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On Quotient Spaces of Quantized Special Orthogonal Groups and their Topological Invariance 量化特殊正交群的商空间及其拓扑不变性
IF 1.2 3区 数学
Mathematical Physics, Analysis and Geometry Pub Date : 2026-07-07 DOI: 10.1007/s11040-026-09570-2
Akshay Bhuva, Surajit Biswas, Bipul Saurabh
{"title":"On Quotient Spaces of Quantized Special Orthogonal Groups and their Topological Invariance","authors":"Akshay Bhuva,&nbsp;Surajit Biswas,&nbsp;Bipul Saurabh","doi":"10.1007/s11040-026-09570-2","DOIUrl":"10.1007/s11040-026-09570-2","url":null,"abstract":"<div><p>In this article, we study a family of quantum homogeneous spaces, namely,<span>(SO_qleft( mathcal {N}right) /SO_qleft( mathcal {N}-2right) )</span>. By applying a two-step Zhelobenko branching rule, we show that the <span>(C^*)</span>-algebras <span>(Cleft( SO_qleft( mathcal {N}right) /SO_qleft( mathcal {N}-2right) right) )</span> are generated by the entries of the first and the last rows of the fundamental matrix of the quantum groups <span>(SO_qleft( mathcal {N}right) )</span>. We then construct a chain of short exact sequences, and using that, we compute <i>K</i>-groups of these spaces with explicit generators. Invoking homogeneous <span>(C^*)</span>-extension theory, we show <i>q</i>-independence of some intermediate <span>(C^*)</span>-algebras arising as the middle <span>(C^*)</span>-algebra of these short exact sequences. As a consequence, we get the <i>q</i>-invariance of <span>(SO_q(3))</span>, <span>(SO_q(5)/SO_q(3))</span>, <span>(SO_q(4)/SO_q(2))</span>, and <span>(SO_q(6)/SO_q(4))</span>.</p></div>","PeriodicalId":694,"journal":{"name":"Mathematical Physics, Analysis and Geometry","volume":"29 3","pages":""},"PeriodicalIF":1.2,"publicationDate":"2026-07-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148465490","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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
On the Relation Between the Dual AKP Equation and an Equation by King and Schief, and its N-soliton Solution 对偶AKP方程与King和Schief方程的关系及其n孤子解
IF 1.2 3区 数学
Mathematical Physics, Analysis and Geometry Pub Date : 2026-07-06 DOI: 10.1007/s11040-026-09574-y
Peter H. van der Kamp, Da-jun Zhang, G. R. W. Quispel
{"title":"On the Relation Between the Dual AKP Equation and an Equation by King and Schief, and its N-soliton Solution","authors":"Peter H. van der Kamp,&nbsp;Da-jun Zhang,&nbsp;G. R. W. Quispel","doi":"10.1007/s11040-026-09574-y","DOIUrl":"10.1007/s11040-026-09574-y","url":null,"abstract":"<div><p>The Dual of the lattice AKP (DAKP) equation [P.H. van der Kamp et al., J. Phys. A 51, 365202 (2018)] is equivalent to a 14-point equation related to the lattice BKP equation, found by King and Schief (KS), and hence it is integrable. We show that the KS equation is dual to Hirota’s version of AKP, and we verify the conjectured <i>N</i>-soliton solution of DAKP, using Miwa’s parametrisation of the AKP and BKP soliton solutions.</p></div>","PeriodicalId":694,"journal":{"name":"Mathematical Physics, Analysis and Geometry","volume":"29 3","pages":""},"PeriodicalIF":1.2,"publicationDate":"2026-07-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s11040-026-09574-y.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148465086","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: 0
Non-squeezing and capacities for some calibrated geometries 非挤压和一些校准几何的能力
IF 1.2 3区 数学
Mathematical Physics, Analysis and Geometry Pub Date : 2026-07-04 DOI: 10.1007/s11040-026-09576-w
Kain Dineen, Spiro Karigiannis
{"title":"Non-squeezing and capacities for some calibrated geometries","authors":"Kain Dineen,&nbsp;Spiro Karigiannis","doi":"10.1007/s11040-026-09576-w","DOIUrl":"10.1007/s11040-026-09576-w","url":null,"abstract":"<div><p>It was shown by Barron–Shafiee that an analogue of Gromov’s non-squeezing theorem holds for affine maps which preserve a power <span>(omega ^k)</span> of the symplectic form <span>(omega )</span> on <span>(mathbb {R}^{2n})</span>. In the present paper, we state and prove in two ways an improved version of their result which is closer to the classical affine non-squeezing theorem. One proof closely follows their argument, and the other consists of a reduction to the classical case by showing that, except for the case <span>(k = n)</span>, every