Reports on Mathematical Physics最新文献

Index 指数

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

Reports on Mathematical Physics

Pub Date : 2026-06-01 Epub Date: 2026-06-19 DOI: 10.1016/S0034-4877(26)00042-X

引用次数: 0

The Multidimensional Thermoelastic System with Variable Coefficients and Wentzell Boundary Conditions: Uniform Stability 具有变系数和温塞尔边界条件的多维热弹性系统：均匀稳定性

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

Reports on Mathematical Physics

Pub Date : 2026-06-01 Epub Date: 2026-06-19 DOI: 10.1016/S0034-4877(26)00041-8

Remissa Boureghida, Hicham Kasri

In this paper, we consider a variable-coefficient linear thermoelastic system with interior localized damping and dynamic Wentzell boundary conditions with delay. The model describes the interaction between the mechanical displacement u and temperature θ, and is subject to dynamic Wentzell-type boundary conditions. Our main result demonstrates that this internal damping, localized on a subset ω ⊂ Ω, where a(x) ≥ a₀ > 0 over ω ⊂ Ω, is sufficient to achieve exponential stabilization of the entire system. To establish the well-posedness of the system, we apply semigroup theory. Then, by combining the multiplier method and the Riemannian geometry approach, we derive suitable energy estimates and prove the exponential decay of energy. The stability result highlights the interplay between interior damping, boundary feedback, and the delay term, and provides a meaningful extension of existing stabilization results for thermoelastic systems.

本文考虑了一类具有内局部阻尼的变系数线性热弹性系统，该系统具有动态Wentzell边界条件。该模型描述了机械位移u与温度θ之间的相互作用，并受动态温泽尔型边界条件约束。我们的主要结果表明，这种内部阻尼（定域在一个子集ω∧Ω上，其中a(x)≥a0 > 0 / ω∧Ω）足以实现整个系统的指数稳定。为了证明系统的适定性，我们应用了半群理论。然后，结合乘数法和黎曼几何方法，推导出合适的能量估计，并证明了能量的指数衰减。稳定性结果突出了内部阻尼、边界反馈和延迟项之间的相互作用，为热弹性系统的现有稳定性结果提供了有意义的推广。本文考虑了一类具有内局部阻尼的变系数线性热弹性系统，该系统具有动态Wentzell边界条件。该模型描述了机械位移u与温度θ之间的相互作用，并受动态温泽尔型边界条件约束。我们的主要结果表明，这种内部阻尼（定域在一个子集ω∧Ω上，其中a(x)≥a0 > 0 / ω∧Ω）足以实现整个系统的指数稳定。为了证明系统的适定性，我们应用了半群理论。然后，结合乘数法和黎曼几何方法，推导出合适的能量估计，并证明了能量的指数衰减。稳定性结果突出了内部阻尼、边界反馈和延迟项之间的相互作用，为热弹性系统的现有稳定性结果提供了有意义的推广。

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引用次数: 0

BPS Skyrme Models and Contact Geometry BPS Skyrme模型和接触几何

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

Reports on Mathematical Physics

Pub Date : 2026-06-01 Epub Date: 2026-06-19 DOI: 10.1016/S0034-4877(26)00037-6

R. Slobodeanu, J.M. Speight

A Skyrme-type energy functional for maps

φ : M \to N

from an oriented Riemannian 3-manifold M to a contact 3-manifold N is defined, generalizing the Bogomol’nyi-Pra-sad-Sommerfeld (BPS) Skyrme energy of Ferreira and Zakrzewski. This energy has a topological lower bound, attained by solutions of a first-order self-duality equation which we call (strong) Beltrami maps. In the case where N is the 3 -sphere, we show that the original Ferreira-Zakrzewski model (which has

N = S^{3}

with the standard contact structure) can have no BPS solutions on

M = S^{3}

with

| \deg (φ) | > 1

if the coupling constant has the lowest admissible value.

