Article
Acoustics
Yunqing Yang, Huanhe Dong, Yong Chen
Summary: In this study, the exact nonlinear wave solutions of the Nonlinear Schrodinger equation were constructed on period wave backgrounds instead of constant backgrounds. Soliton and breather solutions were given on two types of cnoidal wave backgrounds using Darboux-Backlund transformation. The density evolutions of these solutions were presented under different parameters to study their wave structures and dynamical properties.
Article
Engineering, Mechanical
Guoli Ma, Jianbo Zhao, Qin Zhou, Anjan Biswas, Wenjun Liu
Summary: The rapid development of optical fiber communication is driven by the demands of the information age. Research on the variable coefficients fifth-order nonlinear Schrodinger equation reveals that adjusting the values of dispersion and nonlinear effects can affect soliton stability, which is significant for the advancement of optical communication technologies.
NONLINEAR DYNAMICS
(2021)
Article
Mathematics, Applied
Xin Wang, Ling-Ling Zhang, John Fiifi Essel
Summary: In this paper, we investigate two classes of high-order nonlinear Schrodinger equations and obtain the concrete forms of soliton solutions by defining different ansatz equations. The method used is briefly summarized and explained, and applied to two specific classes of equations. Finally, the specific forms of solutions and the necessary conditions for their existence are obtained, with added pictures for better understanding.
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
(2022)
Article
Mathematics, Interdisciplinary Applications
Y. Y. Bao, S. R. Li, Y. H. Liu, T. F. Xu
Summary: We studied gap solitons and nonlinear Bloch waves in the nonlinear fractional order quantum coupler modulated by periodic potential. The results showed a nearly perfect match between the gap solitons and nonlinear Bloch waves. We carefully investigated the stability of the solitons and found that the variations of Levy index and chemical potential had a profound impact on the existence, profile, and stability of solitons.
CHAOS SOLITONS & FRACTALS
(2022)
Article
Physics, Multidisciplinary
Georgi Gary Rozenman, Wolfgang P. Schleich, Lev Shemer, Ady Arie
Summary: In this study, we theoretically investigate and experimentally observe the evolution of periodic wave trains using surface gravity water wave packets. For low steepness waves, the waves form a Talbot carpet in the linear regime. By increasing the wave steepness and the corresponding nonlinear response, the waves follow the Akhmediev breather solution, resulting in the disappearance of higher frequency periodic patterns at the fractional Talbot distance.
PHYSICAL REVIEW LETTERS
(2022)
Article
Mathematics, Applied
Xiu-Bin Wang
Summary: In this paper, the quasi-periodic waves of the defocusing nonlocal coupled nonlinear Schrodinger equation are theoretically calculated using a Darboux-dressing transformation with a separation of variable approach. The quasi-periodic wave solutions are expressed in separation-of-variables form. Furthermore, graphical discussions are conducted by choosing specific values of the free parameters. The results contribute to the understanding and enrichment of corresponding nonlinear wave phenomena in nonlocal wave modes.
APPLIED MATHEMATICS LETTERS
(2022)
Article
Materials Science, Multidisciplinary
Zhiteng Wang, Changyou Luo, Xiaohui Ling, Liezun Chen, Lifu Zhang
Summary: By analytically finding an exact solitary solution of the cubic-quintic nonlinear Schrodinger equation with pure normal fourth-order dispersion, we have shown that this solution can preserve its shape and is formed by a balance between different nonlinear effects. The role of quintic nonlinearity in generating high-energy pulses and the potential control over high-energy pulses have also been discussed in this study.
RESULTS IN PHYSICS
(2021)
Article
Engineering, Mechanical
Yunzhou Sun, Zhonghua Hu, Houria Triki, Mohammad Mirzazadeh, Wenjun Liu, Anjan Biswas, Qin Zhou
Summary: This paper investigates the nonlinear dynamic characteristics of three-soliton interactions in optical fibers. The exact three-soliton solution of the nonlinear Schrodinger equation is obtained, and theoretical simulations of the formation process of the three solitons are conducted. The effects of initial phase, initial spacing, and initial amplitude on the interaction of three solitons are discussed, and the transmission characteristics of the interaction are studied through theoretical analysis.
NONLINEAR DYNAMICS
(2023)
Article
Engineering, Mechanical
Quan M. Nguyen, Toan T. Huynh
Summary: The study investigates the amplitude dynamics of 2D solitons in a fast collision using perturbative techniques, showing that the collision-induced amplitude shift depends on the angle between the colliding solitons. The perturbative approach is also applicable to studying the collision-induced amplitude shift in the collision of 1D solitons.