linear map that preserves <span>(omega ^k)</span> must be symplectic or anti-symplectic. We then study when a calibration form satisfies an (affine) non-squeezing theorem. Particular focus is given to the special Lagrangian case, where we are able to establish an affine non-squeezing theorem for the holomorphic volume form <span>(Omega = dz^1 wedge cdots wedge dz^n)</span>. The classical symplectic affine rigidity theorem states roughly that a non-singular linear map is symplectic or anti-symplectic if and only if it preserves the “capacity” of every ellipsoid. We establish an affine special Lagrangian version of this theorem under the necessary assumption that the map is complex-linear. We also discuss some natural future questions.</p></div>","PeriodicalId":694,"journal":{"name":"Mathematical Physics, Analysis and Geometry","volume":"29 3","pages":""},"PeriodicalIF":1.2,"publicationDate":"2026-07-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148380313","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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 Cellular Automata on Finite Fields of Order (2^n) 有限阶域上的可积元胞自动机 (2^n)
IF 1.2 3区 数学
Mathematical Physics, Analysis and Geometry Pub Date : 2026-06-22 DOI: 10.1007/s11040-026-09569-9
Aoi Araoka, Tetsuji Tokihiro
{"title":"Integrable Cellular Automata on Finite Fields of Order (2^n)","authors":"Aoi Araoka,&nbsp;Tetsuji Tokihiro","doi":"10.1007/s11040-026-09569-9","DOIUrl":"10.1007/s11040-026-09569-9","url":null,"abstract":"<div><p>This paper explores cellular automata (CA) constructed from Yang–Baxter maps over finite fields <span>(mathbb {F}_{2^n})</span>. We define <i>R</i>-matrices using a map <i>f</i> on <span>(mathbb {F}_{2^n})</span> and establish necessary and sufficient conditions for <i>f</i> to satisfy the Yang–Baxter equation. We show that these conditions become remarkably streamlined in characteristic two. An exhaustive search for bijective solutions in fields of order 4, 8, and 16 yields 16, 736, and 269,056 maps, respectively. Analysis of the resulting CA under helical boundary conditions reveals a consistent alignment between the temporal period and the field order. We propose the conjecture that this periodic identity holds generally for <span>(mathbb {F}_{2^n})</span>, supported by analytical proofs for <span>(n=2)</span> and <span>(n=3)</span>. Our results further indicate that bijectivity is a fundamental requirement for this periodic behavior.</p></div>","PeriodicalId":694,"journal":{"name":"Mathematical Physics, Analysis and Geometry","volume":"29 3","pages":""},"PeriodicalIF":1.2,"publicationDate":"2026-06-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148323337","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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
On Some Second Order Equations Associated with Painlevé Third and Fifth Equation 关于与painleve3、5方程相关的一些二阶方程
IF 1.1 3区 数学
Mathematical Physics, Analysis and Geometry Pub Date : 2026-06-15 DOI: 10.1007/s11040-026-09568-w
Ewa Ciechanowicz
{"title":"On Some Second Order Equations Associated with Painlevé Third and Fifth Equation","authors":"Ewa Ciechanowicz","doi":"10.1007/s11040-026-09568-w","DOIUrl":"10.1007/s11040-026-09568-w","url":null,"abstract":"<div><p>We present results concerning value distribution of solutions of two second order equations with transcendental coefficients. The equations are related to Painlevé equations <span>(P_3)</span> and <span>(P_5)</span>, but also interrelated with each other. We mainly focus on the existence of exceptional values, but consider other value distribution and growth properties of their solutions.</p></div>","PeriodicalId":694,"journal":{"name":"Mathematical Physics, Analysis and Geometry","volume":"29 3","pages":""},"PeriodicalIF":1.1,"publicationDate":"2026-06-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148247745","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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 Trouble With Deautonomising Higher Order Maps 去自治高阶映射的麻烦
IF 1.1 3区 数学
Mathematical Physics, Analysis and Geometry Pub Date : 2026-06-11 DOI: 10.1007/s11040-026-09563-1
Ralph Willox, Basil Grammaticos, Alfred Ramani