A Skyrme-type energy functional for maps

φ : M \to N

from an oriented Riemannian 3-manifold M to a contact 3-manifold N is defined, generalizing the Bogomol’nyi-Pra-sad-Sommerfeld (BPS) Skyrme energy of Ferreira and Zakrzewski. This energy has a topological lower bound, attained by solutions of a first-order self-duality equation which we call (strong) Beltrami maps. In the case where N is the 3 -sphere, we show that the original Ferreira-Zakrzewski model (which has

N = S^{3}

with the standard contact structure) can have no BPS solutions on

M = S^{3}

with

| \deg (φ) | > 1

if the coupling constant has the lowest admissible value.

定义了从有向riemanian 3-流形M到接触3-流形N的映射φ:M→N的Skyrme型能量泛函，推广了Ferreira和Zakrzewski的Bogomol 'nyi-Pra-sad-Sommerfeld (BPS) Skyrme能量。这个能量有一个拓扑下界，通过一阶自对偶方程的解得到，我们称之为（强）Beltrami映射。在N为3球的情况下，我们证明了原始Ferreira-Zakrzewski模型（具有标准接触结构的N=S3）在M=S3具有|deg (φ)|>；1时，如果耦合常数具有最低容许值，则不存在BPS解。定义了从有向riemanian 3-流形M到接触3-流形N的映射φ:M→N的Skyrme型能量泛函，推广了Ferreira和Zakrzewski的Bogomol 'nyi-Pra-sad-Sommerfeld (BPS) Skyrme能量。这个能量有一个拓扑下界，通过一阶自对偶方程的解得到，我们称之为（强）Beltrami映射。在N为3球的情况下，我们证明了原始Ferreira-Zakrzewski模型（具有标准接触结构的N=S3）在M=S3具有|deg (φ)|>；1时，如果耦合常数具有最低容许值，则不存在BPS解。

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引用次数: 0

Lattice Paths and Quiver Generating Series with Higher Level Generators 具有高级生成器的点阵路径和颤振生成系列

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

Reports on Mathematical Physics

Pub Date : 2026-06-01 Epub Date: 2026-06-19 DOI: 10.1016/S0034-4877(26)00039-X

Dušan Đorđević, Marko Stošić

The generalized knots-quivers correspondence extends the original knots-quivers correspondence by allowing higher level generators of quiver generating series. In this paper we explore the underlying combinatorics of such generating series, relationship with the Bogo-mol'nyi-Prasad-Sommerfield (BPS) numbers of a corresponding knot, and new combinatorial interpretations of the coefficients of generating series in terms of the count of lattice paths.

广义结-颤振对应通过允许颤振产生序列的更高阶生成元，扩展了原来的结-颤振对应。在本文中，我们探讨了这种生成序列的潜在组合，与相应结的Bogo-mol'nyi-Prasad-Sommerfield （BPS）数的关系，以及根据点阵路径计数对生成序列系数的新的组合解释。广义结-颤振对应通过允许颤振产生序列的更高阶生成元，扩展了原来的结-颤振对应。在本文中，我们探讨了这种生成序列的潜在组合，与相应结的Bogo-mol'nyi-Prasad-Sommerfield （BPS）数的关系，以及根据点阵路径计数对生成序列系数的新的组合解释。

引用次数: 0

Fractional-Order Regularization of Quantum Vacuum Energy Via The Mittag-Leffler Function 基于Mittag-Leffler函数的量子真空能量的分数阶正则化

