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On noncommutative modified KP systems 关于非交换修正 KP 系统
IF 1 4区 物理与天体物理
Theoretical and Mathematical Physics Pub Date : 2024-11-26 DOI: 10.1134/S0040577924110072
Zheng Wang, Chuanzhong Li
{"title":"On noncommutative modified KP systems","authors":"Zheng Wang,&nbsp;Chuanzhong Li","doi":"10.1134/S0040577924110072","DOIUrl":"10.1134/S0040577924110072","url":null,"abstract":"<p> We investigate the gauge transformations of the noncommutative modified KP hierarchy and the noncommutative constrained modified KP hierarchy in the Kupershmidt–Kiso version. By introducing the Orlov–Schulman operator, which depends on time variables and dressing operators, we construct the quantum torus symmetry for the noncommutative modified KP hierarchy. We also give a recursion operator for the noncommutative constrained modified KP hierarchy. We present an extended noncommutative modified KP hierarchy. The compatibility equations between the noncommutative modified KP flows and the extended noncommutative modified KP flows are constructed. </p>","PeriodicalId":797,"journal":{"name":"Theoretical and Mathematical Physics","volume":"221 2","pages":"1882 - 1900"},"PeriodicalIF":1.0,"publicationDate":"2024-11-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142714485","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Cauchy matrix approach to novel extended semidiscrete KP-type systems 新型扩展半离散 KP 型系统的考奇矩阵方法
IF 1 4区 物理与天体物理
Theoretical and Mathematical Physics Pub Date : 2024-11-26 DOI: 10.1134/S0040577924110096
Hong-juan Tian, A. Silem
{"title":"Cauchy matrix approach to novel extended semidiscrete KP-type systems","authors":"Hong-juan Tian,&nbsp;A. Silem","doi":"10.1134/S0040577924110096","DOIUrl":"10.1134/S0040577924110096","url":null,"abstract":"<p> Two novel extended semidiscrete KP-type systems, namely, partial differential–difference systems with one continuous and two discrete variables, are investigated. Introducing an arbitrary function into the Cauchy matrix function or the plane wave factor allows implementing extended integrable systems within the Cauchy matrix approach. We introduce the bilinear <span>(DDelta^2)</span>KP system, the extended <span>(DDelta^2)</span>pKP, <span>(DDelta^2)</span>pmKP, and <span>(DDelta^2)</span>SKP systems, all of which are based on the Cauchy matrix approach. This results in a diversity of solutions for these extended systems as contrasted to the usual multiple soliton solutions. </p>","PeriodicalId":797,"journal":{"name":"Theoretical and Mathematical Physics","volume":"221 2","pages":"1929 - 1939"},"PeriodicalIF":1.0,"publicationDate":"2024-11-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142714487","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Algebraic structures behind the Yang–Baxterization process 杨-巴克斯特化过程背后的代数结构
IF 1 4区 物理与天体物理
Theoretical and Mathematical Physics Pub Date : 2024-11-26 DOI: 10.1134/S0040577924110114
C. Özdemir, I. Gahramanov
{"title":"Algebraic structures behind the Yang–Baxterization process","authors":"C. Özdemir,&nbsp;I. Gahramanov","doi":"10.1134/S0040577924110114","DOIUrl":"10.1134/S0040577924110114","url":null,"abstract":"<p> We discuss the process of Yang–Baxterization in representations of the braid group. We discuss the role played by <span>(n)</span>-CB algebras in Yang–Baxterization. We present diagrams depicting the defining relations for the <span>(4)</span>-CB algebras. These relations are illustrated using the isomorphism between the general free algebra generated by <span>({1})</span>, <span>({E_i})</span>, and <span>({G_i})</span> (the generators of the Birman–Murakami–Wenzl algebra) and Kauffman’s tangle algebra. </p>","PeriodicalId":797,"journal":{"name":"Theoretical and Mathematical Physics","volume":"221 2","pages":"1959 - 1980"},"PeriodicalIF":1.0,"publicationDate":"2024-11-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142714490","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Effects of a global monopole on quantum systems with the exponential potential 全局单极对指数势量子系统的影响
IF 1 4区 物理与天体物理
Theoretical and Mathematical Physics Pub Date : 2024-10-24 DOI: 10.1134/S0040577924100118
F. Ahmed, A. Bouzenada