{"title":"The Trouble With Deautonomising Higher Order Maps","authors":"Ralph Willox,&nbsp;Basil Grammaticos,&nbsp;Alfred Ramani","doi":"10.1007/s11040-026-09563-1","DOIUrl":"10.1007/s11040-026-09563-1","url":null,"abstract":"<div><p>The deautonomisation of birational maps that have the singularity confinement property, i.e. the construction of nonautonomous versions of such maps that preserve the singularity properties of the original, has proven crucial in our understanding of the mathematical properties behind the integrability of second order maps. For example, the deautonomisation procedure led directly to the development of a general theory of discrete Painlevé equations, and it seems highly likely it will play a crucial role in any future theory of higher dimensional Painlevé equations as well. Generally speaking however, higher order integrable mappings may have non-confined singularities and it is important to understand if, and how, deautonomisation should work for such mappings. In this paper we explore different deautonomisation scenarios on a series of carefully constructed higher order mappings, integrable as well as non-integrable, that possess non-confined singularities and we challenge some common assumptions regarding the co-dimensionality of the singular loci that might play a role in the deautonomisation process. Along the way we also propose a novel procedure to calculate the growth of the multiplicities of singularities that appear in so-called anticonfined singularity patterns, based on an ultradiscrete version of the mapping.</p></div>","PeriodicalId":694,"journal":{"name":"Mathematical Physics, Analysis and Geometry","volume":"29 2","pages":""},"PeriodicalIF":1.1,"publicationDate":"2026-06-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s11040-026-09563-1.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148236784","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: 0
Braided Symmetries of (SU_{q,phi }(2)) and Podleś Spheres (SU_{q,phi }(2))和podleka球的编织对称性
IF 1.1 3区 数学
Mathematical Physics, Analysis and Geometry Pub Date : 2026-06-05 DOI: 10.1007/s11040-026-09565-z
Rafał Bistroń, Andrzej Sitarz
{"title":"Braided Symmetries of (SU_{q,phi }(2)) and Podleś Spheres","authors":"Rafał Bistroń,&nbsp;Andrzej Sitarz","doi":"10.1007/s11040-026-09565-z","DOIUrl":"10.1007/s11040-026-09565-z","url":null,"abstract":"<div><p>We present an explicit formulation of the braided symmetries of quantum spheres by introducing a braided quantum Hopf algebra <span>({mathcal {U}}_{q, phi })</span> and demonstrating that the quantum spheres are <span>({mathcal {U}}_{q, phi })</span> braided Hopf module algebras. Furthermore, we demonstrate that they are the only quadratic algebras generated by the fundamental representation of <span>({mathcal {U}}_{q, phi })</span> which are braided <span>({mathcal {U}}_{q, phi })</span>-modules.</p></div>","PeriodicalId":694,"journal":{"name":"Mathematical Physics, Analysis and Geometry","volume":"29 2","pages":""},"PeriodicalIF":1.1,"publicationDate":"2026-06-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s11040-026-09565-z.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148172934","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: 0
Soliton and Rational Solutions in the Modified Boussinesq Equation 修正Boussinesq方程的孤子解和有理解
IF 1.1 3区 数学
Mathematical Physics, Analysis and Geometry Pub Date : 2026-06-05 DOI: 10.1007/s11040-026-09567-x
Fang-Cheng Fan, Wei Huang, Guo-Fu Yu
{"title":"Soliton and Rational Solutions in the Modified Boussinesq Equation","authors":"Fang-Cheng Fan,&nbsp;Wei Huang,&nbsp;Guo-Fu Yu","doi":"10.1007/s11040-026-09567-x","DOIUrl":"10.1007/s11040-026-09567-x","url":null,"abstract":"<div><p>This paper investigates soliton and rational solutions to the modified Boussinesq equation. The main methods employed in this work to construct these solutions are Hirota’s bilinear method combined with the Kadomtsev-Petviashvili (KP) hierarchy reduction technique. These solutions are expressed in terms of <span>(N times N)</span> Gram-type determinants. Dark solitons, bright solitons, and periodic solutions are derived herein. Asymptotic analysis of the two-soliton solution reveals that the interaction between the two solitons is elastic. By introducing two well-designed differential operators in the dimension reduction process, the matrix elements in the determinants of the rational solutions are expressed in terms of Schur polynomials. The rational solutions exhibit an X-shaped evolution pattern in both the <span>(x)</span>- and <span>(t)</span>-directions. The dynamics of these solutions are systematically studied, and the relationship between parameters and solution structures is also discussed. The results presented in this paper may contribute to a better understanding of certain physical phenomena in fluid dynamics.