Article
Physics, Multidisciplinary
Myungwon Hwang, Andres F. Arrieta
Summary: This paper introduces a metastructure architecture with a bistable microstructure that enables extreme broadband frequency conversion, showcasing the relationship between input excitations and output responses. It identifies soliton-lattice mode resonances leading to input-independent energy transfer and observes incommensurate frequency interactions enabling energy exchange between bands two orders of magnitude apart. This architecture breaks the dependence of macroscopic dynamics on unit cell properties, providing potential applications in broadband frequency regulation and energy transduction.
PHYSICAL REVIEW LETTERS
(2021)
Article
Engineering, Multidisciplinary
N. Alam, W. A. Khan, S. Obeidat, G. Muhiuddin, N. S. Diab, H. N. Zaidi, A. Altaleb, L. Bachioua
Summary: In this article, we construct generating functions for special polynomials and investigate their properties and relations. We obtain computational and derivative formulas for these polynomials, as well as finite combinatorial sums involving them. In addition, we provide some remarks and observations on these polynomials.
CMES-COMPUTER MODELING IN ENGINEERING & SCIENCES
(2023)
Article
Computer Science, Interdisciplinary Applications
Yan Jiang, Qi-Xing Qu
Summary: This paper investigates a generalized nonlinear Schrodinger equation in single-mode optical fibers, obtaining a more general bilinear form and analytic solutions through binary Bell polynomials. The parametric regions for the existence of solitons and breathers on a nonzero background are presented, along with elastic soliton interactions and various breather solutions with different parametric conditions. The study also explores rational solutions, parametric conditions for soliton interactions, and rogue waves.
MATHEMATICS AND COMPUTERS IN SIMULATION
(2021)
Article
Optics
Xiao-Min Wang, Xiao-Xiao Hu
Summary: This paper investigates variable coefficient coupled nonlinear Schroddinger equations for fiber couplers with asymmetric self-phase modulation and cross-phase modulation. By using the developed Hirota bilinear method, bilinear forms and periodic two-soliton solutions are obtained. The influences of different parameters on soliton interactions, including collisions between solitons propagating in the same direction and different directions, are discussed. The results provide theoretical guidance for the stable transmission of periodic solitons in fiber couplers.
Article
Mathematics, Interdisciplinary Applications
Su -Su Chen, Bo Tian, Qi-Xing Qu, He Li, Yan Sun, Xia-Xia Du
Summary: This paper investigates the propagation of nonlinear Alfven waves in inhomogeneous plasma through a variable-coefficient derivative nonlinear Schrodinger equation. Various properties of Alfven soliton solutions are derived, including width, amplitude, velocity, trajectory, interactions, and collapses. The study provides insights into the behavior of Alfven waves in plasma environments.
CHAOS SOLITONS & FRACTALS
(2021)
Article
Mathematics
Noor Alam, Waseem Ahmad Khan, Cheon Seoung Ryoo
Summary: This paper introduces a new class of polynomials and investigates their properties, including summation formulas and symmetric identities. Parametric forms are also introduced, and beautiful computer-aided graphs are shown.
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, Electrical & Electronic
Jie Jin, Yi Zhang
Summary: In this article, a seventh-order variable-coefficient nonlinear Schrodinger equation in an optical fiber is studied. Soliton and breather solutions are derived using the Darboux transformation, leading to the following findings: (i) The structures of one soliton and interactions between two solitons are presented, exhibiting parabolic-like, cubic, and periodical-oscillating solitons; (ii) The dynamics of first-order breather and interactions between two breathers are investigated. Various interesting nonlinear wave patterns, such as cow-shaped breathers and breathers with periodic properties, are displayed; (iii) The variable coefficients have an impact on the dynamic behaviors of solitons and breather waves.
OPTICAL AND QUANTUM ELECTRONICS
(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
Chuanxin Xu, Tao Xu, Dexin Meng, Tianli Zhang, Licong An, Lijun Han
Summary: This paper investigates the focusing nonlocal nonlinear Schrodinger equation and establishes the N-fold binary Darboux transformation. Two new types of soliton solutions, including exponential and exponential-and-rational types, are obtained using the Darboux transformation. These solutions have a wide range of parameter regimes and can describe elastic soliton interactions over a nonzero background, remaining stable with an asymptotic phase difference of pi.
