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On invariant analysis and conservation law for fractional differential equations with mixed fractional derivative: Time-fractional Fokas–Lenells equation
IF 1 4区 物理与天体物理
Reports on Mathematical Physics Pub Date : 2024-12-01 DOI: 10.1016/S0034-4877(24)00087-9
Wei Feng, Songlin Zhao
{"title":"On invariant analysis and conservation law for fractional differential equations with mixed fractional derivative: Time-fractional Fokas–Lenells equation","authors":"Wei Feng,&nbsp;Songlin Zhao","doi":"10.1016/S0034-4877(24)00087-9","DOIUrl":"10.1016/S0034-4877(24)00087-9","url":null,"abstract":"<div><div>This paper provides extensions of the methods of Lie symmetry group and nonlinear self–adjointness to fractional differential equations involving mixed derivatives of Riemann–Liouville time-fractional derivative and first-order partial derivative. We present explicitly the general prolongation formulae expressing the action of Lie group on the mixed fractional derivatives and the expressions of conserved vectors in conservation laws. Moreover, the obtained results are used to investigate the symmetry groups and conservation laws of time-fractional Fokas–Lenells equation, whose exact solution and nontrivial conservation law are thereby constructed.</div></div>","PeriodicalId":49630,"journal":{"name":"Reports on Mathematical Physics","volume":"94 3","pages":"Pages 405-420"},"PeriodicalIF":1.0,"publicationDate":"2024-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143317096","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
Algebro-geometric integration of the Hirota equation and the Riemann–Hilbert problem
IF 1 4区 物理与天体物理
Reports on Mathematical Physics Pub Date : 2024-12-01 DOI: 10.1016/S0034-4877(24)00085-5
Qijie Cao, Peng Zhao
{"title":"Algebro-geometric integration of the Hirota equation and the Riemann–Hilbert problem","authors":"Qijie Cao,&nbsp;Peng Zhao","doi":"10.1016/S0034-4877(24)00085-5","DOIUrl":"10.1016/S0034-4877(24)00085-5","url":null,"abstract":"<div><div>Based on the Riemann–Hilbert method, the Riemann theta function representations for algebro-geometric solutions of the Hirota equation are derived. It is shown that the Baker–Akhiezer function of the Hirota equation can be described by solvable matrix Riemann–Hilbert problems on complex plane. The procedure avoids the use of Dubrovin's equations and Jacobi inverse problem.</div></div>","PeriodicalId":49630,"journal":{"name":"Reports on Mathematical Physics","volume":"94 3","pages":"Pages 365-394"},"PeriodicalIF":1.0,"publicationDate":"2024-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143356489","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 stability of the quaternion projective space
IF 1 4区 物理与天体物理
Reports on Mathematical Physics Pub Date : 2024-12-01 DOI: 10.1016/S0034-4877(24)00086-7
Crina-Daniela Neacşu
{"title":"On the stability of the quaternion projective space","authors":"Crina-Daniela Neacşu","doi":"10.1016/S0034-4877(24)00086-7","DOIUrl":"10.1016/S0034-4877(24)00086-7","url":null,"abstract":"<div><div>The aim of this note is to prove that index of the identity map on a quaternion projective space of any dimension is zero. As an immediate consequence, it is established that any quaternion projective space is stable.</div></div>","PeriodicalId":49630,"journal":{"name":"Reports on Mathematical Physics","volume":"94 3","pages":"Pages 395-404"},"PeriodicalIF":1.0,"publicationDate":"2024-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143317095","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
Lie algebra representation and hybrid families related to Hermite polynomials
IF 1 4区 物理与天体物理
Reports on Mathematical Physics Pub Date : 2024-12-01 DOI: 10.1016/S0034-4877(24)00083-1
Subuhi Khan, Mahammad Lal Mia, Mahvish Ali