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

Reports on Mathematical Physics

Pub Date : 2026-06-01 Epub Date: 2026-06-19 DOI: 10.1016/S0034-4877(26)00038-8

Arturo Tozzi

<div><div>The challenge of the vacuum catastrophe arises from the discrepancy between quantum field theoretical predictions and the observed vacuum energy density. Using analytic continuation techniques and asymptotic analysis to ensure physical consistency, we explored the Mittag-Leffler function (MLF), a generalized exponential function applied in fractional calculus and anomalous diffusion, as a potential framework to address the vacuum catastrophe. We computed the MLFregularized vacuum energy integral, evaluated renormalization group equations, derived modified field equations for different parameter choices and provided numerical solutions of the modified Friedmann equations to track the evolution of the scale factor. Unlike conventional approaches relying on arbitrary cutoffs and standard QFT predictions, which exhibit uncontrolled growth at high energies, MLF regulates coupling divergences by attenuating high-energy contributions while preserving Lorentz invariance and renormalization group consistency. The field propagation profile exhibited suppression of high-energy components, consistent with modified dispersion relations predicted by fractional-order formulations. The scale factor evolution indicated a reduced contribution from vacuum energy, aligning with the expectation that MLF diminishes the effective cosmological constant over cosmic timescales. We found minimal deviations in the cosmic microwave background power spectrum relative to the standard cosmological model, consistent with current observational constraints.</div></div><div>The challenge of the vacuum catastrophe arises from the discrepancy between quantum field theoretical predictions and the observed vacuum energy density. Using analytic continuation techniques and asymptotic analysis to ensure physical consistency, we explored the Mittag-Leffler function (MLF), a generalized exponential function applied in fractional calculus and anomalous diffusion, as a potential framework to address the vacuum catastrophe. We computed the MLFregularized vacuum energy integral, evaluated renormalization group equations, derived modified field equations for different parameter choices and provided numerical solutions of the modified Friedmann equations to track the evolution of the scale factor. Unlike conventional approaches relying on arbitrary cutoffs and standard QFT predictions, which exhibit uncontrolled growth at high energies, MLF regulates coupling divergences by attenuating high-energy contributions while preserving Lorentz invariance and renormalization group consistency. The field propagation profile exhibited suppression of high-energy components, consistent with modified dispersion relations predicted by fractional-order formulations. The scale factor evolution indicated a reduced contribution from vacuum energy, aligning with the expectation that MLF diminishes the effective cosmological constant over cosmic timescales. We found minimal deviations in the cosmic microwav

真空灾难的挑战来自量子场理论预测与观测到的真空能量密度之间的差异。利用解析延拓技术和渐近分析来确保物理一致性，我们探索了mittagg - leffler函数（MLF），一个应用于分数阶微积分和反常扩散的广义指数函数，作为解决真空突变的潜在框架。计算了mlf正则化真空能量积分，评估了重整化群方程，推导了不同参数选择下的修正场方程，并给出了修正Friedmann方程的数值解，以跟踪尺度因子的演化。与依赖于任意截止点和标准QFT预测的传统方法不同，这些方法在高能量下表现出不受控制的增长，MLF通过衰减高能贡献来调节耦合发散，同时保持洛伦兹不变性和重整化群一致性。场传播剖面表现出对高能组分的抑制，与分数阶公式预测的修正色散关系一致。尺度因子演化表明真空能量的贡献减小，这与MLF在宇宙时间尺度上减小有效宇宙常数的预期一致。我们发现宇宙微波背景功率谱相对于标准宇宙学模型的偏差很小，符合当前的观测约束。真空灾难的挑战来自量子场理论预测与观测到的真空能量密度之间的差异。利用解析延拓技术和渐近分析来确保物理一致性，我们探索了mittagg - leffler函数（MLF），一个应用于分数阶微积分和反常扩散的广义指数函数，作为解决真空突变的潜在框架。计算了mlf正则化真空能量积分，评估了重整化群方程，推导了不同参数选择下的修正场方程，并给出了修正Friedmann方程的数值解，以跟踪尺度因子的演化。与依赖于任意截止点和标准QFT预测的传统方法不同，这些方法在高能量下表现出不受控制的增长，MLF通过衰减高能贡献来调节耦合发散，同时保持洛伦兹不变性和重整化群一致性。场传播剖面表现出对高能组分的抑制，与分数阶公式预测的修正色散关系一致。尺度因子演化表明真空能量的贡献减小，这与MLF在宇宙时间尺度上减小有效宇宙常数的预期一致。我们发现宇宙微波背景功率谱相对于标准宇宙学模型的偏差很小，符合当前的观测约束。