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
(2022)
Article
Mathematics, Applied
M. Nurul Islam, Onur Alp Ilhan, M. Ali Akbar, Fatma Berna Benli, Danyal Soybas
Summary: This article examines the nonlinear Landau-Ginsberg-Higgs model, which characterizes wave propagation and scattering systems in nonlinear media, classifies wave velocities, and effectively generates real events. By utilizing the complex traveling wave transformation and the recently enhanced couple of rising procedures, important, applicable, and general solitary wave solutions to the nonlinear wave model are extracted. These solitons are constructed using hyperbolic, exponential, rational, and trigonometric functions as well as their integration. The physical implications of the extracted wave solutions are illustrated graphically for specific parameter values, and the internal structure of the associated physical phenomena is analyzed using the Wolfram Mathematica program. The study demonstrates the effectiveness of the employed method in finding closed-form solitary solitons for various nonlinear evolution equations.
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION
(2022)
Article
Physics, Applied
Zhi-Qiang Li, Shou-Fu Tian, Tian-Tian Zhang, Jin-Jie Yang
Summary: The study successfully derived multi-soliton solutions of a variable-coefficient fifth-order nonlinear Schrodinger equation using the inverse scattering transformation method, with the reflection coefficient possessing N distinct arbitrary-order poles. By analyzing properties like eigenfunctions and scattering matrices, a RH problem was constructed and further analyzed graphically.
MODERN PHYSICS LETTERS B
(2021)
Article
Physics, Multidisciplinary
Xuefeng Zhang, Tao Xu, Min Li, Yue Meng
Summary: This work focuses on the quantitative study of soliton interactions in the nonlinear Schrodinger equation (NLSE) and its variable-coefficient counterpart. The expressions of asymptotic solitons for regular two-soliton and double-pole solutions of the NLSE are obtained using asymptotic analysis method, and the interaction properties are analyzed based on soliton physical quantities, particularly the soliton accelerations and interaction forces. For the bounded two-soliton solution, the soliton center positions and accelerations are numerically calculated, and the soliton interaction scenarios are discussed in three typical bounded cases. In addition, the inhomogeneous regular two-soliton and double-pole solutions for the variable-coefficient NLSE are obtained through variable transformations. The influence of the variable dispersion function f(t) on the soliton interaction dynamics is quantitatively studied based on the expressions of asymptotic solitons.
Article
Physics, Multidisciplinary
Zhao Zhang, Biao Li, Junchao Chen, Qi Guo, Yury Stepanyants
Summary: In this paper, we use the Hirota bilinear method to derive resonant solutions to the KP1 equation. Resonant solutions describe differently oriented lump chains in the (x, y)-plane and arise as the limiting case of more general non-resonant solutions. The method used in this paper can be applied to other integrable systems in two and three spatial dimensions.
Article
Materials Science, Multidisciplinary
H. I. Abdel-Gawad, Choonkil Park
Summary: Researchers analyzed the solutions of two-mode RNLSE, investigating novel shapes and characteristics of pulses propagation in optical fibers, alongside the dynamics of colliding waves. The study revealed complex geometric structures of pulse propagation and important spectral characteristics.
RESULTS IN PHYSICS
(2021)
Article
Mathematics, Applied
Manh Tuan Hoang, Matthias Ehrhardt
Summary: In this paper, a simple approach for solving stiff problems is proposed. Through nonlinear approximation and rigorous mathematical analysis, a class of explicit second-order one-step methods with L-stability and second-order convergence are constructed. The proposed methods generalize and improve existing nonstandard explicit integration schemes, and can be extended to higher-order explicit one-step methods.
APPLIED MATHEMATICS LETTERS
(2024)
Article
Mathematics, Applied
Jian Liu, Zengqin Zhao
Summary: In this article, we investigate p(x)-biharmonic equations involving Leray-Lions type operators and Hardy potentials. Some new theorems regarding the existence of generalized solutions are reestablished for such equations when the Leray-Lions type operator and the nonlinearity satisfy suitable hypotheses in variable exponent Lebesgue spaces.
APPLIED MATHEMATICS LETTERS
(2024)
Article
Mathematics, Applied
Chengcheng Cheng, Rong Yuan
Summary: This paper investigates the spreading dynamics of a nonlocal diffusion KPP model with free boundaries in time almost periodic media. By applying the novel positive time almost periodic function and satisfying the threshold condition for the kernel function, the unique asymptotic spreading speed of the free boundary problem is accurately expressed.
