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On an equation arising by reduction of the Drinfeld-Sokolov hierarchy 关于德林费尔德-索科洛夫层次还原法产生的方程
arXiv - PHYS - Exactly Solvable and Integrable Systems Pub Date : 2024-05-21 DOI: arxiv-2405.12606
R. ConteENS Paris Saclay
{"title":"On an equation arising by reduction of the Drinfeld-Sokolov hierarchy","authors":"R. ConteENS Paris Saclay","doi":"arxiv-2405.12606","DOIUrl":"https://doi.org/arxiv-2405.12606","url":null,"abstract":"A seventh order ordinary differential equation (ODE) arising by reduction of\u0000the Drinfeld-Sokolov hierarchyis shown to be identical to a similarity\u0000reduction of an equationin the hierarchy of Sawada-Kotera.We also exhibit its\u0000link with a particular F-VI,a fourth order ODE isolated by Cosgrove which is\u0000likely to define a higher order Painlev'e function.","PeriodicalId":501592,"journal":{"name":"arXiv - PHYS - Exactly Solvable and Integrable Systems","volume":"46 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-05-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141151530","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
On integrable reductions of two-dimensional Toda-type lattices 论二维托达型网格的可积分还原
arXiv - PHYS - Exactly Solvable and Integrable Systems Pub Date : 2024-05-17 DOI: arxiv-2405.10666
I. T. Habibullin, A. U. Sakieva
{"title":"On integrable reductions of two-dimensional Toda-type lattices","authors":"I. T. Habibullin, A. U. Sakieva","doi":"arxiv-2405.10666","DOIUrl":"https://doi.org/arxiv-2405.10666","url":null,"abstract":"The article considers lattices of the two-dimensional Toda type, which can be\u0000interpreted as dressing chains for spatially two-dimensional generalizations of\u0000equations of the class of nonlinear Schr\"odinger equations. The well-known\u0000example of this kind of generalization is the Davey-Stewartson equation. It\u0000turns out that the finite-field reductions of these lattices, obtained by\u0000imposing cutoff boundary conditions of an appropriate type, are Darboux\u0000integrable, i.e., they have complete sets of characteristic integrals. An\u0000algorithm for constructing complete sets of characteristic integrals of finite\u0000field systems using Lax pairs and Miura-type transformations is discussed.","PeriodicalId":501592,"journal":{"name":"arXiv - PHYS - Exactly Solvable and Integrable Systems","volume":"33 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-05-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141151555","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
Emergent magnetic field and vector potential of the toroidal magnetic hopfions 环状磁性霍普夫子的新兴磁场和矢量势
arXiv - PHYS - Exactly Solvable and Integrable Systems Pub Date : 2024-05-15 DOI: arxiv-2405.10811
Konstantin Y. Guslienko
{"title":"Emergent magnetic field and vector potential of the toroidal magnetic hopfions","authors":"Konstantin Y. Guslienko","doi":"arxiv-2405.10811","DOIUrl":"https://doi.org/arxiv-2405.10811","url":null,"abstract":"Magnetic hopfions are localized magnetic solitons with non-zero 3D\u0000topological charge (Hopf index). Here I present an analytical calculation of\u0000the toroidal magnetic hopfion vector potential, emergent magnetic field, the\u0000Hopf index, and the magnetization configuration. The calculation method is\u0000based on the concept of the spinor representation of the Hopf mapping. The\u0000hopfions with arbitrary values of the azimuthal and poloidal vorticities are\u0000considered. The special role of the toroidal coordinates and their connection\u0000with the emergent vector po tential gauge are demonstrated. The hopfion\u0000magnetization field is found explicitly for the arbitrary Hopf indices. It is\u0000shown that the Hopf charge density can be represented as a Jacobian of the\u0000transformation from the toroidal to the cylindrical coordinates.","PeriodicalId":501592,"journal":{"name":"arXiv - PHYS - Exactly Solvable and Integrable Systems","volume":"51 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-05-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141151529","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
On Lax representations under the gauge equivalence relation and Miura-type transformations for lattice equations 论格网方程的轨距等价关系下的拉克斯表征和米乌拉型变换
arXiv - PHYS - Exactly Solvable and Integrable Systems Pub Date : 2024-05-14 DOI: arxiv-2405.08579
Sergei Igonin