</p></div>","PeriodicalId":694,"journal":{"name":"Mathematical Physics, Analysis and Geometry","volume":"29 2","pages":""},"PeriodicalIF":1.1,"publicationDate":"2026-06-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148172933","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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
Inverse Scattering and Riemann-Hilbert Problems for a Class of High-Dimensional Modified Pavlov Systems 一类高维修正巴甫洛夫系统的逆散射和Riemann-Hilbert问题
IF 1.1 3区 数学
Mathematical Physics, Analysis and Geometry Pub Date : 2026-06-01 DOI: 10.1007/s11040-026-09566-y
Linlin Gui, Yufeng Zhang
{"title":"Inverse Scattering and Riemann-Hilbert Problems for a Class of High-Dimensional Modified Pavlov Systems","authors":"Linlin Gui,&nbsp;Yufeng Zhang","doi":"10.1007/s11040-026-09566-y","DOIUrl":"10.1007/s11040-026-09566-y","url":null,"abstract":"<div><p>In this paper, we introduce a pair of 2+1-dimensional non-isospectral vector fields whose commutation gives rise to a new integrable system which can reduces to the celebrated Pavlov equation. We refer to the new integrable system as the modified Pavlov (mP) system: (a) We study the inverse scattering problem for the multidimensional vector field and Cauchy Problem, and analyze the longtime behaviour of the formal solutions of mP system by introducing a nonlinear Riemann-Hilbert (RH) problem. Meanwhile, a class of particular solutions with arbitrary differential functions is characterized; (b) The complexification of the independent variables <i>x</i>, <i>y</i>, <i>t</i> of the 2+1-dimensional mP system yields the 4+2 dimensions, then reducing the systems from 4+2 to the 3+1 and 3+2 dimensions, and the Lax pairs of the reduced systems are constructed; (c) The Cauchy initial value problems (IVPs) of the high-dimensional mP systems, i.e., 3+1, 3+2 and 4+2 dimensions, are solved by the inverse scattering transform (IST) method; (d) In analogy to 2+1 dimensions, the asymptotics behaviour of the solutions for the 3+1-dimensional mP system is investigated.</p></div>","PeriodicalId":694,"journal":{"name":"Mathematical Physics, Analysis and Geometry","volume":"29 2","pages":""},"PeriodicalIF":1.1,"publicationDate":"2026-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148172128","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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
Geometry of Associated Quantum Vector Bundles and the Quantum Gauge Group 相关量子向量束的几何和量子规范群
IF 1.1 3区 数学
Mathematical Physics, Analysis and Geometry Pub Date : 2026-05-09 DOI: 10.1007/s11040-026-09564-0
Gustavo Amilcar Saldaña Moncada
{"title":"Geometry of Associated Quantum Vector Bundles and the Quantum Gauge Group","authors":"Gustavo Amilcar Saldaña Moncada","doi":"10.1007/s11040-026-09564-0","DOIUrl":"10.1007/s11040-026-09564-0","url":null,"abstract":"<div><p>It is well–known that, given a principal <i>G</i>–bundle equipped with a principal connection, one can associate to every unitary finite–dimensional representation of <i>G</i> a linear connection and a compatible Hermitian structure on the corresponding associated vector bundle. Moreover, the gauge group acts both on the space of principal connections and on the space of induced linear connections defined on the associated vector bundles. The aim of this paper is to present the <i>non–commutative geometrical</i> counterpart of these <i>classical</i> facts within the framework of quantum principal bundles and quantum principal connections.</p></div>","PeriodicalId":694,"journal":{"name":"Mathematical Physics, Analysis and Geometry","volume":"29 2","pages":""},"PeriodicalIF":1.1,"publicationDate":"2026-05-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147829975","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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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