Applied Mathematics Letters最新文献

英文中文

FEM-DtN-SIM method for computing resonances of Schrödinger operators 计算Schrödinger算子共振的FEM-DtN-SIM方法

IF 2.8 2区数学 Q1 MATHEMATICS, APPLIED

Applied Mathematics Letters

Pub Date : 2025-10-28 DOI: 10.1016/j.aml.2025.109803

Bo Gong , Takumi Sato , Jiguang Sun , Xinming Wu

The study of resonances of the Schrödinger operator has a long-standing tradition in mathematical physics. Extensive theoretical investigations have explored the proximity of resonances to the real axis, their distribution, and bounds on the counting functions. However, computational results beyond one dimension remain scarce due to the nonlinearity of the problem and the unbounded nature of the domain. We propose a novel approach that integrates finite elements, Dirichlet-to-Neumann (DtN) mapping, and the spectral indicator method. The DtN mapping, imposed on the boundary of a truncated computational domain, enforces the outgoing condition. Finite elements allow for the efficient handling of complicated potential functions. Finally, the spectral indicator method is employed to compute (complex) eigenvalues of the resulting nonlinear algebraic system. The viability of this approach is demonstrated through a range of numerical examples.

研究Schrödinger算符的共振在数学物理中有着悠久的传统。广泛的理论研究探索了共振与实轴的接近程度，它们的分布以及计数函数的界限。然而，由于问题的非线性和领域的无界性质，一维以外的计算结果仍然很少。我们提出了一种新的方法，集成了有限元，Dirichlet-to-Neumann （DtN）映射和谱指示法。DtN映射，施加在截断计算域的边界上，强制输出条件。有限单元允许有效地处理复杂的势函数。最后，利用谱指示法计算得到的非线性代数系统的（复）特征值。通过一系列数值算例证明了该方法的可行性。

引用次数: 0

On the Riemann–Hilbert problem method to rogue wave solution of the focusing Hirota equation 聚焦Hirota方程异常波解的Riemann-Hilbert问题方法

IF 2.8 2区数学 Q1 MATHEMATICS, APPLIED

Applied Mathematics Letters

Pub Date : 2025-10-24 DOI: 10.1016/j.aml.2025.109800

Jian Xu , Ning Guo

The rogue wave solutions of the focusing Hirota equation are usually obtained via the Darboux transformation or the bilinear method. In this paper, however, we derive these solutions under nonzero boundary conditions by employing a limiting technique applied at the branch point of the spectral parameter, based on the Riemann–Hilbert problem formulation. Furthermore, we demonstrate that the N-double-pole solutions can be generated by taking appropriate limits of the corresponding simple-pole soliton solutions with nonzero boundary conditions.

聚焦Hirota方程的异常波解通常通过达布变换或双线性方法得到。然而，在本文中，我们在黎曼-希尔伯特问题的基础上，利用谱参数分支点处的极限技术，在非零边界条件下导出了这些解。进一步证明了在非零边界条件下，通过对相应的单极孤子解取适当的极限，可以得到n个双极解。

引用次数: 0

Two families of weighted-θ compact ADI difference schemes for the three-dimensional space fractional complex Ginzburg–Landau equation 三维空间分数阶复金兹堡-朗道方程的两族加权- θ紧致ADI差分格式

IF 2.8 2区数学 Q1 MATHEMATICS, APPLIED

Applied Mathematics Letters

Pub Date : 2025-10-24 DOI: 10.1016/j.aml.2025.109798

Li Chai, Yang Liu, Hong Li

Two families of weighted-

θ

compact alternating direction implicit (ADI) difference methods are developed to solve three-dimensional space fractional complex Ginzburg–Landau (3DSFCGL) equation. The article focuses primarily on the high-accuracy and computational efficiency of the constructed methods. To this end, the compact ADI difference schemes are introduced. By a combination of two families of weighted-

θ

methods and the compact ADI difference method, the fully discrete scheme is designed, and the corresponding theoretical results are presented. Finally, numerical tests are carried out to demonstrate the feasibility of our schemes and to simulate the dynamic diffusion behavior of the wave function.