{"title":"On Lax representations under the gauge equivalence relation and Miura-type transformations for lattice equations","authors":"Sergei Igonin","doi":"arxiv-2405.08579","DOIUrl":"https://doi.org/arxiv-2405.08579","url":null,"abstract":"We study matrix Lax representations (MLRs) for differential-difference\u0000(lattice) equations. For a given equation, two MLRs are said to be gauge\u0000equivalent if one of them can be obtained from the other by means of a matrix\u0000gauge transformation. We present results on the following questions: 1. When is a given MLR gauge equivalent to an MLR suitable for constructing\u0000differential-difference Miura-type transformations by the method of [G.\u0000Berkeley, S. Igonin, J. Phys. A (2016), arXiv:1512.09123]? 2. When is a given MLR gauge equivalent to a trivial MLR? Furthermore, we present new examples of integrable differential-difference\u0000equations with Miura-type transformations.","PeriodicalId":501592,"journal":{"name":"arXiv - PHYS - Exactly Solvable and Integrable Systems","volume":"253 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-05-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141059138","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
Signatures of Integrability and Exactly Solvable Dynamics in an Infinite-Range Many-Body Floquet Spin System 无限范围多体浮凸自旋系统中的积分性和精确可解动力学特征
arXiv - PHYS - Exactly Solvable and Integrable Systems Pub Date : 2024-05-10 DOI: arxiv-2405.15797
Harshit Sharma, Udaysinh T. Bhosale
{"title":"Signatures of Integrability and Exactly Solvable Dynamics in an Infinite-Range Many-Body Floquet Spin System","authors":"Harshit Sharma, Udaysinh T. Bhosale","doi":"arxiv-2405.15797","DOIUrl":"https://doi.org/arxiv-2405.15797","url":null,"abstract":"In a recent work Sharma and Bhosale [Phys. Rev. B, 109, 014412 (2024)],\u0000$N$-spin Floquet model having infinite range Ising interaction was introduced.\u0000In this paper, we generalized the strength of interaction to $J$, such that\u0000$J=1$ case reduces to the aforementioned work. We show that for $J=1/2$ the\u0000model still exhibits integrability for an even number of qubits only. We\u0000analytically solve the cases of $6$, $8$, $10$, and $12$ qubits, finding its\u0000eigensystem, dynamics of entanglement for various initial states, and the\u0000unitary evolution operator. These quantities exhibit the signature of quantum\u0000integrability (QI). For the general case of even-$N > 12$ qubits, we\u0000conjuncture the presence of QI using the numerical evidences such as spectrum\u0000degeneracy, and the exact periodic nature of both the entanglement dynamics and\u0000the time-evolved unitary operator. We numerically show the absence of QI for\u0000odd $N$ by observing a violation of the signatures of QI. We analytically and\u0000numerically find that the maximum value of time-evolved concurrence\u0000($C_{mbox{max}}$) decreases with $N$, indicating the multipartite nature of\u0000entanglement. Possible experiments to verify our results are discussed.","PeriodicalId":501592,"journal":{"name":"arXiv - PHYS - Exactly Solvable and Integrable Systems","volume":"27 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-05-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141170132","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
On quadrirational pentagon maps 关于四边五边形映射
arXiv - PHYS - Exactly Solvable and Integrable Systems Pub Date : 2024-05-08 DOI: arxiv-2405.04945
Charalampos Evripidou, Pavlos Kassotakis, Anastasios Tongas
{"title":"On quadrirational pentagon maps","authors":"Charalampos Evripidou, Pavlos Kassotakis, Anastasios Tongas","doi":"arxiv-2405.04945","DOIUrl":"https://doi.org/arxiv-2405.04945","url":null,"abstract":"We classify rational solutions of a specific type of the set theoretical\u0000version of the pentagon equation. That is, we find all quadrirational maps\u0000$R:(x,y)mapsto (u(x,y),v(x,y)),$ where $u, v$ are two rational functions on\u0000two arguments, that serve as solutions of the pentagon equation. Furthermore,\u0000provided a pentagon map that admits a partial inverse, we obtain genuine\u0000entwining pentagon set theoretical solutions.","PeriodicalId":501592,"journal":{"name":"arXiv - PHYS - Exactly Solvable and Integrable Systems","volume":"22 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-05-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140930360","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
Simple recursions displaying interesting evolutions 显示有趣演变的简单递归
arXiv - PHYS - Exactly Solvable and Integrable Systems Pub Date : 2024-05-01 DOI: arxiv-2405.00370
Francesco Calogero
{"title":"Simple recursions displaying interesting evolutions","authors":"Francesco Calogero","doi":"arxiv-2405.00370","DOIUrl":"https://doi.org/arxiv-2405.00370","url":null,"abstract":"Some simple nonlinear recursions which can be completely managed are\u0000identified and the behaviour of all their solutions is ascertained.","PeriodicalId":501592,"journal":{"name":"arXiv - PHYS - Exactly Solvable and Integrable Systems","volume":"103 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140833988","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
