arXiv - PHYS - Exactly Solvable and Integrable Systems最新文献_第10页

On the Obtaining Solutions of Nonlinear Differential Equations by Means of the Solutions of Simpler Linear or Nonlinear Differential Equations 论通过较简单线性或非线性微分方程的解来获取非线性微分方程的解

arXiv - PHYS - Exactly Solvable and Integrable Systems Pub Date : 2023-12-06 DOI: arxiv-2312.03621

Nikolay K. Vitanov

{"title":"On the Obtaining Solutions of Nonlinear Differential Equations by Means of the Solutions of Simpler Linear or Nonlinear Differential Equations","authors":"Nikolay K. Vitanov","doi":"arxiv-2312.03621","DOIUrl":"https://doi.org/arxiv-2312.03621","url":null,"abstract":"In this article, we follow an idea that is opposite to the idea of Hopf and\u0000Cole: we use transformations in order to transform simpler linear or nonlinear\u0000differential equations (with known solutions) to more complicated nonlinear\u0000differential equations. In such a way, we can obtain numerous exact solutions\u0000of nonlinear differential equations. We apply this methodology to the classical\u0000parabolic differential equation (the wave equation), to the classical\u0000hyperbolic differential equation (the heat equation), and to the classical\u0000elliptic differential equation (Laplace equation). In addition, we use the\u0000methodology to obtain exact solutions of nonlinear ordinary differential\u0000equations by means of the solutions of linear differential equations and by\u0000means of the solutions of the nonlinear differential equations of Bernoulli and\u0000Riccati. Finally, we demonstrate the capacity of the methodology to lead to\u0000exact solutions of nonlinear partial differential equations on the basis of\u0000known solutions of other nonlinear partial differential equations. As an\u0000example of this, we use the Korteweg--de Vries equation and its solutions.\u0000Traveling wave solutions of nonlinear differential equations are of special\u0000interest in this article. We demonstrate the existence of the following\u0000phenomena described by some of the obtained solutions: (i) occurrence of the\u0000solitary wave--solitary antiwave from the solution, which is zero at the\u0000initial moment (analogy of an occurrence of particle and antiparticle from the\u0000vacuum); (ii) splitting of a nonlinear solitary wave into two solitary waves\u0000(analogy of splitting of a particle into two particles); (iii) soliton behavior\u0000of some of the obtained waves; (iv) existence of solitons which move with the\u0000same velocity despite the different shape and amplitude of the solitons.","PeriodicalId":501592,"journal":{"name":"arXiv - PHYS - Exactly Solvable and Integrable Systems","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-12-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138547624","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Integrability, multifractality, and two-photon dynamics in disordered Tavis-Cummings models 无序塔维斯-康明斯模型中的积分性、多折射性和双光子动力学

arXiv - PHYS - Exactly Solvable and Integrable Systems Pub Date : 2023-12-06 DOI: arxiv-2312.03833

Agnieszka Wierzchucka, Francesco Piazza, Pieter W. Claeys

{"title":"Integrability, multifractality, and two-photon dynamics in disordered Tavis-Cummings models","authors":"Agnieszka Wierzchucka, Francesco Piazza, Pieter W. Claeys","doi":"arxiv-2312.03833","DOIUrl":"https://doi.org/arxiv-2312.03833","url":null,"abstract":"The Tavis-Cummings model is a paradigmatic central-mode model where a set of\u0000two-level quantum emitters (spins) are coupled to a collective cavity mode.\u0000Here we study the eigenstate spectrum, its localization properties and the\u0000effect on dynamics, focusing on the two-excitation sector relevant for\u0000nonlinear photonics. These models admit two sources of disorder: in the\u0000coupling between the spins and the cavity and in the energy shifts of the\u0000individual spins. While this model was known to be exactly solvable in the\u0000limit of a homogeneous coupling and inhomogeneous energy shifts, we here\u0000establish the solvability in the opposite limit of a homogeneous energy shift\u0000and inhomogeneous coupling, presenting the exact solution and corresponding\u0000conserved quantities. We identify three different classes of eigenstates,\u0000exhibiting different degrees of multifractality and semilocalization closely\u0000tied to the integrable points, and study their stability to perturbations away\u0000from these solvable points. The dynamics of the cavity occupation number away\u0000from equilibrium, exhibiting boson bunching and a two-photon blockade, is\u0000explicitly related to the localization properties of the eigenstates and\u0000illustrates how these models support a collective spin description despite the\u0000presence of disorder.","PeriodicalId":501592,"journal":{"name":"arXiv - PHYS - Exactly Solvable and Integrable Systems","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-12-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138554879","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Classification of semidiscrete hyperbolic type equations. The case of fifth order symmetries 半离散双曲型方程的分类。五阶对称的情况

arXiv - PHYS - Exactly Solvable and Integrable Systems Pub Date : 2023-11-30 DOI: arxiv-2312.03745

R. N. Garifullin

引用次数: 0

Entwining Yang-Baxter maps over Grassmann algebras Grassmann代数上的缠绕Yang-Baxter映射

arXiv - PHYS - Exactly Solvable and Integrable Systems Pub Date : 2023-11-30 DOI: arxiv-2311.18673

P. Adamopoulou, G. Papamikos

引用次数: 0

Yang-Baxter integrable open quantum systems Yang-Baxter可积开放量子系统

arXiv - PHYS - Exactly Solvable and Integrable Systems Pub Date : 2023-11-29 DOI: arxiv-2312.00064