提出了求解三维空间分数阶复金兹堡-朗道（3DSFCGL）方程的两类加权-θ紧变方向隐式差分方法。本文主要关注所构建方法的高精度和计算效率。为此，介绍了紧凑的ADI差分格式。结合两族加权-θ方法和紧致ADI差分法，设计了全离散格式，并给出了相应的理论结果。最后，通过数值试验验证了所提方案的可行性，并模拟了波函数的动态扩散行为。

引用次数: 0

Preservation of geometry property of delayed parabolic equations 时滞抛物型方程几何性质的保存

IF 2.8 2区数学 Q1 MATHEMATICS, APPLIED

Applied Mathematics Letters

Pub Date : 2025-10-23 DOI: 10.1016/j.aml.2025.109799

Qingyang Yuan, Guangying Lv

This paper is concerned with the preservation of concave property of delayed parabolic system. By introducing new variable, we translate the delayed parabolic system into a parabolic system without delay. Then by using the comparison principle, we obtain the preservation of concavity of parabolic system.

本文研究了时滞抛物型系统凹性的保持问题。通过引入新变量，将时滞抛物型系统转化为无时滞抛物型系统。然后利用比较原理，得到了抛物型方程组的凹性保持性。

引用次数: 0

Numerical radius approach to asymptotic stability of quaternion-tensor delay systems 四元数张量时滞系统渐近稳定性的数值半径法

IF 2.8 2区数学 Q1 MATHEMATICS, APPLIED

Applied Mathematics Letters

Pub Date : 2025-10-22 DOI: 10.1016/j.aml.2025.109795

Renjie Xu , Wanli Ma , Maolin Che

In this article, we investigate the asymptotic stability of the system of third-order quaternion-tensor delay differential equations. Sufficient conditions for stability are established based on the T-product algebra, using both the quaternion logarithmic norm and numerical radius. A numerical example is provided to illustrate the effectiveness of the proposed criteria.

本文研究了一类三阶四元数张量时滞微分方程的渐近稳定性。在t积代数的基础上，利用四元数对数范数和数值半径建立了稳定性的充分条件。数值算例说明了所提准则的有效性。

引用次数: 0

Numerical algorithms using reproducing kernels for oscillatory boundary value problems 振荡边值问题的再现核数值算法

IF 2.8 2区数学 Q1 MATHEMATICS, APPLIED

Applied Mathematics Letters

Pub Date : 2025-10-21 DOI: 10.1016/j.aml.2025.109794

F.Z. Geng , X.Y. Wu

As is known, it is perceived as a difficult problem to obtain an effective approximate solution to boundary value problems (BVPs) with highly oscillatory solutions. Traditional reproducing kernel methods (RKMs) are not effective for highly oscillatory BVPs although the RKM is a useful approach to approximation theory. The aim of the letter is to propose a novel class of RKMs to solve highly oscillatory second-order BVPs. To this end, we begin with the variation-of-constants formula (VCF). We then derive RKMs for highly oscillatory BVPs. Our simulations confirm the high accuracy of the introduced techniques.

众所周知，对于具有高振荡解的边值问题，获得有效的近似解是一个困难的问题。传统的再现核方法（RKM）虽然是逼近理论的一种有效方法，但对高度振荡的bvp并不有效。这封信的目的是提出一类新的rkm来解决高振荡的二阶bvp。为此，我们从常数变分公式（VCF）开始。然后，我们推导了高振荡bvp的rkm。仿真结果表明，该方法具有较高的精度。

引用次数: 0

Darboux transformation and exact solutions of the three-component generalized Sasa–Satsuma system 三分量广义Sasa-Satsuma系统的Darboux变换及精确解

IF 2.8 2区数学 Q1 MATHEMATICS, APPLIED

Applied Mathematics Letters

Pub Date : 2025-10-21 DOI: 10.1016/j.aml.2025.109796

Jinxia Wu, Lin Huang

This paper is devoted to the investigation of exact solutions of the three-component generalized Sasa–Satsuma equation. Starting from the associated Lax pair, we establish the corresponding Darboux transformation, which is subsequently applied to generate explicit solutions such as soliton, breather, and periodic wave solutions. The dynamical properties of these solutions are further analyzed and visualized through graphical simulations produced with Maple. These results contribute to the analytical study of multi-component integrable systems and provide deeper insights into their nonlinear wave phenomena.

