Reports on Mathematical Physics最新文献

{"title":"On Recurrent \u0000\t\tB Form Space-Times","authors":"Dilek Kurt, Hülya Bağdatli Yilmaz","doi":"10.1016/S0034-4877(26)00036-4","DOIUrl":"10.1016/S0034-4877(26)00036-4","url":null,"abstract":"<div><div>In this paper, we introduce and study recurrent \u0000\t\t\t\t<span><math><mrow><mi>B</mi></mrow></math></span> form manifolds, which serve as a natural generalization of weakly \u0000\t\t\t\t<span><math><mrow><mi>B</mi></mrow></math></span>-symmetric and pseudo \u0000\t\t\t\t<span><math><mrow><mi>B</mi></mrow></math></span>-symmetric manifolds. We begin by defining a \u0000\t\t\t\t<span><math><mrow><mi>B</mi></mrow></math></span> form associated with the \u0000\t\t\t\t<span><math><mrow><mi>B</mi></mrow></math></span> tensor and investigate the structure of recurrent \u0000\t\t\t\t<span><math><mrow><mi>B</mi></mrow></math></span> form manifolds in the context of general relativity. A nontrivial example is constructed to demonstrate the existence of a \u0000\t\t\t\t<span><math><msub><mrow><mrow><mo>(</mo></mrow><mrow><mi>R</mi></mrow><mrow><mi>B</mi></mrow><mrow><mi>F</mi></mrow><mrow><mo>)</mo></mrow></mrow><mn>4</mn></msub></math></span> space-time. Subsequently, we prove that if the \u0000\t\t\t\t<span><math><mrow><mi>B</mi></mrow></math></span> tensor is of Codazzi type, the resulting recurrent \u0000\t\t\t\t<span><math><mrow><mi>B</mi></mrow></math></span> form space-time is quasi-Einstein. Under suitable conditions, we examine whether such a space-time can model a perfect fluid and further show that a conformally flat \u0000\t\t\t\t<span><math><msub><mrow><mo>(</mo><mrow><mi>R</mi></mrow><mrow><mi>B</mi></mrow><mrow><mi>F</mi></mrow><mrow><mo>)</mo></mrow></mrow><mn>4</mn></msub></math></span> space-time exhibits infinitesimal spatial isotropy with respect to a unit time-like vector field ρ. Then, we examine the setting in which the \u0000\t\t\t\t<span><math><mrow><mi>B</mi></mrow></math></span> tensor is of Codazzi type and the Weyl tensor <em>C</em> is harmonic. It is shown that, under certain geometric conditions, the associated vector field ρ characterizes a static space-time. Additionally, we prove that this space-time admits a matter collineation, provided that further assumptions are satisfied.</div></div><div>In this paper, we introduce and study recurrent \u0000\t\t\t\t<span><math><mrow><mi>B</mi></mrow></math></span> form manifolds, which serve as a natural generalization of weakly \u0000\t\t\t\t<span><math><mrow><mi>B</mi></mrow></math></span>-symmetric and pseudo \u0000\t\t\t\t<span><math><mrow><mi>B</mi></mrow></math></span>-symmetric manifolds. We begin by defining a \u0000\t\t\t\t<span><math><mrow><mi>B</mi></mrow></math></span> form associated with the \u0000\t\t\t\t<span><math><mrow><mi>B</mi></mrow></math></span> tensor and investigate the structure of recurrent \u0000\t\t\t\t<span><math><mrow><mi>B</mi></mrow></math></span> form manifolds in the context of general relativity. A nontrivial example is constructed to demonstrate the existence of a \u0000\t\t\t\t<span><math><msub><mrow><mrow><mo>(</mo></mrow><mrow><mi>R</mi></mrow><mrow><mi>B</mi></mrow><mrow><mi>F</mi></mrow><mrow><mo>)</mo></mrow></mrow><mn>4</mn></msub></math></span> space-time. Subsequently, we prove that if the \u0000\t\t\t\t<span><math><mrow><mi>B</mi></mrow></math></span> tensor is of Codazzi type, the resultin","PeriodicalId":49630,"journal":{"name":"Reports on Mathematical Physics","volume":"97 3","pages":"Pages 287-301"},"PeriodicalIF":1.0,"publicationDate":"2026-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148571864","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}

{"title":"Integrable Reductions of Matrix AKNS Soliton Hierarchies","authors":"Wen-Xiu Ma,&nbsp;Chaudry Masood Khalique","doi":"10.1016/S0034-4877(26)00035-2","DOIUrl":"10.1016/S0034-4877(26)00035-2","url":null,"abstract":"<div><div>A type of group reduction or similarity transformation is proposed and studied for the matrix AKNS spectral problem with two square matrix potentials. The corresponding integrable hierarchies of the reduced matrix AKNS equations, including reduced matrix nonlinear Schrödinger equations, are presented, demonstrating the diversity of matrix AKNS soliton hierarchies. The zero curvature formulation plays a crucial role in the development of these integrable models.</div></div><div>A type of group reduction or similarity transformation is proposed and studied for the matrix AKNS spectral problem with two square matrix potentials. The corresponding integrable hierarchies of the reduced matrix AKNS equations, including reduced matrix nonlinear Schrödinger equations, are presented, demonstrating the diversity of matrix AKNS soliton hierarchies. The zero curvature formulation plays a crucial role in the development of these integrable models.</div>","PeriodicalId":49630,"journal":{"name":"Reports on Mathematical Physics","volume":"97 3","pages":"Pages 275-286"},"PeriodicalIF":1.0,"publicationDate":"2026-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148571863","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}

