsic frequencies if and only if the underlying graph is bipartite, and that they do not exist for generic intrinsic frequencies. In the case of zero intrinsic frequencies, we prove that they exist if and only if the graph has an Euler circuit such that the number of steps between any two visits at the same vertex is a multiple of 4. The simplest example is the cycle graph with 4 vertices. We prove that graphs with this property exist for every number of vertices and that they become asymptotically rare for N large. Regarding stability, we prove that for any choice of intrinsic frequencies, any coupling strength and any graph with at least one edge, completely degenerate equilibria are not Lyapunov stable. As a corollary, we obtain that stable equilibria in Kuramoto Networks must have at least one strictly negative eigenvalue.","PeriodicalId":54715,"journal":{"name":"Nonlinearity","volume":"41 1","pages":""},"PeriodicalIF":1.7,"publicationDate":"2024-08-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141944283","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

Random expansive measures 随机扩张措施

IF 1.7 2区数学

Nonlinearity Pub Date : 2024-08-01 DOI: 10.1088/1361-6544/ad673f

Rafael A Bilbao, Marlon Oliveira, Eduardo Santana

引用次数: 0

Response solutions for elliptic-hyperbolic equations with nonlinearities and periodic external forces 具有非线性和周期性外力的椭圆-超双曲方程的响应解

IF 1.7 2区数学

Nonlinearity Pub Date : 2024-08-01 DOI: 10.1088/1361-6544/ad673e

Yingdu Dong, Xiong Li

引用次数: 0