ADVANCES IN MATHEMATICAL PHYSICS 发表的论文旨在理解物理现象的数学基础，并通过数学方法解决物理问题。该杂志欢迎数学物理学家、理论物理学家和数学家的投稿。除了原创研究，《数学物理学进展》还发表重点评论文章，检查最新技术，确定新兴趋势，并为发展领域提出未来方向。

The papers published in Advances in Mathematical Physics aim to deepen the understanding of the mathematical foundations of physical phenomena and to solve physical problems through mathematical methods. The journal welcomes submissions from mathematical physicists, theoretical physicists, and mathematicians. In addition to original research articles, Advances in Mathematical Physics also publishes review articles that examine the latest techniques, identify emerging trends, and propose future directions for the development of the field.

《Advances in Mathematical Physics》发表的论文旨在深入理解物理现象的数学基础，并通过数学方法解决相关的物理问题。该杂志欢迎数学物理学家、理论物理学家和数学家的投稿。除了原创研究文章外，《Advances in Mathematical Physics》还发表重点评论文章，探讨最新技术，识别新兴趋势，并为该领域的发展提出未来方向。

Advances in Mathematical Physics

The known publications related to the gyroscope theory consider only several geometries of the spinning rotors, like the disc, bars, rings, spheres, and others. The geometries of the spinning objects in engineering can have many designs that generate different values of inertial torques. A computing of inertial torques produced by the object’s rotating masses depends on the radii of their locations. Gyroscopic devices with a spinning torus or ring like other objects should be computed for the quality of their operation. The simplified expression for the radius of the mass disposition for the ring is presented by its middle radius which does not give the correct results for inertial torques and motions of gyroscopic devices. The radius of distributed masses of a ring is bigger than its middle radius because of the differences in the external and internal semirings. A torus is a ring whose exact expression of the radius for distributed mass should be derived for the correct solution for the inertial torques generated by the rotating mass. The precise formulas for inertial torques acting on the spinning torus enable finding its optimal size for the gyroscopic devices. This paper presents the method and derivation of mathematical models for the inertial torques produced by the spinning torus and its interrelated angular velocities about the axes of rotations that manifest gyroscopic effects.

Ryspek Usubamatov

Gyroscopic Torques Generated by a Spinning Ring Torus

旋转环形圆环产生的陀螺力矩

This paper investigates exact solutions of the potential Burgers equation with variable coefficients (PBEVCs), contributing to communication engineering, nonlinear acoustics, and fluid mechanics. It explores novel solutions using the improved modified extended tanh–function method (IMETFM), revealing diverse characteristics and providing deeper insights into nonlinear wave dynamics. The study also analyzes the long‐term behavior of PBEVC under noise influence, highlighting insights into noise‐perturbed systems’ robustness. Moreover, it establishes connections to practical applications like 5G optical fiber transmission and ocean wave oscillations, showcasing the wide applicability of the IMETFM approach. This work’s novelty lies in uncovering diverse solution characteristics and bridging theoretical understanding with real‐world applications.

Xiuchuan He

Hui Xiong

Jianming Qi

Yiqun Sun

Wave Dynamics in Design: The Role of Nonlinear Potential Burgers’ Equation With Variable Coefficients

设计中的波动动力学：变系数非线性势Burgers方程的作用

In this paper, a numerical scheme for a time‐dependent singularly perturbed parabolic convection–diffusion problem with boundary turning points is presented. The problem exhibits a left boundary layer in the spatial domain. We use the Crank–Nicolson method for temporal discretization and a nonstandard finite difference approach for spatial discretization on uniform meshes. Through rigorous error analysis, it has been shown that the scheme is stable and parameter‐uniform convergence with a second‐order accuracy in time and a first‐order accuracy in space. Three model examples are provided to show the applicability of the scheme. It is shown that the numerical results are in agreement with the theoretical findings.