{"title":"On The Geometry of Isomonodromic Deformations on The Torus and The Elliptic Calogero-Moser System","authors":"Mohamad Alameddine","doi":"10.1016/S0034-4877(26)00040-6","DOIUrl":"10.1016/S0034-4877(26)00040-6","url":null,"abstract":"<div><div>We consider isomonodromic deformations of connections with a simple pole on the torus, motivated by the elliptic version of the sixth Painlevé equation. We establish an extended symmetry, complementing known results. The Calogero-Moser system in its elliptic version is shown to fit nicely in the geometric framework, the extended symplectic two-form is introduced and shown to be closed.</div></div><div>We consider isomonodromic deformations of connections with a simple pole on the torus, motivated by the elliptic version of the sixth Painlevé equation. We establish an extended symmetry, complementing known results. The Calogero-Moser system in its elliptic version is shown to fit nicely in the geometric framework, the extended symplectic two-form is introduced and shown to be closed.</div>","PeriodicalId":49630,"journal":{"name":"Reports on Mathematical Physics","volume":"97 3","pages":"Pages 353-378"},"PeriodicalIF":1.0,"publicationDate":"2026-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148571861","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}

{"title":"Nonlocal \u0000\t\t∂¯ METHODS FOR AN INTEGRABLE GENERALIZED FIFTH-ORDER KORTEWEG-DE VRIES EQUATION","authors":"Huan-Huan Lu,&nbsp;Jian-Gen Liu","doi":"10.1016/S0034-4877(26)00022-4","DOIUrl":"10.1016/S0034-4877(26)00022-4","url":null,"abstract":"<div><div>The content of this paper includes two parts: (i) A detailed analysis for constructing integrable (4+2)-dimensional generalized fifth-order Korteweg-de Vries (KdV) equation by complexifying the independent variables is presented. Two three-spatial-dimensions equations are obtained by concrete reduction. The spectral analysis of the <em>t</em>-independent part of the Lax pair yields the nonlinear Fourier transform pair comprising both direct and inverse transforms, which is used to solve the Cauchy initial value problem of the three-spatial-dimensions KdV equation with two temporal variables after taking into account the appropriate time evolution. (ii) We initially impose this real condition on the potential function <em>u</em>, thereby deriving the restriction on the degenerate kernel <em>R</em>₀ in the limit of weak field. Several kernel functions <em>R</em>₀ that satisfy the restriction are selected to construct solutions with functional parameters, line soliton solutions, and rational solutions of (2+1)-dimensional generalized fifth-order KdV equation in terms of Zakharov-Manakov (ZM) \u0000\t\t\t\t<span><math><mrow><mover><mi>∂</mi><mo>¯</mo></mover></mrow></math></span>-dressing method.</div></div>","PeriodicalId":49630,"journal":{"name":"Reports on Mathematical Physics","volume":"97 2","pages":"Pages 157-179"},"PeriodicalIF":1.2,"publicationDate":"2026-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147826909","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}

{"title":"Remling's theorem for vector-valued discrete Schrödinger operators","authors":"Keshav Raj Acharya","doi":"10.1016/S0034-4877(26)00025-X","DOIUrl":"10.1016/S0034-4877(26)00025-X","url":null,"abstract":"<div><div>This paper extends Remling's theorem to vector-valued discrete Schrödinger operators, showing that the ω limit points of the matrix potentials, under the shift map, are reflectionless on the absolutely continuous spectrum with full multiplicity.</div></div>","PeriodicalId":49630,"journal":{"name":"Reports on Mathematical Physics","volume":"97 2","pages":"Pages 219-240"},"PeriodicalIF":1.2,"publicationDate":"2026-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147826843","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}

{"title":"Generalized symmetric metric connection on statistical manifolds","authors":"Sohrab Azimpour,&nbsp;Shiva Salahvarzi","doi":"10.1016/S0034-4877(26)00026-1","DOIUrl":"10.1016/S0034-4877(26)00026-1","url":null,"abstract":"<div><div>We define the generalized symmetric metric connection of type (α,β) on almost contact statistical manifolds and Sasakian statistical manifolds. The curvature properties of these manifolds admitting such a connection are derived. Additionally, we investigate the symmetry properties of the curvature tensor with respect to this metric connection. New results are presented for Sasakian statistical manifolds equipped with a generalized symmetric metric connection of type (α,β). Finally, explicit examples of Sasakian statistical manifolds are constructed to illustrate the theoretical framework.</div></div>","PeriodicalId":49630,"journal":{"name":"Reports on Mathematical Physics","volume":"97 2","pages":"Pages 241-255"},"PeriodicalIF":1.2,"publicationDate":"2026-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147826844","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}