Chiara Paletta

{"title":"Yang-Baxter integrable open quantum systems","authors":"Chiara Paletta","doi":"arxiv-2312.00064","DOIUrl":"https://doi.org/arxiv-2312.00064","url":null,"abstract":"This work is based on the author's PhD thesis. The main result of the thesis\u0000is the use of the boost operator to develop a systematic method to construct\u0000new integrable spin chains with nearest-neighbour interaction and characterized\u0000by an R-matrix of non-difference form. This method has the advantage of being\u0000more feasible than directly solving the Yang-Baxter equation. We applied this\u0000approach to various contexts, in particular, in the realm of open quantum\u0000systems, we achieved the first classification of integrable Lindbladians. These\u0000operators describe the dynamics of physical systems in contact with a Markovian\u0000environment. Within this classification, we discovered a novel deformation of\u0000the Hubbard model spanning three sites of the spin chain. Additionally, we\u0000applied our method to classify models with $mathfrak{su}(2)oplus\u0000mathfrak{su}(2)$ symmetry and we recovered the matrix part of the S-matrix of\u0000$AdS_5 times S^5$ derived by requiring centrally extended $mathfrak{su}(2|2)$\u0000symmetry. Furthermore, we focus on spin 1/2 chain on models of 8-Vertex type\u0000and we showed that the models of this class satisfy the free fermion condition.\u0000This enables us to express the transfer matrix associated to some of the models\u0000in a diagonal form, simplifying the computation of the eigenvalues and\u0000eigenvectors. The thesis is based on the works: 2003.04332, 2010.11231,\u00002011.08217, 2101.08279, 2207.14193, 2301.01612, 2305.01922.","PeriodicalId":501592,"journal":{"name":"arXiv - PHYS - Exactly Solvable and Integrable Systems","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-11-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138544037","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Réductions d'un système bidimensionnel de sine-Gordon à la sixième équation de Painlevé 将二维sine-Gordon系统简化为第六painleve方程

arXiv - PHYS - Exactly Solvable and Integrable Systems Pub Date : 2023-11-29 DOI: arxiv-2311.17469

Robert ConteENS Paris-Saclay, France and U of Hong Kong, A. Michel GrundlandUQTR, Canada

引用次数: 0

Spectral theory for self-adjoint Dirac operators with periodic potentials and inverse scattering transform for the defocusing nonlinear Schroedinger equation with periodic boundary conditions 具有周期势的自伴随狄拉克算子的谱理论和具有周期边界条件的非线性薛定谔方程的逆散射变换

arXiv - PHYS - Exactly Solvable and Integrable Systems Pub Date : 2023-11-29 DOI: arxiv-2311.18127

Gino Biondini, Zechuan Zhang

{"title":"Spectral theory for self-adjoint Dirac operators with periodic potentials and inverse scattering transform for the defocusing nonlinear Schroedinger equation with periodic boundary conditions","authors":"Gino Biondini, Zechuan Zhang","doi":"arxiv-2311.18127","DOIUrl":"https://doi.org/arxiv-2311.18127","url":null,"abstract":"We formulate the inverse spectral theory for a self-adjoint one-dimensional\u0000Dirac operator associated periodic potentials via a Riemann-Hilbert problem\u0000approach. We also use the resulting formalism to solve the initial value\u0000problem for the nonlinear Schroedinger equation. We establish a uniqueness\u0000theorem for the solutions of the Riemann-Hilbert problem, which provides a new\u0000method for obtaining the potential from the spectral data. Two additional,\u0000scalar Riemann-Hilbert problems are also formulated that provide conditions for\u0000the periodicity in space and time of the solution generated by arbitrary sets\u0000of spectral data. The formalism applies for both finite-genus and\u0000infinite-genus potentials. Importantly, the formalism shows that only a single\u0000set of Dirichlet eigenvalues is needed in order to uniquely reconstruct the\u0000potential of the Dirac operator and the corresponding solution of the\u0000defocusing NLS equation, in contrast with the representation of the solution of\u0000the NLS equation via the finite-genus formalism, in which two different sets of\u0000Dirichlet eigenvalues are used.","PeriodicalId":501592,"journal":{"name":"arXiv - PHYS - Exactly Solvable and Integrable Systems","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-11-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138543902","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Discretization of Camassa-Holm peakon equation using orthogonal polynomials and matrix $LR$ transformations 用正交多项式和矩阵LR变换离散Camassa-Holm peakon方程

arXiv - PHYS - Exactly Solvable and Integrable Systems Pub Date : 2023-11-28 DOI: arxiv-2311.16582

R. Watanabe, M. Iwasaki, S. Tsujimoto

引用次数: 0

Periodic finite-band solutions to the focusing nonlinear Schrödinger equation by the Riemann--Hilbert approach: inverse and direct problems 聚焦非线性Schrödinger方程的周期有限带解法:逆问题和正问题

arXiv - PHYS - Exactly Solvable and Integrable Systems Pub Date : 2023-11-28 DOI: arxiv-2311.16902

Dmitry Shepelsky, Iryna Karpenvko, Stepan Bogdanov, Jaroslaw E. Prilepsky

引用次数: 0

Space-like asymptotics of the thermal two-point functions of the XXZ spin-1/2 chain XXZ自旋1/2链的热两点函数的类空间渐近性

arXiv - PHYS - Exactly Solvable and Integrable Systems Pub Date : 2023-11-28 DOI: arxiv-2311.17196

F. Göhmann, K. K. Kozlowski

引用次数: 0