Yimesgen Mehari Kebede

Awoke Andargie Tiruneh

Endalew Getnet Tsega

Crank–Nicolson Method for Singularly Perturbed Unsteady Parabolic Problem With Multiple Boundary Turning Points

奇异摄动非定常抛物问题的Crank-Nicolson方法及多重边界转向点

In this paper, we study a two‐dimensional (2D) bidirectional fluid–solid coupling problem in blood vessels and prove the existence of weak solutions to this kind of problem. When studying the fluid motion of arterial blood flow in arterial vascular tissue, where the density of the vessel wall is roughly equal to that of the blood, the coupling between the blood and the vessel wall is highly nonlinear. In this case, the fluid space where the arterial blood flow is located is no longer fixed in the fluid–structure interaction (FSI) model, and its boundary position is determined by the position of the elastic vessel wall. The contact force exerted by the elastic vascular structure on the blood flow also affects the movement of the blood flow, while the position of the blood vessel is determined by the contact force exerted by the blood flow on the blood vessel; that is, two‐way coupling occurs between the vascular diameter and the blood flow space. MSC2020 Classification: 35D30, 35M31

Weifeng Hu

Yunzhang Cheng

The Existence of Weak Solutions for Bidirectional Fluid–Structure Coupling Problem in 2D Arterial Blood Flow

二维动脉血流中双向流固耦合问题的弱解存在性

The two‐dimensional (2D) nonlinear coupled sine‐Gordon equations play a significant role in nonlinear physics, describing phenomena in areas such as solid‐state physics, fluid dynamics, and nonlinear optics. Fundamentally, the sine‐Gordon equation is a nonlinear partial differential equation (PDE) commonly used to model wave propagation, soliton dynamics, and particle interactions across various physical systems. This article focuses on the analytical solution of the 2D nonlinear coupled sine‐Gordon equations in nonlinear wave contexts, considering specific boundary and initial conditions. The solution approach combines the triple Sumudu transform (TST) with an iterative method, detailing the analytical techniques and discussing their convergence properties. The exact solution, presented as a convergent series, is visually depicted through graphs. To address the nonlinear part of the equations, a successive iterative method was applied. The efficiency of the proposed method is illustrated through two test problems, with examples from engineering applications demonstrating its applicability. In conclusion, this method proves to be highly effective, efficient, and promising for finding exact solutions. Overall, the 2D nonlinear coupled sine‐Gordon equations capture the intricate dynamics of nonlinear wave propagation, soliton interactions, and energy conservation in systems with multiple interacting components, making them a powerful tool for modeling a broad range of physical systems.

Wubshet Ibrahim

Teresa Negesa

Analytical Treatments for a Coupled (2+1)‐Dimensional Partial Differential Equations in Nonlinear Physics

非线性物理中耦合(2+1)维偏微分方程的解析处理

The boundary element method is widely used in practical engineering problems, especially in the field of acoustics. For flow-induced noise, the main target of acoustic calculations is to solve the wave equation with the flow field information. However, the sound field distribution of noncompact structures in half-space is especially complex because of the strong scattering effect, while the object surface boundary integration often brings a large workload and generates numerical singularities. In this paper, an improved boundary element method for predicting the aeroacoustic noise of noncompact structures is proposed, which can consider the characteristic distribution of sound field induced by complex structures in half-space. The smooth permeable boundary surrounding the object is used as the integration boundary, while the scattering effect of the ground boundary is investigated by combining the mirror Green’s function method, and the numerical prediction of aeroacoustic noise is carried out for the dipole source and NACA0012 airfoil in half-space. Numerical results show that the far-field noise obtained by using the permeable surface is consistent with that obtained by integrating the direct object boundary under the influence of ground boundary scattering. The mirror image Green’s function method is able to finely capture the ground scattering effect, which has a significant effect on the sound field as the frequency increases.

Wensi Zheng

Fang Wang

An Improved Boundary Element Method for Predicting Half-Space Scattered Noise Combined with Permeable Boundaries

一种改进的边界元方法用于预测带有渗透边界的半空间散射噪声

The multilinear variable separation (MLVS) approach has been proven to be very useful in solving (2 + 1)-dimensional integrable systems. Taking the (3 + 1)-dimensional Burgers hierarchy as an example, we extend the MLVS approach to a whole family of (3 + 1)-dimensional Burgers hierarchy. New exact solutions and universal formulas are obtained, which lead to abundant (3 + 1)-dimensional coherent structures. In particular, two ring-type soliton molecules and their interactions are shown in detail. We also generalize the MLVS results of the (3 + 1)-dimensional Jimbo–Miwa (JM) equation and modified JM equation.