{"title":"Lie algebra representation and hybrid families related to Hermite polynomials","authors":"Subuhi Khan,&nbsp;Mahammad Lal Mia,&nbsp;Mahvish Ali","doi":"10.1016/S0034-4877(24)00083-1","DOIUrl":"10.1016/S0034-4877(24)00083-1","url":null,"abstract":"<div><div>In this article, the Bessel and Tricomi functions are combined with Appell polynomials to introduce the families of Appell–Bessel and Appell–Tricomi functions. The 2-variable 2-parameter Hermite–Bessel and Hermite–Tricomi functions are considered as members of these families, and framed within the representation of the Lie algebra T3. Consequently, the implicit summation formulae for these functions are derived. Certain examples are also considered. The article concludes with the derivation of a relation involving the 2-variable 2-parameter Hermite–Tricomi functions by following the Weisner's approach.</div></div>","PeriodicalId":49630,"journal":{"name":"Reports on Mathematical Physics","volume":"94 3","pages":"Pages 335-352"},"PeriodicalIF":1.0,"publicationDate":"2024-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143317065","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
Boundary condition problems for the Ising-Potts model on the binary tree
IF 1 4区 物理与天体物理
Reports on Mathematical Physics Pub Date : 2024-12-01 DOI: 10.1016/S0034-4877(24)00084-3
Begzod M. Isakov
{"title":"Boundary condition problems for the Ising-Potts model on the binary tree","authors":"Begzod M. Isakov","doi":"10.1016/S0034-4877(24)00084-3","DOIUrl":"10.1016/S0034-4877(24)00084-3","url":null,"abstract":"<div><div>We shall construct a class of boundary conditions which will produce any given translationinvariant splitting Gibbs measure (TISGM) of the Ising–Potts model on the binary tree.</div></div>","PeriodicalId":49630,"journal":{"name":"Reports on Mathematical Physics","volume":"94 3","pages":"Pages 353-363"},"PeriodicalIF":1.0,"publicationDate":"2024-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143317064","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
Index
IF 1 4区 物理与天体物理
Reports on Mathematical Physics Pub Date : 2024-12-01 DOI: 10.1016/S0034-4877(24)00088-0
{"title":"Index","authors":"","doi":"10.1016/S0034-4877(24)00088-0","DOIUrl":"10.1016/S0034-4877(24)00088-0","url":null,"abstract":"","PeriodicalId":49630,"journal":{"name":"Reports on Mathematical Physics","volume":"94 3","pages":"Pages 421-422"},"PeriodicalIF":1.0,"publicationDate":"2024-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143317097","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
The Covariant Langevin Equation of Diffusion on Riemannian Manifolds 黎曼曼体上扩散的共变朗格文方程
IF 1 4区 物理与天体物理
Reports on Mathematical Physics Pub Date : 2024-10-01 DOI: 10.1016/S0034-4877(24)00073-9
Lajos Diósi
{"title":"The Covariant Langevin Equation of Diffusion on Riemannian Manifolds","authors":"Lajos Diósi","doi":"10.1016/S0034-4877(24)00073-9","DOIUrl":"10.1016/S0034-4877(24)00073-9","url":null,"abstract":"<div><div>The covariant form of the multivariable diffusion-drift process is described by the covariant Fokker–Planck equation using the standard toolbox of Riemann geometry. The covariant form of the adapted Langevin stochastic differential equation is long sought after in both physics and mathematics. We show that the simplest covariant Stratonovich stochastic differential equation depending on the local orthogonal frame (cf. vielbein) becomes the desired covariant Langevin equation provided we impose an additional covariant constraint: the vectors of the frame must be divergence-free.</div></div>","PeriodicalId":49630,"journal":{"name":"Reports on Mathematical Physics","volume":"94 2","pages":"Pages 143-148"},"PeriodicalIF":1.0,"publicationDate":"2024-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142698821","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
The Group Law for The New Internal-Spacetime Mapping Between The Group of Internal Yang-Mills Gauge Transformations and The Groups (õLB1)3 and (õLB2)3 of Spacetime Tetrad Transformations 杨-米尔斯内部量规变换群与时空四元变换群 (õLB1)3 和 (õLB2)3 之间的新内部时空映射的群法则
IF 1 4区 物理与天体物理
Reports on Mathematical Physics Pub Date : 2024-10-01 DOI: 10.1016/S0034-4877(24)00076-4
Alcides Garat
