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A mixed integrable lattice hierarchy associated with the relativistic toda lattice: conservation laws, N-fold Darboux transformation and soliton solutions 与相对论今日格相关的混合可积格层次：守恒定律、n重达布变换和孤子解
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)00080-6
Guang-Hao Zhang, Fang-Cheng Fan
{"title":"A mixed integrable lattice hierarchy associated with the relativistic toda lattice: conservation laws, N-fold Darboux transformation and soliton solutions","authors":"Guang-Hao Zhang,&nbsp;Fang-Cheng Fan","doi":"10.1016/S0034-4877(24)00080-6","DOIUrl":"10.1016/S0034-4877(24)00080-6","url":null,"abstract":"<div><div>Beginning with a more generalized discrete 2 × 2 matrix spectral problem and applying the Tu scheme, a mixed integrable lattice hierarchy based on the negative and positive lattice hierarchies is constructed, it includes the well-known relativistic Toda lattice hierarchy and can reduce to other new integrable lattice hierarchies. For the first nontrivial lattice equation in the mixed hierarchy, the corresponding infinite number of conservation laws and <em>N</em>-fold Darboux transformation are established on the base of its Lax pair. As an application of the obtained Darboux transformation, we obtain the discrete <em>N</em>-fold explicit solutions in determinant form, from which we get one-and two-soliton solutions with proper parameters and their dynamical properties and evolutions are illustrated graphically. Some interesting soliton structures are presented, such as kink and bell-shaped two-soliton, bell and anti-bell shaped two-soliton and anti-bell shaped two-soliton and so on. What is more, we observe that these solitary waves pass through without change of shapes, amplitudes, wave-lengths and directions, which means they are much stable during the propagation. These results and properties given in this paper may help us better understand nonlinear lattice dynamics.</div></div>","PeriodicalId":49630,"journal":{"name":"Reports on Mathematical Physics","volume":"94 3","pages":"Pages 279-304"},"PeriodicalIF":1.0,"publicationDate":"2024-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143317283","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 existence, asymptotic behaviour and blow-up of solution of a plate equation with nonlinear averaged damping 具有非线性平均阻尼的平板方程解的存在性、渐近性态和爆破性
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)00081-8
Hongwei Zhang, Ling Liu, Hongyun Yue, Donghao Li, Khaled Zennir
{"title":"The existence, asymptotic behaviour and blow-up of solution of a plate equation with nonlinear averaged damping","authors":"Hongwei Zhang,&nbsp;Ling Liu,&nbsp;Hongyun Yue,&nbsp;Donghao Li,&nbsp;Khaled Zennir","doi":"10.1016/S0034-4877(24)00081-8","DOIUrl":"10.1016/S0034-4877(24)00081-8","url":null,"abstract":"<div><div>The initial boundary-value problem for a plate equation with nonlocal damping is considered. The local existence of solution is proved by the monotone operator theory with locally Lipschitz perturbation. By using the potential well theory, we get the global existence of solution. By Nakao's inequality, the decay estimate of polynomial type is obtained. We provide also the sufficient conditions of finite time blow-up of weak solutions with suitable conditions on the initial data by an ordinary differential inequality for an appropriately chosen functional.</div></div>","PeriodicalId":49630,"journal":{"name":"Reports on Mathematical Physics","volume":"94 3","pages":"Pages 305-323"},"PeriodicalIF":1.0,"publicationDate":"2024-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143317066","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 invariant analysis and conservation law for fractional differential equations with mixed fractional derivative: Time-fractional Fokas–Lenells equation 具有混合分数阶导数的分数阶微分方程的不变分析与守恒律：时间-分数阶Fokas-Lenells方程
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 Hirota方程和Riemann-Hilbert问题的代数几何积分
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 四元数投影空间的稳定性
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 与厄米特多项式相关的李代数表示和杂化族
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 二叉树上Ising-Potts模型的边界条件问题
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 指数
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
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