{"title":"Effects of a global monopole on quantum systems with the exponential potential","authors":"F. Ahmed,&nbsp;A. Bouzenada","doi":"10.1134/S0040577924100118","DOIUrl":"10.1134/S0040577924100118","url":null,"abstract":"<p> We study the Schrödinger wave equation with an exponential potential in the context of a point-like global monopole. This exponential potential is composed of a generalized <span>(q)</span>-deformed Hulthen potential and a Yukawa-type potential. We incorporate the Greene–Aldrich approximation scheme to handle the centrifugal and other terms and obtain an approximate eigenvalue solutions in terms of special functions. We show that the eigenvalue solution is influenced by the topological defect with this exponential potential, and therefore breaks the degeneracy of the spectrum compared to the flat-space case. We then use this eigenvalue solution to analyze a few superposed potential models, and discuss the results. </p>","PeriodicalId":797,"journal":{"name":"Theoretical and Mathematical Physics","volume":"221 1","pages":"1756 - 1765"},"PeriodicalIF":1.0,"publicationDate":"2024-10-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142518704","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","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 constrained discrete mKP hierarchies: Gauge transformations and the generalized Wronskian solutions 关于受约束离散 mKP 层次：量子变换与广义弗伦斯基解
IF 1 4区 物理与天体物理
Theoretical and Mathematical Physics Pub Date : 2024-10-24 DOI: 10.1134/S0040577924100064
Ge Yi, Liyun Wang, Kelei Tian, Ying Xu
{"title":"On the constrained discrete mKP hierarchies: Gauge transformations and the generalized Wronskian solutions","authors":"Ge Yi,&nbsp;Liyun Wang,&nbsp;Kelei Tian,&nbsp;Ying Xu","doi":"10.1134/S0040577924100064","DOIUrl":"10.1134/S0040577924100064","url":null,"abstract":"<p> We apply the gauge transformations <span>(T_mathrm{D})</span> (differential type) and <span>(T_mathrm{I})</span> (integral type) to study the discrete mKP hierarchies. We prove that <span>(T_mathrm{D})</span> and <span>(T_mathrm{I})</span> can be commutative and the product of <span>(T_mathrm{D})</span> and <span>(T_mathrm{I})</span> satisfies the Sato equation. By means of gauge transformations, we arrive at the necessary and sufficient condition for reducing the generalized Wronskian solutions to constrained hierarchies. Finally, we give an example in the Appendix. </p>","PeriodicalId":797,"journal":{"name":"Theoretical and Mathematical Physics","volume":"221 1","pages":"1675 - 1694"},"PeriodicalIF":1.0,"publicationDate":"2024-10-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142518791","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Quasi-Grammian soliton and kink dynamics of an (M)-component semidiscrete coupled integrable system 一个（M）分量半离散耦合可积分系统的准格拉米安孤子和扭结动力学
IF 1 4区 物理与天体物理
Theoretical and Mathematical Physics Pub Date : 2024-10-24 DOI: 10.1134/S0040577924100052
A. Inam, M. ul Hassan
{"title":"Quasi-Grammian soliton and kink dynamics of an (M)-component semidiscrete coupled integrable system","authors":"A. Inam,&nbsp;M. ul Hassan","doi":"10.1134/S0040577924100052","DOIUrl":"10.1134/S0040577924100052","url":null,"abstract":"<p> We investigate the standard binary Darboux transformation (SBDT) for an <span>(M)</span>-component sdC integrable system. For this, we construct the Darboux matrix using specific eigenvector solutions associated to the Lax pair, not only in the direct space but also in the adjoint space, resulting in the binary Darboux matrix. By the iterative application of the SBDT, we derive quasi-Grammian soliton solutions of the <span>(M)</span>-component sdC integrable system. We also examine the Darboux transformation (DT) applied to matrix solutions of the sdC integrable system, expressing solutions using quasideterminants. Additionally, we thoroughly discuss the DT applied to scalar solutions of the system, expressing solutions as ratios of determinants. Furthermore, we investigate the SBDT and its application to obtaining quasi-Grammian multikink and multisoliton solutions for the <span>(M)</span>-component sdC integrable system. Additionally, we demonstrate that quasi-Grammian solutions can be simplified to elementary solutions by reducing spectral parameters. </p>","PeriodicalId":797,"journal":{"name":"Theoretical and Mathematical Physics","volume":"221 1","pages":"1650 - 1674"},"PeriodicalIF":1.0,"publicationDate":"2024-10-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142518892","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Spectral asymptotics of a non-self-adjoint fourth-order operator with periodic boundary conditions 具有周期性边界条件的非自交四阶算子的谱渐近性
IF 1 4区 物理与天体物理
Theoretical and Mathematical Physics Pub Date : 2024-10-24 DOI: 10.1134/S0040577924100039
D. M. Polyakov