NONLINEAR DYNAMICS
(2021)
Editorial Material
Physics, Multidisciplinary
Amiya Das, Sujata Paul, Sudipta Jash
Summary: In this study, the theory of Madelung fluid description was utilized to analyze the correspondence between the envelope soliton like solutions of a generalized derivative resonant nonlinear Schrodinger equation (GDRNLSE) and the soliton like solutions of a stationary generalized Gardner equation. Bright and dark envelope soliton solutions, as well as periodic wave envelope solutions with phase dependence on space and time, were derived from the corresponding equations.
Article
Physics, Fluids & Plasmas
Yinong Tai, Hongwei Li, Zhaojie Zhou, Ziwen Jiang
Summary: In this paper, the numerical solution of coupled nonlinear Klein-Gordon equations on unbounded domains is solved using the artificial boundary method. By introducing artificial boundaries and designing local artificial boundary conditions, the original problem is transformed into an initial boundary value problem on a bounded domain, which can be efficiently solved using the finite difference method. Numerical examples are provided to validate the proposed method's accuracy and effectiveness.
Review
Engineering, Mechanical
Yan Zhang, Hui-Qin Hao
Summary: In this paper, we explore the periodic solutions and Whitham modulation theory for the fifth-order nonlinear Schrodinger equation, which describes the one-dimensional anisotropic Heisenberg ferromagnetic spin chain. The principle of the finite-gap integration method is introduced, followed by the discussion of single-phase periodic solutions and their degenerate forms in two limit cases. The influence of higher-order term parameters on the propagation of periodic solutions and solitons is also analyzed. Furthermore, the single-phase and two-phase periodic solutions along with their corresponding Whitham modulation equations are systematically derived.
NONLINEAR DYNAMICS
(2023)
Article
Optics
Yuqin Cui, Fenfen Ma
Summary: The main focus of this research is on finding solitary wave solutions for the variable coefficient nonlinear Schrodinger equation with an external potential, including bright soliton, dark soliton, periodic soliton, and triangular soliton derived through the complete discrimination system. Particularly, the Cross-shaped and T-shaped dark soliton are demonstrated.
Article
Mathematics, Applied
Xiaoxiao Zheng, Qizhen Xiao, Zigen Ouyang
Summary: This paper discusses solutions of a Novikov equation using the bifurcation method of dynamical systems. By establishing a Hamiltonian function, the existence of a smooth soliton solution and a periodic cuspon solution for the corresponding traveling wave system are proven. Numerical results provide evidence for the feasibility of the main results, filling gaps in prior literature.
APPLIED MATHEMATICS LETTERS
(2021)
Article
Materials Science, Multidisciplinary
Zhi-Ping Dai, Qiao Zeng, Shuang Shen, Zhen-Jun Yang
Summary: This paper investigates the evolution characteristics of periodically revived elliptical cos-Gaussian solitons and breathers based on nonlocal nonlinear Schr?dinger equation. Mathematical expressions are derived to describe the soliton propagation, the intensity pattern, the statistical spot size, and the axial intensity. Various evolution characteristics are discussed and illustrated by numerical simulations.
RESULTS IN PHYSICS
(2021)
Article
Mathematics, Applied
Peter Frolkovic, Nikola Gajdosova
Summary: This paper presents compact semi-implicit finite difference schemes for solving advection problems using level set methods. Through numerical tests and stability analysis, the accuracy and stability of the proposed schemes are verified.
APPLIED MATHEMATICS AND COMPUTATION
(2024)
Article
Mathematics, Applied
Md. Rajib Arefin, Jun Tanimoto
Summary: Human behaviors are strongly influenced by social norms, and this study shows that injunctive social norms can lead to bi-stability in evolutionary games. Different games exhibit different outcomes, with some showing the possibility of coexistence or a stable equilibrium.
APPLIED MATHEMATICS AND COMPUTATION
(2024)
Article
Mathematics, Applied
Dingyi Du, Chunhong Fu, Qingxiang Xu
Summary: A correction and improvement are made on a recent joint work by the second and third authors. An optimal perturbation bound is also clarified for certain 2 x 2 Hermitian matrices.
APPLIED MATHEMATICS AND COMPUTATION
(2024)
Article
Mathematics, Applied
Pingrui Zhang, Xiaoyun Jiang, Junqing Jia
Summary: In this study, improved uniform error bounds are developed for the long-time dynamics of the nonlinear space fractional Dirac equation in two dimensions. The equation is discretized in time using the Strang splitting method and in space using the Fourier pseudospectral method. The major local truncation error of the numerical methods is established, and improved uniform error estimates are rigorously demonstrated for the semi-discrete scheme and full-discretization. Numerical investigations are presented to verify the error bounds and illustrate the long-time dynamical behaviors of the equation with honeycomb lattice potentials.
APPLIED MATHEMATICS AND COMPUTATION
(2024)
Article
Mathematics, Applied
Kuan Zou, Wenchen Han, Lan Zhang, Changwei Huang
Summary: This research extends the spatial PGG on hypergraphs and allows cooperators to allocate investments unevenly. The results show that allocating more resources to profitable groups can effectively promote cooperation. Additionally, a moderate negative value of investment preference leads to the lowest level of cooperation.