Wei Zhu

Jian-Yong Wang

Kai Zhou

Shoufeng Shen

Bo Ren

New Multilinear Variable Separation Solutions of the (3 + 1)-Dimensional Burgers Hierarchy

(3+1)维Burgers层次结构的新多线性变量分离解

To improve the complexity of the chaotic system and achieve the effective transmission of image information, in this paper, a five-dimensional memristive chaotic system with cubic nonlinear terms is constructed, which has four pairs of symmetric coordinates. First, the cubic nonlinear memristive chaotic system is analyzed using the Lyapunov exponential map, bifurcation map, and attractor phase diagram. The experimental results show that under four pairs of symmetric coordinates, the system exists not only parameter-dependent symmetric rotational coexisting attractor and transient chaotic phenomena but also exists super-multistationary with alternating chaotic cycles dependent on the initial value of the memristor. Then, it is proposed to add a constant term to the linear state variable to explore the effect of the offset increment of the linear state variable on the system in four pairs of symmetric coordinates, while circuit simulation of the five-dimensional chaotic system is carried out using Simulink to verify its existence and realisability. Finally, the synchronization of the dimensionality reduction system and the confidential transmission of the image are achieved, using the control voltage of the system to replace the internal state variables of the memristor to achieve the one-dimensional reduction process, and an adaptive synchronization controller is designed to synchronize the system before and after the dimensionality reduction. Based on the above, an image to be transmitted is modulated into a one-dimensional array and then subjected to the fractional and cyclic operations and combined with the linear encryption and decryption functions and the chaotic masking technique, the simple encryption and decryption of the image processes are realized.

Lina Ding

Pan Wang

Analysis of the Dynamics of a Cubic Nonlinear Five-Dimensional Memristive Chaotic System and the Study of Reduced-Dimensional Synchronous Masking

立方非线性五维忆阻混沌系统的动力学分析与降维同步掩蔽研究

In this paper, we consider the existence and iterative approximation of solutions for a class of nonlinear fourth-order integro-differential equations (IDEs) with Navier boundary conditions. We first prove the existence and uniqueness of analytical solutions for a linear fourth-order IDE, which has rich applications in engineering and physics, and then we establish a maximum principle for the corresponding operator. Based upon the maximum principle, we develop a monotone iterative technique in the presence of lower and upper solutions to obtain iterative solutions for the nonlocal nonlinear problem under certain conditions. Some examples are presented to illustrate the main results.

Yan Wang

Jinxiang Wang

Xiaobin Yao

Monotone Iterative Technique for a Kind of Nonlinear Fourth-Order Integro-Differential Equations and Its Application

一类非线性四阶积分微分方程的单调迭代技术及其应用

The mechanical behavior of the fine-grained piezoelectric/substrate structure with multiple interface cracks under the electromechanical impact loading is investigated. Using the Laplace and Fourier integral transforms, the double-coupled singular integral equations and single-valued conditions of the problems are formulated. Both the singular integral equation and single-valued conditions are simplified into an algebraic equation through the Chebyshev point placement method and solved by numerical calculation. Then, the expression of the dynamic energy release rate is given with the help of the dynamic intensity factors of electric displacement and stress obtained. Finally, numerical results of the dynamic energy release rate with material parameters are demonstrated. The results show that the dynamic energy release rate depends on the size of the interface cracks, coating thickness, and the mechanical–electrical loading. Meanwhile, the fine-grained piezoelectric structures exhibit safer structural performance compared to normal one.

Abbreviation	Adv. Math. Phys.
Journal Impact	0.95
Quartiles(Global)	PHYSICS, MATHEMATICAL(Q3)

ISSN	1687-9120, 1687-9139
h-index	31

Publication Information	Publisher: Hindawi Publishing Corporation，Publishing cycle: ，Journal Type: journal，Open Access Journals: Yes
Basic data	Year of publication: 2009，Proportion of original research papers: 100.00%，Self Citation Rate:10.00%， Gold OA Rate: 99.33%
Journal Fees	$2450Details
Average review cycle	网友分享经验：>12周，或约稿
Average recruitment ratio	网友分享经验：容易

Advances in Mathematical Physics

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