{"title":"Spectral asymptotics of a non-self-adjoint fourth-order operator with periodic boundary conditions","authors":"D. M. Polyakov","doi":"10.1134/S0040577924100039","DOIUrl":"10.1134/S0040577924100039","url":null,"abstract":"<p> A non-self-adjoint fourth-order differential operator with nonsmooth coefficients and periodic boundary conditions is considered. Results concerning the asymptotics of the spectrum of this operator are obtained. </p>","PeriodicalId":797,"journal":{"name":"Theoretical and Mathematical Physics","volume":"221 1","pages":"1615 - 1632"},"PeriodicalIF":1.0,"publicationDate":"2024-10-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142518700","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Nonisospectral Kadomtsev–Petviashvili equations from the Cauchy matrix approach 从考奇矩阵方法看非谱卡多姆采夫-彼得维亚什维利方程
IF 1 4区 物理与天体物理
Theoretical and Mathematical Physics Pub Date : 2024-10-24 DOI: 10.1134/S0040577924100040
A. Y. Tefera, Da-jun Zhang
{"title":"Nonisospectral Kadomtsev–Petviashvili equations from the Cauchy matrix approach","authors":"A. Y. Tefera,&nbsp;Da-jun Zhang","doi":"10.1134/S0040577924100040","DOIUrl":"10.1134/S0040577924100040","url":null,"abstract":"<p> The Cauchy matrix approach is developed for solving nonisospectral Kadomtsev–Petviashvili equation and the nonisospectral modified Kadomtsev–Petviashvili equation. By means of a Sylvester equation <span>( boldsymbol{L} boldsymbol{M} - boldsymbol{M} boldsymbol{K} = boldsymbol{r} boldsymbol{s} ^{mathrm T})</span>, a set of scalar master functions <span>({S^{(i,j)}})</span> are defined. We derive the evolution of scalar functions using the nonisospectral dispersion relations. Some explicit solutions are illustrated together with the analysis of their dynamics. </p>","PeriodicalId":797,"journal":{"name":"Theoretical and Mathematical Physics","volume":"221 1","pages":"1633 - 1649"},"PeriodicalIF":1.0,"publicationDate":"2024-10-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142518699","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
(3)-split Casimir operator of the (sl(M|N)) and (osp(M|N)) simple Lie superalgebras in the representation (operatorname{ad}^{otimes 3}) and the Vogel parameterization sl(M|N)和osp(M|N)简单列超拉的((operatorname{ad}^{otimes 3})表示中的(3)-分裂卡西米尔算子和沃格尔参数化
IF 1 4区 物理与天体物理
Theoretical and Mathematical Physics Pub Date : 2024-10-24 DOI: 10.1134/S004057792410009X
A. P. Isaev, A. A. Provorov
{"title":"(3)-split Casimir operator of the (sl(M|N)) and (osp(M|N)) simple Lie superalgebras in the representation (operatorname{ad}^{otimes 3}) and the Vogel parameterization","authors":"A. P. Isaev,&nbsp;A. A. Provorov","doi":"10.1134/S004057792410009X","DOIUrl":"10.1134/S004057792410009X","url":null,"abstract":"<p> We find universal characteristic identities for the <span>(3)</span>-split Casimir operator in the representation <span>(operatorname{ad}^{otimes 3})</span> of the <span>(osp(M|N))</span> and <span>(sl(M|N))</span> Lie superalgebras. Using these identities, we construct projectors onto the invariant subspaces of these representations and find universal formulas for their superdimensions. All the formulas are in accordance with the universal description of subrepresentations of the <span>(operatorname{ad}^{otimes 3})</span> representation of simple basic Lie superalgebras in terms of the Vogel parameters. </p>","PeriodicalId":797,"journal":{"name":"Theoretical and Mathematical Physics","volume":"221 1","pages":"1726 - 1743"},"PeriodicalIF":1.0,"publicationDate":"2024-10-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142518703","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","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 linear equations associated with dispersionless integrable systems 论与无分散可积分系统相关的一些线性方程
IF 1 4区 物理与天体物理
Theoretical and Mathematical Physics Pub Date : 2024-10-24 DOI: 10.1134/S0040577924100015
L. V. Bogdanov
{"title":"On some linear equations associated with dispersionless integrable systems","authors":"L. V. Bogdanov","doi":"10.1134/S0040577924100015","DOIUrl":"10.1134/S0040577924100015","url":null,"abstract":"<p> We use a recently proposed scheme of matrix extension of dispersionless integrable systems in the Abelian case, leading to linear equations related to the original dispersionless system. In the examples considered, these equations can be interpreted in terms of Abelian gauge fields on the geometric background defined by a dispersionless system. They are also connected with the linearization of the original systems. We construct solutions of these linear equations in terms of wave functions of the Lax pair for the dispersionless system, which is represented in terms of some vector fields. </p>","PeriodicalId":797,"journal":{"name":"Theoretical and Mathematical Physics","volume":"221 1","pages":"1589 - 1602"},"PeriodicalIF":1.0,"publicationDate":"2024-10-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142518895","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","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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