{"title":"Solution formula for the general birth-death chemical diffusion master equation","authors":"Alberto Lanconelli,&nbsp;Berk Tan Perçin,&nbsp;Mauricio J. del Razo","doi":"10.1016/S0034-4877(26)00023-6","DOIUrl":"10.1016/S0034-4877(26)00023-6","url":null,"abstract":"<div><div>We propose a solution formula for chemical diffusion master equations of birth and death type. These equations, proposed and formalized in the recent paper [<span><span>27</span></span>], aim at incorporating the spatial diffusion of molecules into the description provided by the classical chemical master equation. We start from the general approach developed in [<span><span>16</span></span>] and perform a more detailed analysis of the representation found there. This leads to a solution formula for birth-death chemical diffusion master equations which is expressed in terms of the solution to the reaction-diffusion partial differential equation associated with the system under investigation. Such representation also reveals a striking analogy with the solution to the classical birth-death chemical master equations. The solutions of our findings are also illustrated for several examples.</div></div>","PeriodicalId":49630,"journal":{"name":"Reports on Mathematical Physics","volume":"97 2","pages":"Pages 181-200"},"PeriodicalIF":1.2,"publicationDate":"2026-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147826870","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}

{"title":"The focusing and defocusing fifth-order semi-discrete mKdV equation: bÄcklund transformation, soliton solution and continuous limit","authors":"Ning-Ning Gao,&nbsp;Fang-Cheng Fan","doi":"10.1016/S0034-4877(26)00024-8","DOIUrl":"10.1016/S0034-4877(26)00024-8","url":null,"abstract":"<div><div>The integrable discretization of a nonlinear partial differential equation and the continuous limits of the relevant discrete integrability properties are one of the most important research subjects in soliton theory. In this paper we construct the spatial discrete version of the focusing and defocusing fifth-order mKdV equation and study the continuous limits of the related discrete integrable properties. Firstly, starting from a discrete spectral problem, we derive integrable equation hierarchies and then obtain the focusing and defocusing fifth-order semi-discrete mKdV equation by using a linear combination of them. Secondly, the Bäcklund transformation and soliton solutions of the equation are presented, the relationship between parameters and solutions’ structures is discussed, some important physical quantities related to solutions are analyzed, the dynamics of soliton solutions are illustrated graphically. Thirdly, we show that the fifth-order mKdV theory including the Lax pairs, the Bäcklund transformation and soliton solutions is recovered through the continuous limits of corresponding theory for the fifth-order semi-discrete mKdV equation. As a conclusion, we believe that the focusing and defocusing fifth-order semidiscrete mKdV equation which we construct in this paper is an extremely useful model for the numerical analysis for considering the Cauchy problem with a general initial data of the fifth-order mKdV equation.</div></div>","PeriodicalId":49630,"journal":{"name":"Reports on Mathematical Physics","volume":"97 2","pages":"Pages 201-218"},"PeriodicalIF":1.2,"publicationDate":"2026-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147826871","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}

{"title":"Explicit solutions in inverse scattering method for negative-order AKNS equations","authors":"Cihan Sabaz,&nbsp;Mansur I. Ismailov","doi":"10.1016/S0034-4877(26)00027-3","DOIUrl":"10.1016/S0034-4877(26)00027-3","url":null,"abstract":"<div><div>In this paper, the Lax pairs of the negative-order AKNS equations are presented. The explicit solutions (classical <em>N</em>-soliton and singular kink wave solutions) are derived using the inverse scattering method. The auxiliary spectral problem is formulated as the classical Zakharov-Shabat system with real symmetric and real anti-symmetric potentials. By recalling results from the inverse scattering problem and utilizing the time evolution of the scattering data, explicit solutions for the negative-order AKNS equations corresponding to symmetric and anti-symmetric potentials are obtained through the Gelfand-Levitan-Marchenko equation.</div></div>","PeriodicalId":49630,"journal":{"name":"Reports on Mathematical Physics","volume":"97 2","pages":"Pages 257-273"},"PeriodicalIF":1.2,"publicationDate":"2026-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147826906","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}

{"title":"Gray's decomposition of mixed generalized Quasi-Einstein manifolds with applications","authors":"Hülya Bağdatli Yilmaz,&nbsp;Uday Chand De","doi":"10.1016/S0034-4877(26)00021-2","DOIUrl":"10.1016/S0034-4877(26)00021-2","url":null,"abstract":"<div><div>In the present article, we consider mixed generalized quasi-Einstein manifolds in the perspective of Gray's decomposition. We begin by analyzing the properties of these manifolds in the context of the subspaces defined by Gray. Furthermore, we apply principles of general relativity to derive significant physical results.</div></div>","PeriodicalId":49630,"journal":{"name":"Reports on Mathematical Physics","volume":"97 2","pages":"Pages 143-155"},"PeriodicalIF":1.2,"publicationDate":"2026-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147826908","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}