本文研究了三分量广义Sasa-Satsuma方程的精确解。从相关的Lax对出发，我们建立了相应的Darboux变换，随后将其应用于生成显式解，如孤子解、呼吸波解和周期波解。通过Maple生成的图形仿真，进一步分析和可视化了这些解的动态特性。这些结果有助于多分量可积系统的分析研究，并对其非线性波动现象提供更深入的认识。

引用次数: 0

A symbol-based preconditioner for a sixth-order scheme from multi-dimensional steady-state Riesz space fractional diffusion equations 多维稳态Riesz空间分数扩散方程六阶格式的基于符号的预条件

IF 2.8 2区数学 Q1 MATHEMATICS, APPLIED

Applied Mathematics Letters

Pub Date : 2025-10-20 DOI: 10.1016/j.aml.2025.109791

Yuan-Yuan Huang , Wei Qu , Siu-Long Lei , Sean Y. Hon

In this paper, we employ a sixth-order numerical scheme to approximate the multi-dimensional steady-state Riesz space-fractional diffusion equations (RSFDEs) and subsequently propose a preconditioned conjugate gradient (PCG) method with a symbol-based preconditioner for solving the resulting linear systems. Theoretically, we prove that the PCG solver achieves an optimal convergence rate — i.e., a convergence rate independent of discretization step size — by showing that the spectra of the preconditioned matrices are uniformly bounded within the open interval

(45 / 136, 34 / 15)

. Numerical experiments validate the effectiveness of the proposed preconditioner for three-dimensional steady-state RSFDEs and confirm the rapid convergence of the PCG method.

在本文中，我们采用六阶数值格式来近似多维稳态Riesz空间-分数扩散方程（RSFDEs），并随后提出了一种带有基于符号的预条件共轭梯度（PCG）方法来求解所得到的线性系统。从理论上讲，我们证明了PCG解算器达到了一个最优的收敛速率——即，一个与离散步长无关的收敛速率——通过表明预条件矩阵的谱在开区间（45/136,34/15）内是一致有界的。数值实验验证了所提预条件对三维稳态RSFDEs的有效性，并证实了PCG方法的快速收敛性。

引用次数: 0

An entropy-correct regularization of a system of equations for dynamics of heterogeneous multicomponent mixtures 非均质多组分混合物动力学方程组的熵校正正则化

IF 2.8 2区数学 Q1 MATHEMATICS, APPLIED

Applied Mathematics Letters

Pub Date : 2025-10-20 DOI: 10.1016/j.aml.2025.109793

Alexander Zlotnik

The system of equations for dynamics of the heterogeneous multicomponent mixtures with the common temperature, pressure and velocity of components is considered in the case of general equations of state. The phase transitions are taken into account. Recently, a kinetic (quasi-gasdynamic)-type regularization of the system has been developed and verified in computer simulations in the case of binary mixtures with specific equations of state. In this paper, we construct more advanced entropy-correct regularization of this type such that, in the balance equation for the total entropy of the mixture, the entropy production is nonnegative that is crucial physical and mathematical property. The point is to ensure the decomposition of the total regularizing entropy production as a weighted sum of the regularizing entropy productions of the components that was not available previously.

在一般状态方程的情况下，考虑具有共同温度、压力和速度的非均质多组分混合物的动力学方程组。考虑了相变。最近，在具有特定状态方程的二元混合物的计算机模拟中，系统的动力学（准气体动力学）型正则化得到了发展和验证。在本文中，我们构造了这种类型的更高级的熵正确正则化，使得在混合物总熵的平衡方程中，熵产生是非负的，这是一个重要的物理和数学性质。关键是要确保将总正则化熵产生分解为以前不可用的组件的正则化熵产生的加权和。

引用次数: 0

Periodic wave, soliton and mixed solutions for an extended Benjamin–Ono equation 扩展benjami - ono方程的周期波、孤子和混合解

IF 2.8 2区数学 Q1 MATHEMATICS, APPLIED

Applied Mathematics Letters

Pub Date : 2025-10-18 DOI: 10.1016/j.aml.2025.109790

Yunjuan Jin , Zehua Wu , Huiling Wu

An extended Benjamin–Ono equation with the Hilbert transform is proposed and its bilinear form is presented explicitly. Based on this bilinear equation, multi-periodic wave solutions are obtained via the perturbation technique. By taking a long wave limit on these periodic wave solutions, soliton solutions and mixed solutions representing the interaction between solitons and periodic waves are further derived. The dynamic behaviors of these solutions are visually illustrated through numerical plots.