APPLIED MATHEMATICS AND COMPUTATION
(2024)
Article
Mathematics, Applied
Kui Du
Summary: This article introduces two new regularized randomized iterative algorithms for finding solutions with certain structures of a linear system ABx = b. Compared to other randomized iterative algorithms, these new algorithms can find sparse solutions and have better performance.
APPLIED MATHEMATICS AND COMPUTATION
(2024)
Article
Mathematics, Applied
Shadi Malek Bagomghaleh, Saeed Pishbin, Gholamhossein Gholami
Summary: This study combines the concept of vanishing delay arguments with a linear system of integral-algebraic equations (IAEs) for the first time. The piecewise collocation scheme is used to numerically solve the Hessenberg type IAEs system with vanishing delays. Well-established results regarding regularity, existence, uniqueness, and convergence of the solution are presented. Two test problems are studied to verify the theoretical achievements in practice.
APPLIED MATHEMATICS AND COMPUTATION
(2024)
Article
Mathematics, Applied
Qi Hu, Tao Jin, Yulian Jiang, Xingwen Liu
Summary: Public supervision plays an important role in guiding and influencing individual behavior. This study proposes a reputation incentives mechanism with public supervision, where each player has the authority to evaluate others. Numerical simulations show that reputation provides positive incentives for cooperation.
APPLIED MATHEMATICS AND COMPUTATION
(2024)
Article
Mathematics, Applied
Werner M. Seiler, Matthias Seiss
Summary: This article proposes a geometric approach for the numerical integration of (systems of) quasi-linear differential equations with singular initial and boundary value problems. It transforms the original problem into computing the unstable manifold at a stationary point of an associated vector field, allowing efficient and robust solutions. Additionally, the shooting method is employed for boundary value problems. Examples of (generalized) Lane-Emden equations and the Thomas-Fermi equation are discussed.
APPLIED MATHEMATICS AND COMPUTATION
(2024)
Article
Mathematics, Applied
Lisandro A. Raviola, Mariano F. De Leo
Summary: We evaluated the performance of novel numerical methods for solving one-dimensional nonlinear fractional dispersive and dissipative evolution equations and showed that the proposed methods are effective in terms of accuracy and computational cost. They can be applied to both irreversible models and dissipative solitons, offering a promising alternative for solving a wide range of evolutionary partial differential equations.
APPLIED MATHEMATICS AND COMPUTATION
(2024)
Article
Mathematics, Applied
Yong Wang, Jie Zhong, Qinyao Pan, Ning Li
Summary: This paper studies the set stability of Boolean networks using the semi-tensor product of matrices. It introduces an index-vector and an algorithm to verify and achieve set stability, and proposes a hybrid pinning control technique to reduce computational complexity. The issue of synchronization is also discussed, and simulations are presented to demonstrate the effectiveness of the results obtained.
APPLIED MATHEMATICS AND COMPUTATION
(2024)
Article
Mathematics, Applied
Ling Cheng, Sirui Zhang, Yingchun Wang
Summary: This paper considers the optimal capacity allocation problem of integrated energy systems (IESs) with power-gas systems for clean energy consumption. It establishes power-gas network models with equality and inequality constraints, and designs a novel full distributed cooperative optimal regulation scheme to tackle this problem. A distributed projection operator is developed to handle the inequality constraints in IESs. The simulation demonstrates the effectiveness of the distributed optimization approach.
APPLIED MATHEMATICS AND COMPUTATION
(2024)
Article
Mathematics, Applied
Abdurrahim Toktas, Ugur Erkan, Suo Gao, Chanil Pak
Summary: This study proposes a novel image encryption scheme based on the Bessel map, which ensures the security and randomness of the ciphered images through the chaotic characteristics and complexity of the Bessel map.
APPLIED MATHEMATICS AND COMPUTATION
(2024)
Article
Mathematics, Applied
Xinjie Fu, Jinrong Wang
Summary: In this paper, we establish an SAIQR epidemic network model and explore the global stability of the disease in both disease-free and endemic equilibria. We also consider the control of epidemic transmission through non-instantaneous impulsive vaccination and demonstrate the sustainability of the model. Finally, we validate the results through numerical simulations using a scale-free network.
APPLIED MATHEMATICS AND COMPUTATION
(2024)
Article
Mathematics, Applied
Maria Han Veiga, Lorenzo Micalizzi, Davide Torlo
Summary: The paper focuses on the iterative discretization of weak formulations in the context of ODE problems. Several strategies to improve the accuracy of the method are proposed, and the method is combined with a Deferred Correction framework to introduce efficient p-adaptive modifications. Analytical and numerical results demonstrate the stability and computational efficiency of the modified methods.
APPLIED MATHEMATICS AND COMPUTATION
(2024)