Mathematical Physics, Analysis and Geometry最新文献_第6页

Long Time Asymptotic Behavior for the Nonlocal mKdV Equation in Solitonic Space–Time Regions 孤子时空区域中非局部mKdV方程的长时间渐近行为

IF 1 3区数学

Mathematical Physics, Analysis and Geometry Pub Date : 2023-01-28 DOI: 10.1007/s11040-023-09445-w

Xuan Zhou, Engui Fan

{"title":"Long Time Asymptotic Behavior for the Nonlocal mKdV Equation in Solitonic Space–Time Regions","authors":"Xuan Zhou, Engui Fan","doi":"10.1007/s11040-023-09445-w","DOIUrl":"10.1007/s11040-023-09445-w","url":null,"abstract":"<div>We study the long time asymptotic behavior for the Cauchy problem of an integrable real nonlocal mKdV equation with nonzero initial data in the solitonic regions <div><div>$$begin{aligned}&q_t(x,t)-6sigma q(x,t)q(-x,-t)q_{x}(x,t)+q_{xxx}(x,t)=0, &quad q(x,0)=q_{0}(x), lim _{xrightarrow pm infty } q_{0}(x)=q_{pm }, end{aligned}$$</div></div>where (|q_{pm }|=1) and (q_{+}=delta q_{-}), (sigma delta =-1). In our previous article, we have obtained long time asymptotics for the nonlocal mKdV equation in the solitonic region (-6<xi <6) with (xi =frac{x}{t}). In this paper, we give the asymptotic expansion of the solution q(x, t) for other solitonic regions (xi <-6) and (xi >6). Based on the Riemann–Hilbert formulation of the Cauchy problem, further using the ({bar{partial }}) steepest descent method, we derive different long time asymptotic expansions of the solution q(x, t) in above two different space-time solitonic regions. In the region (xi <-6), phase function (theta (z)) has four stationary phase points on the ({mathbb {R}}). Correspondingly, q(x, t) can be characterized with an ({mathcal {N}}(Lambda ))-soliton on discrete spectrum, the leading order term on continuous spectrum and an residual error term, which are affected by a function (textrm{Im}nu (zeta _i)). In the region (xi >6), phase function (theta (z)) has four stationary phase points on (i{mathbb {R}}), the corresponding asymptotic approximations can be characterized with an ({mathcal {N}}(Lambda ))-soliton with diverse residual error order ({mathcal {O}}(t^{-1})).</div>","PeriodicalId":694,"journal":{"name":"Mathematical Physics, Analysis and Geometry","volume":"26 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2023-01-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s11040-023-09445-w.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"5082235","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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: 1

Lusztig Factorization Dynamics of the Full Kostant–Toda Lattices 全Kostant-Toda格的Lusztig分解动力学

IF 1 3区数学

Mathematical Physics, Analysis and Geometry Pub Date : 2023-01-17 DOI: 10.1007/s11040-022-09444-3

Nicholas M. Ercolani, Jonathan Ramalheira-Tsu

引用次数: 1

Heisenberg Dynamics for Non Self-Adjoint Hamiltonians: Symmetries and Derivations 非自伴随哈密顿量的Heisenberg动力学:对称性和推导

IF 1 3区数学

Mathematical Physics, Analysis and Geometry Pub Date : 2022-12-19 DOI: 10.1007/s11040-022-09443-4

F. Bagarello

引用次数: 2

Slit-Strip Ising Boundary Conformal Field Theory 1: Discrete and Continuous Function Spaces 裂隙-带状Ising边界共形场理论1:离散与连续函数空间

IF 1 3区数学

Mathematical Physics, Analysis and Geometry Pub Date : 2022-12-05 DOI: 10.1007/s11040-022-09442-5