提出了一类具有Hilbert变换的扩展Benjamin-Ono方程，并给出了其双线性形式。在此双线性方程的基础上，通过摄动技术得到了多周期波解。通过对这些周期波解取长波极限，进一步导出了表示周期波与孤子相互作用的孤子解和混合解。通过数值图直观地说明了这些解的动力学行为。

引用次数: 0

首页上一页

下一页尾页

类型

全部化学•材料生命科学医学物理工程技术环境•农林材料科学地球科学法学管理学化学环境科学与生态学计算机科学教育学经济学农林科学人文科学生物学数学物理与天体物理心理学综合性期刊其他工业工程理学历史学农学文学信息工程

数据库

全部 ACS Publications Elsevier ieeexplore Springer The Royal Society of Chemistry Wiley

期刊

Applied Mathematics Letters

全部 Acc. Chem. Res. ACS Applied Bio Materials ACS Appl. Electron. Mater. ACS Appl. Energy Mater. ACS Appl. Mater. Interfaces ACS Appl. Nano Mater. ACS Appl. Polym. Mater. ACS BIOMATER-SCI ENG ACS Catal. ACS Cent. Sci. ACS Chem. Biol. ACS Chemical Health & Safety ACS Chem. Neurosci. ACS Comb. Sci. ACS Earth Space Chem. ACS Energy Lett. ACS Infect. Dis. ACS Macro Lett. ACS Mater. Lett. ACS Med. Chem. Lett. ACS Nano ACS Omega ACS Photonics ACS Sens. ACS Sustainable Chem. Eng. ACS Synth. Biol. Anal. Chem. BIOCHEMISTRY-US Bioconjugate Chem. BIOMACROMOLECULES Chem. Res. Toxicol. Chem. Rev. Chem. Mater. CRYST GROWTH DES ENERG FUEL Environ. Sci. Technol. Environ. Sci. Technol. Lett. Eur. J. Inorg. Chem. IND ENG CHEM RES Inorg. Chem. J. Agric. Food. Chem. J. Chem. Eng. Data J. Chem. Educ. J. Chem. Inf. Model. J. Chem. Theory Comput. J. Med. Chem. J. Nat. Prod. J PROTEOME RES J. Am. Chem. Soc. LANGMUIR MACROMOLECULES Mol. Pharmaceutics Nano Lett. Org. Lett. ORG PROCESS RES DEV ORGANOMETALLICS J. Org. Chem. J. Phys. Chem. J. Phys. Chem. A J. Phys. Chem. B J. Phys. Chem. C J. Phys. Chem. Lett. Analyst Anal. Methods Biomater. Sci. Catal. Sci. Technol. Chem. Commun. Chem. Soc. Rev. CHEM EDUC RES PRACT CRYSTENGCOMM Dalton Trans. Energy Environ. Sci. ENVIRON SCI-NANO ENVIRON SCI-PROC IMP ENVIRON SCI-WAT RES Faraday Discuss. Food Funct. Green Chem. Inorg. Chem. Front. Integr. Biol. J. Anal. At. Spectrom. J. Mater. Chem. A J. Mater. Chem. B J. Mater. Chem. C Lab Chip Mater. Chem. Front. Mater. Horiz. MEDCHEMCOMM Metallomics Mol. Biosyst. Mol. Syst. Des. Eng. Nanoscale Nanoscale Horiz. Nat. Prod. Rep. New J. Chem. Org. Biomol. Chem. Org. Chem. Front. PHOTOCH PHOTOBIO SCI PCCP Polym. Chem.

﹀