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引用次数: 0

On Recurrent B Form Space-Times 关于循环B形式时空

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

Reports on Mathematical Physics

Pub Date : 2026-06-01 Epub Date: 2026-06-19 DOI: 10.1016/S0034-4877(26)00036-4

Dilek Kurt, Hülya Bağdatli Yilmaz

<div><div>In this paper, we introduce and study recurrent <span><math><mrow><mi>B</mi></mrow></math></span> form manifolds, which serve as a natural generalization of weakly <span><math><mrow><mi>B</mi></mrow></math></span>-symmetric and pseudo <span><math><mrow><mi>B</mi></mrow></math></span>-symmetric manifolds. We begin by defining a <span><math><mrow><mi>B</mi></mrow></math></span> form associated with the <span><math><mrow><mi>B</mi></mrow></math></span> tensor and investigate the structure of recurrent <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 <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 <span><math><mrow><mi>B</mi></mrow></math></span> tensor is of Codazzi type, the resulting recurrent <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 <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 <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 <span><math><mrow><mi>B</mi></mrow></math></span> form manifolds, which serve as a natural generalization of weakly <span><math><mrow><mi>B</mi></mrow></math></span>-symmetric and pseudo <span><math><mrow><mi>B</mi></mrow></math></span>-symmetric manifolds. We begin by defining a <span><math><mrow><mi>B</mi></mrow></math></span> form associated with the <span><math><mrow><mi>B</mi></mrow></math></span> tensor and investigate the structure of recurrent <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 <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 <span><math><mrow><mi>B</mi></mrow></math></span> tensor is of Codazzi type, the resultin

本文引入并研究了循环B形流形，它是弱B对称流形和伪B对称流形的自然推广。我们首先定义与B张量相关的B形式，并在广义相对论的背景下研究循环B形式流形的结构。构造了一个非平凡的例子来证明（RBF）4时空的存在性。随后，我们证明了如果B张量是Codazzi型，则得到的循环B形式时空是准爱因斯坦的。在适当的条件下，我们研究了这样的时空是否可以模拟完美流体，并进一步证明了共形平坦（RBF）4时空相对于单位时间向量场ρ具有无限小的空间各向同性。然后，我们研究了B张量为Codazzi型和Weyl张量C为调和的情况。结果表明，在一定的几何条件下，相关向量场ρ是静态时空的特征。此外，我们证明，如果进一步的假设得到满足，这个时空允许物质共理。本文引入并研究了循环B形流形，它是弱B对称流形和伪B对称流形的自然推广。我们首先定义与B张量相关的B形式，并在广义相对论的背景下研究循环B形式流形的结构。构造了一个非平凡的例子来证明（RBF）4时空的存在性。随后，我们证明了如果B张量是Codazzi型，则得到的循环B形式时空是准爱因斯坦的。在适当的条件下，我们研究了这样的时空是否可以模拟完美流体，并进一步证明了共形平坦（RBF）4时空相对于单位时间向量场ρ具有无限小的空间各向同性。然后，我们研究了B张量为Codazzi型和Weyl张量C为调和的情况。结果表明，在一定的几何条件下，相关向量场ρ是静态时空的特征。此外，我们证明，如果进一步的假设得到满足，这个时空允许物质共理。

引用次数: 0

Integrable Reductions of Matrix AKNS Soliton Hierarchies 矩阵AKNS孤子层次的可积约简

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

Reports on Mathematical Physics

Pub Date : 2026-06-01 Epub Date: 2026-06-19 DOI: 10.1016/S0034-4877(26)00035-2

Wen-Xiu Ma, Chaudry Masood Khalique

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.

