Reports on Mathematical Physics最新文献

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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 Q3 PHYSICS, MATHEMATICAL

Reports on Mathematical Physics

Pub Date : 2024-12-01 DOI: 10.1016/S0034-4877(24)00080-6

Guang-Hao Zhang, Fang-Cheng Fan

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 N-fold Darboux transformation are established on the base of its Lax pair. As an application of the obtained Darboux transformation, we obtain the discrete N-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.

从广义的离散2 × 2矩阵谱问题出发，应用Tu格式，构造了一个基于正、负格层次的混合可积格层次，它包含了众所周知的相对论Toda格层次，并可简化为其他新的可积格层次。对于混合层次中的第一个非平凡格方程，在其Lax对的基础上建立了相应的无限个守恒律和n次Darboux变换。作为所得到的Darboux变换的应用，我们得到了离散的n次显式解的行列式形式，由此得到了具有适当参数的单孤子解和双孤子解，并图解了它们的动力学性质和演化过程。提出了一些有趣的孤子结构，如扭结钟形双孤子、钟形反钟形双孤子和反钟形双孤子等。更重要的是，我们观察到这些孤立波通过时没有改变形状、振幅、波长和方向，这意味着它们在传播过程中非常稳定。这些结果和性质有助于我们更好地理解非线性晶格动力学。

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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 Q3 PHYSICS, MATHEMATICAL

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

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.

研究了具有非局部阻尼的平板方程的初边值问题。利用具有局部Lipschitz摄动的单调算子理论证明了解的局部存在性。利用势阱理论，得到了解的整体存在性。利用Nakao不等式，得到了多项式型的衰减估计。对一个适当选择的泛函，给出了用常微分不等式在初始数据上具有适当条件的弱解的有限时间爆破的充分条件。

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 Q3 PHYSICS, MATHEMATICAL

Reports on Mathematical Physics

Pub Date : 2024-12-01 DOI: 10.1016/S0034-4877(24)00087-9

Wei Feng, Songlin Zhao

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.

给出了黎曼-刘维尔时间-分数阶导数和一阶偏导数混合导数分数阶微分方程的李对称群和非线性自伴随方法的推广。给出了李群对混合分数阶导数作用的一般扩展公式和守恒律中守恒向量的表达式。此外，利用所得结果研究了时间分数型Fokas-Lenells方程的对称群和守恒律，从而构造了该方程的精确解和非平凡守恒律。

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 Q3 PHYSICS, MATHEMATICAL

Reports on Mathematical Physics

Pub Date : 2024-12-01 DOI: 10.1016/S0034-4877(24)00085-5

Qijie Cao, Peng Zhao

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.

基于黎曼-希尔伯特方法，导出了Hirota方程代数-几何解的黎曼函数表示。证明了Hirota方程的Baker-Akhiezer函数可以用复平面上的可解矩阵Riemann-Hilbert问题来描述。该程序避免了杜布洛文方程和雅可比反问题的使用。

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 Q3 PHYSICS, MATHEMATICAL

Reports on Mathematical Physics

Pub Date : 2024-12-01 DOI: 10.1016/S0034-4877(24)00086-7

Crina-Daniela Neacşu

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.

本文的目的是证明任意维的四元数射影空间上的恒等映射的索引为零。作为一个直接的结果，我们证明了任何四元数投影空间都是稳定的。

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 Q3 PHYSICS, MATHEMATICAL

Reports on Mathematical Physics

Pub Date : 2024-12-01 DOI: 10.1016/S0034-4877(24)00083-1

Subuhi Khan, Mahammad Lal Mia, Mahvish Ali

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.

本文将贝塞尔函数和Tricomi函数与阿佩尔多项式结合，引入了阿佩尔-贝塞尔函数族和阿佩尔- Tricomi函数族。2变量2参数Hermite-Bessel和Hermite-Tricomi函数被认为是这些族的成员，并被框架在李代数T3的表示中。因此，导出了这些函数的隐式求和公式。还考虑了某些例子。本文最后用Weisner的方法推导了涉及2变量2参数Hermite-Tricomi函数的关系。

引用次数: 0

Index 指数

IF 1 4区物理与天体物理 Q3 PHYSICS, MATHEMATICAL

Reports on Mathematical Physics

Pub Date : 2024-12-01 DOI: 10.1016/S0034-4877(24)00088-0

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 Q3 PHYSICS, MATHEMATICAL

Reports on Mathematical Physics

Pub Date : 2024-12-01 DOI: 10.1016/S0034-4877(24)00084-3

Begzod M. Isakov

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.

我们将构造一类边界条件，它将产生二叉树上Ising-Potts模型的任意给定平移不变分裂吉布斯测度（TISGM）。

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 Q3 PHYSICS, MATHEMATICAL

Reports on Mathematical Physics

Pub Date : 2024-10-01 DOI: 10.1016/S0034-4877(24)00073-9

Lajos Diósi

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.

多变量扩散漂移过程的协变形式由协变福克-普朗克方程利用黎曼几何的标准工具箱来描述。物理学和数学界长期以来一直在寻求改编朗之文随机微分方程的协变形式。我们的研究表明，最简单的协变斯特拉托诺维奇随机微分方程取决于局部正交框架（参见 vielbein），只要我们施加额外的协变约束：框架的矢量必须是无发散的，它就会变成所需的协变朗格文方程。

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 Q3 PHYSICS, MATHEMATICAL

Reports on Mathematical Physics

Pub Date : 2024-10-01 DOI: 10.1016/S0034-4877(24)00076-4

Alcides Garat

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.

PACS numbers: 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.

在以前的研究中，我们已经证明了所有标准模型的局部轨距群都与特殊四元变换的局部群同构。骨架-量规-矢量四元组矢量结构能够证明所有这些同构定理。这些新的四元组是专门为四维洛伦兹时空中的杨-米尔斯理论、阿贝尔和非阿贝尔理论构建的。在本文中，杨-米尔斯 SU(2) × U(1) 公式采用了新的四元组。这些新的四元组建立了轨距变换局部组与时空四元组变换局部组之间的联系。我们将证明这些杨-米尔斯四元组在局部杨-米尔斯规规变换下不仅能把一个局部群变换成另一个局部群，而且还满足群律：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.

引用次数: 0

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