{"title":"The Group Law for The New Internal-Spacetime Mapping Between The Group of Internal Yang-Mills Gauge Transformations and The Groups (õLB1)3 and (õLB2)3 of Spacetime Tetrad Transformations","authors":"Alcides Garat","doi":"10.1016/S0034-4877(24)00076-4","DOIUrl":"10.1016/S0034-4877(24)00076-4","url":null,"abstract":"<div><div>In previous works it has been demonstrated that all the standard model local gauge groups are isomorphic to local groups of special tetrad transformations. The skeleton-gauge-vector tetrad vector structure enables to prove all of these isomorphism theorems. These new tetrads have been specially constructed for Yang–Mills theories, Abelian and non-Abelian in four-dimensional Lorentzian spacetimes. In the present paper a new tetrad is employed for the Yang–Mills SU(2) × U(1) formulation. These new tetrads establish a connection between local groups of gauge transformations and local groups of spacetime tetrad transformations. We will prove that these Yang–Mills tetrads under the local Yang-Mills gauge transformations not only transform a local group into another local group but also satisfy the group law.</div><div><strong>PACS numbers:</strong> 12.10.-g, 04.40.Nr, 04.20.Cv, 11.15.-q, 02.40.Ky, 02.20.Qs, MSC2010, 51H25, 53c50, 20F65, 70s15, 70G65, 70G45.</div></div>","PeriodicalId":49630,"journal":{"name":"Reports on Mathematical Physics","volume":"94 2","pages":"Pages 189-218"},"PeriodicalIF":1.0,"publicationDate":"2024-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142698847","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
Extensions of Conformal Modules Over Finite Lie Conformal Algebras of Planar Galilean Type 平面伽利略型有限Lie共形布尔上的共形模数扩展
IF 1 4区 物理与天体物理
Reports on Mathematical Physics Pub Date : 2024-10-01 DOI: 10.1016/S0034-4877(24)00077-6
Xiu Han, Dengyin Wang, Chunguang Xia
{"title":"Extensions of Conformal Modules Over Finite Lie Conformal Algebras of Planar Galilean Type","authors":"Xiu Han,&nbsp;Dengyin Wang,&nbsp;Chunguang Xia","doi":"10.1016/S0034-4877(24)00077-6","DOIUrl":"10.1016/S0034-4877(24)00077-6","url":null,"abstract":"<div><div>We classify extensions between finite irreducible conformal modules over Lie conformal algebras <strong>B</strong>ℌ(<em>a, b)</em> of planar Galilean type, where <em>a</em> and <em>b</em> are complex numbers. We find that although finite irreducible conformal modules over <strong>B</strong>ℌ(<em>a</em>, <em>b)</em> are simply conformal modules over its Heisenberg–Virasoro conformal subalgebra, there exist more nontrivial extensions between conformal <strong>B</strong>ℌ(<em>a, b</em>)-modules.</div></div>","PeriodicalId":49630,"journal":{"name":"Reports on Mathematical Physics","volume":"94 2","pages":"Pages 219-233"},"PeriodicalIF":1.0,"publicationDate":"2024-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142698844","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
Exploring Harmonic and Magnetic Fields on The Tangent Bundle with A Ciconia Metric Over An Anti-Parakähler Manifold 在反帕拉克勒曼体上用西科尼娅公设探索切线束上的谐波场和磁场
IF 1 4区 物理与天体物理
Reports on Mathematical Physics Pub Date : 2024-10-01 DOI: 10.1016/S0034-4877(24)00074-0
Nour Elhouda Djaa, Aydin Gezer
{"title":"Exploring Harmonic and Magnetic Fields on The Tangent Bundle with A Ciconia Metric Over An Anti-Parakähler Manifold","authors":"Nour Elhouda Djaa,&nbsp;Aydin Gezer","doi":"10.1016/S0034-4877(24)00074-0","DOIUrl":"10.1016/S0034-4877(24)00074-0","url":null,"abstract":"<div><div>The primary objective of this study is to examine harmonic and generalized magnetic vector fields as mappings from an anti-paraKählerian manifold to its associated tangent bundle, endowed with a ciconia metric. Initially, the conditions under which a vector field is harmonic (or magnetic) concerning a ciconia metric are investigated. Subsequently, the mappings between any given Riemannian manifold and the tangent bundle of an anti-paraKählerian manifold are explored. The paper delves into identifying the circumstances under which vector fields exhibit harmonicity or magnetism within the framework of a ciconia metric. Additionally, it explores the relationships between specific harmonic and magnetic vector fields, particularly emphasizing their behaviour under conformal transformations of metrics.</div></div>","PeriodicalId":49630,"journal":{"name":"Reports on Mathematical Physics","volume":"94 2","pages":"Pages 149-173"},"PeriodicalIF":1.0,"publicationDate":"2024-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142698845","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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