针对具有两个方阵势的矩阵AKNS谱问题，提出并研究了一类群约简或相似变换。给出了相应的约简矩阵AKNS方程的可积层次，包括约简矩阵非线性Schrödinger方程，证明了矩阵AKNS孤子层次的多样性。零曲率公式在这些可积模型的发展中起着至关重要的作用。针对具有两个方阵势的矩阵AKNS谱问题，提出并研究了一类群约简或相似变换。给出了相应的约简矩阵AKNS方程的可积层次，包括约简矩阵非线性Schrödinger方程，证明了矩阵AKNS孤子层次的多样性。零曲率公式在这些可积模型的发展中起着至关重要的作用。

引用次数: 0

On The Geometry of Isomonodromic Deformations on The Torus and The Elliptic Calogero-Moser System 关于环面和椭圆卡罗杰-莫泽系统等同构变形的几何

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

Reports on Mathematical Physics

Pub Date : 2026-06-01 Epub Date: 2026-06-19 DOI: 10.1016/S0034-4877(26)00040-6

Mohamad Alameddine

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.

我们考虑环面上具有简单极点的连接的等单调变形，由第六painlevevl方程的椭圆版本驱动。我们建立了一个扩展的对称性，补充了已知的结果。证明了Calogero-Moser系统的椭圆型能很好地拟合几何框架，引入了扩展的辛二型并证明了它是封闭的。我们考虑环面上具有简单极点的连接的等单调变形，由第六painlevevl方程的椭圆版本驱动。我们建立了一个扩展的对称性，补充了已知的结果。证明了Calogero-Moser系统的椭圆型能很好地拟合几何框架，引入了扩展的辛二型并证明了它是封闭的。

引用次数: 0

Nonlocal ∂¯ METHODS FOR AN INTEGRABLE GENERALIZED FIFTH-ORDER KORTEWEG-DE VRIES EQUATION 可积广义五阶KORTEWEG-DE VRIES方程的非局部∂¯方法

IF 1.2 4区物理与天体物理 Q3 PHYSICS, MATHEMATICAL

Reports on Mathematical Physics

Pub Date : 2026-04-01 Epub Date: 2026-05-05 DOI: 10.1016/S0034-4877(26)00022-4

Huan-Huan Lu, Jian-Gen Liu

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 t-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 u, thereby deriving the restriction on the degenerate kernel R₀ in the limit of weak field. Several kernel functions R₀ 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)

\bar{\partial}

-dressing method.

本文的内容包括两个部分：(i)给出了用复化自变量构造可积（4+2）维广义五阶Korteweg-de Vries （KdV）方程的详细分析。通过具体约简得到了两个三维空间方程。对Lax对的t无关部分进行频谱分析，得到包含正变换和逆变换的非线性傅里叶变换对，该变换对在考虑适当的时间演化后，用于求解具有两个时间变量的三维KdV方程的Cauchy初值问题。（ii）将此实条件初始施加于势函数u上，从而推导出弱场极限下简并核R0的约束。选择几个满足约束的核函数R0，用Zakharov-Manakov (ZM)∂¯-dressing方法构造（2+1）维广义五阶KdV方程的泛函参数解、线孤子解和有理解。

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引用次数: 0

Remling's theorem for vector-valued discrete Schrödinger operators 向量值离散Schrödinger算子的Remling定理

IF 1.2 4区物理与天体物理 Q3 PHYSICS, MATHEMATICAL

Reports on Mathematical Physics

Pub Date : 2026-04-01 Epub Date: 2026-05-05 DOI: 10.1016/S0034-4877(26)00025-X

Keshav Raj Acharya

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.

本文将Remling定理推广到向量值离散Schrödinger算子，证明了位移映射下矩阵势的ω极限点在完全复数的绝对连续谱上是无反射的。

引用次数: 0