Taha Ameen, Kalle Kytölä, S. C. Park, David Radnell

{"title":"Slit-Strip Ising Boundary Conformal Field Theory 1: Discrete and Continuous Function Spaces","authors":"Taha Ameen, Kalle Kytölä, S. C. Park, David Radnell","doi":"10.1007/s11040-022-09442-5","DOIUrl":"10.1007/s11040-022-09442-5","url":null,"abstract":"<div>This is the first in a series of articles about recovering the full algebraic structure of a boundary conformal field theory (CFT) from the scaling limit of the critical Ising model in slit-strip geometry. Here, we introduce spaces of holomorphic functions in continuum domains as well as corresponding spaces of discrete holomorphic functions in lattice domains. We find distinguished sets of functions characterized by their singular behavior in the three infinite directions in the slit-strip domains, and note in particular that natural subsets of these functions span analogues of Hardy spaces. We prove convergence results of the distinguished discrete holomorphic functions to the continuum ones. In the subsequent articles, the discrete holomorphic functions will be used for the calculation of the Ising model fusion coefficients (as well as for the diagonalization of the Ising transfer matrix), and the convergence of the functions is used to prove the convergence of the fusion coefficients. It will also be shown that the vertex operator algebra of the boundary conformal field theory can be recovered from the limit of the fusion coefficients via geometric transformations involving the distinguished continuum functions.</div>","PeriodicalId":694,"journal":{"name":"Mathematical Physics, Analysis and Geometry","volume":"25 4","pages":""},"PeriodicalIF":1.0,"publicationDate":"2022-12-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s11040-022-09442-5.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"4204234","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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: 3

Bispectrality of (AG_2) Calogero–Moser–Sutherland System (AG_2) Calogero-Moser-Sutherland系统的双谱性

IF 1 3区数学

Mathematical Physics, Analysis and Geometry Pub Date : 2022-11-28 DOI: 10.1007/s11040-022-09440-7

Misha Feigin, Martin Vrabec

引用次数: 1

Stability of the Classical Catenoid and Darboux–Pöschl–Teller Potentials 经典链链电位和Darboux-Pöschl-Teller电位的稳定性

IF 1 3区数学

Mathematical Physics, Analysis and Geometry Pub Date : 2022-10-29 DOI: 10.1007/s11040-022-09437-2

Jens Hoppe, Per Moosavi

引用次数: 0

Bi-infinite Solutions for KdV- and Toda-Type Discrete Integrable Systems Based on Path Encodings 基于路径编码的KdV-和toda型离散可积系统的双无穷解

IF 1 3区数学

Mathematical Physics, Analysis and Geometry Pub Date : 2022-10-22 DOI: 10.1007/s11040-022-09435-4

David A. Croydon, Makiko Sasada, Satoshi Tsujimoto

{"title":"Bi-infinite Solutions for KdV- and Toda-Type Discrete Integrable Systems Based on Path Encodings","authors":"David A. Croydon, Makiko Sasada, Satoshi Tsujimoto","doi":"10.1007/s11040-022-09435-4","DOIUrl":"10.1007/s11040-022-09435-4","url":null,"abstract":"<div>We define bi-infinite versions of four well-studied discrete integrable models, namely the ultra-discrete KdV equation, the discrete KdV equation, the ultra-discrete Toda equation, and the discrete Toda equation. For each equation, we show that there exists a unique solution to the initial value problem when the given data lies within a certain class, which includes the support of many shift ergodic measures. Our unified approach, which is also applicable to other integrable systems defined locally via lattice maps, involves the introduction of a path encoding (that is, a certain antiderivative) of the model configuration, for which we are able to describe the dynamics more generally than in previous work on finite size systems, periodic systems and semi-infinite systems. In particular, in each case we show that the behaviour of the system is characterized by a generalization of the classical ‘Pitman’s transformation’ of reflection in the past maximum, which is well-known to probabilists. The picture presented here also provides a means to identify a natural ‘carrier process’ for configurations within the given class, and is convenient for checking that the systems we discuss are all-time reversible. Finally, we investigate links between the different systems, such as showing that bi-infinite all-time solutions for the ultra-discrete KdV (resp. Toda) equation may appear as ultra-discretizations of corresponding solutions for the discrete KdV (resp. Toda) equation.</div>","PeriodicalId":694,"journal":{"name":"Mathematical Physics, Analysis and Geometry","volume":"25 4","pages":""},"PeriodicalIF":1.0,"publicationDate":"2022-10-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s11040-022-09435-4.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"4876694","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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: 3

Quasilinear Systems of First Order PDEs with Nonlocal Hamiltonian Structures 具有非局部哈密顿结构的一阶偏微分方程拟线性系统

IF 1 3区数学

Mathematical Physics, Analysis and Geometry Pub Date : 2022-10-15 DOI: 10.1007/s11040-022-09438-1

Pierandrea Vergallo

引用次数: 3

On Bose–Einstein condensates in the Thomas–Fermi regime 论托马斯-费米体系中的玻色-爱因斯坦凝聚体

IF 1 3区数学

Mathematical Physics, Analysis and Geometry Pub Date : 2022-10-14 DOI: 10.1007/s11040-022-09439-0

Daniele Dimonte, Emanuela L. Giacomelli

引用次数: 4

Limit Theorems for Multi-group Curie–Weiss Models via the Method of Moments 基于矩量法的多群Curie-Weiss模型极限定理