Investigation of shallow water waves near the coast or in lake environments via the KdV-Calogero-Bogoyavlenskii-Schiff equation 通过 KdV-Calogero-Bogoyavlenskii-Schiff 方程研究海岸附近或湖泊环境中的浅水波
arXiv - PHYS - Exactly Solvable and Integrable Systems Pub Date : 2024-04-29 DOI: arxiv-2404.18697
Peng-Fei Han, Yi Zhang
{"title":"Investigation of shallow water waves near the coast or in lake environments via the KdV-Calogero-Bogoyavlenskii-Schiff equation","authors":"Peng-Fei Han, Yi Zhang","doi":"arxiv-2404.18697","DOIUrl":"https://doi.org/arxiv-2404.18697","url":null,"abstract":"Shallow water waves phenomena in nature attract the attention of scholars and\u0000play an important role in fields such as tsunamis, tidal waves, solitary waves,\u0000and hydraulic engineering. Hereby, for the shallow water waves phenomena in\u0000various natural environments, we study the KdV-Calogero-Bogoyavlenskii-Schiff\u0000(KdV-CBS) equation. Based on the Bell polynomial theory, the B{\"a}cklund\u0000transformation, Lax pair and infinite conservation laws of the KdV-CBS equation\u0000are derived, and it is proved that it is completely integrable in Lax pair\u0000sense. Various types of mixed solutions are constructed by using a combination\u0000of Homoclinic test method and Mathematica symbolic computations. These findings\u0000have important significance for the discipline, offering vital insights into\u0000the intricate dynamics of the KdV-CBS equation. We hope that our research\u0000results could help the researchers understand the nonlinear complex phenomena\u0000of the shallow water waves in oceans, rivers and coastal areas.","PeriodicalId":501592,"journal":{"name":"arXiv - PHYS - Exactly Solvable and Integrable Systems","volume":"38 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-04-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140834245","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
The symmetric (2+1)-dimensional Lotka-Volterra equation with self-consistent sources 具有自洽源的对称 (2+1)- 维 Lotka-Volterra 方程
arXiv - PHYS - Exactly Solvable and Integrable Systems Pub Date : 2024-04-23 DOI: arxiv-2404.14969
Mengyuan Cui, Chunxia Li, Yuqin Yao
{"title":"The symmetric (2+1)-dimensional Lotka-Volterra equation with self-consistent sources","authors":"Mengyuan Cui, Chunxia Li, Yuqin Yao","doi":"arxiv-2404.14969","DOIUrl":"https://doi.org/arxiv-2404.14969","url":null,"abstract":"The symmetric (2+1)-dimensional Lotka-Volterra equation with self-consistent\u0000sources is constructed using the source generation producure, whose solutions\u0000are expressed in terms of pfaffians. As special cases of the pfaffian\u0000solutions, different types of explicit solutions are presented, including\u0000dromions, soliton solutions and breather solutions.","PeriodicalId":501592,"journal":{"name":"arXiv - PHYS - Exactly Solvable and Integrable Systems","volume":"118 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-04-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140798586","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
Discrete nonlinear Schrödinger type equations: Solutions and continuum limits 离散非线性薛定谔型方程：解与连续极限
arXiv - PHYS - Exactly Solvable and Integrable Systems Pub Date : 2024-04-22 DOI: arxiv-2404.14060
Song-lin Zhao, Xiao-hui Feng, Wei Feng
{"title":"Discrete nonlinear Schrödinger type equations: Solutions and continuum limits","authors":"Song-lin Zhao, Xiao-hui Feng, Wei Feng","doi":"arxiv-2404.14060","DOIUrl":"https://doi.org/arxiv-2404.14060","url":null,"abstract":"As local and nonlocal reductions of a discrete second-order\u0000Ablowitz-Kaup-Newell-Segur equation, two discrete nonlinear Schr\"odinger type\u0000equations are considered. Through the bilinearization reduction method, we\u0000construct double Casoratian solutions of the reduced discrete nonlinear\u0000Schr\"odinger type equations, including soliton solutions and Jordan-block\u0000solutions.Dynamics of the obtained one-soliton and two-soliton solutions are\u0000analyzed and illustrated. Moreover,both semi-continuous limit and full\u0000continuous limit, are applied to obtain solutions of the local and nonlocal\u0000semi-discrete nonlinear Schr\"odinger type equations, as well as the local and\u0000nonlocal continuous nonlinear Schr\"odinger type equations.","PeriodicalId":501592,"journal":{"name":"arXiv - PHYS - Exactly Solvable and Integrable Systems","volume":"29 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-04-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140798813","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
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