APPLIED MATHEMATICS LETTERS
(2024)
Article
Mathematics, Applied
Xia Wang, Xin Meng, Libin Rong
Summary: In this study, a multiscale model incorporating the modes of infection and types of immune responses of HCV is developed. The basic and immune reproduction numbers are derived and five equilibria are identified. The global asymptotic stability of the equilibria is established using Lyapunov functions, highlighting the significant impact of the reproduction numbers on the overall stability of the model.
APPLIED MATHEMATICS LETTERS
(2024)
Article
Mathematics, Applied
Junpu Li, Lan Zhang, Shouyu Cai, Na Li
Summary: This research proposes a regularized singular boundary method for quickly calculating the singularity of the special Green's function at origin. By utilizing the special Green's function and the origin intensity factor technique, an explicit intensity factor suitable for three-dimensional ocean dynamics is derived. The method does not involve singular integrals, resulting in improved computational efficiency and accuracy.
APPLIED MATHEMATICS LETTERS
(2024)
Article
Mathematics, Applied
Ying Dong, Shuai Zhang, Yichen Zhang
Summary: This paper investigates a 2D chemotaxis-consumption system with rotation and no-flux-Dirichlet boundary conditions. It proves that under certain conditions on the rotation angle, the corresponding initial-boundary value problem has a classical solution that blows up at a finite time.
APPLIED MATHEMATICS LETTERS
(2024)
Article
Mathematics, Applied
Shuhan Yao, Qi Hong, Yuezheng Gong
Summary: In this article, an extended quadratic auxiliary variable method is introduced for a droplet liquid film model. The method shows good numerical solvability and accuracy.
APPLIED MATHEMATICS LETTERS
(2024)
Article
Mathematics, Applied
Tong Wang, Binxiang Dai
Summary: This paper investigates the spreading speed and traveling wave of an impulsive reaction-diffusion model with non-monotone birth function and age structure, which models the evolution of annually synchronized emergence of adult population with maturation. The result extends the work recently established in Bai, Lou, and Zhao (J. Nonlinear Sci. 2022). Numerical simulations are conducted to illustrate the findings.
APPLIED MATHEMATICS LETTERS
(2024)
Article
Mathematics, Applied
Dinghao Zhu, Xiaodong Zhu
Summary: This paper constructs the soliton solutions of the KdV equation with non-zero background using the Riemann-Hilbert approach. The irregular Riemann-Hilbert problem is first constructed by direct and inverse scattering transform, and then regularized by introducing a novel transformation. The residue theorem is applied to derive the multi-soliton solutions at the simple poles of the Riemann-Hilbert problem. In particular, the interaction dynamics of the two-soliton solution are illustrated by considering their evolutions at different time.
APPLIED MATHEMATICS LETTERS
(2024)
Article
Mathematics, Applied
Danhua He, Liguang Xu
Summary: This paper investigates the stability of conformable fractional delay differential systems with impulses. By establishing a conformable fractional Halanay inequality, the paper provides sufficient criteria for the conformable exponential stability of the systems.
APPLIED MATHEMATICS LETTERS
(2024)
Article
Mathematics, Applied
Fei Sun, Xiaoli Li, Hongxing Rui
Summary: This paper presents a high-order numerical scheme for solving the compressible wormhole propagation problem. The scheme utilizes the fourth-order implicit Runge-Kutta method and the block-centered finite difference method, along with high-order interpolation technique and cut-off approach to achieve high-order and bound-preserving.
APPLIED MATHEMATICS LETTERS
(2024)
Article
Mathematics, Applied
Zhijie Du, Huoyuan Duan
Summary: This study analyzes a direct discretization method for computing the eigenvalues of the Maxwell eigenproblem. It utilizes a specific finite element space and the classical variational formulation, and proves the convergence of the obtained finite element solutions.
APPLIED MATHEMATICS LETTERS
(2024)
Article
Mathematics, Applied
Hongliang Li, Pingbing Ming
Summary: This paper proposes an asymptotic-preserving finite element method for solving a fourth order singular perturbation problem, which preserves the asymptotic transition of the underlying partial differential equation. The NZT element is analyzed as a representative, and a linear convergence rate is proved for the solution with sharp boundary layer. Numerical examples in two and three dimensions are consistent with the theoretical prediction.
APPLIED MATHEMATICS LETTERS
(2024)
Article
Mathematics, Applied
Shuyang Xue, Yongli Song
Summary: This paper investigates the spatiotemporal dynamics of the memory-based diffusion equation driven by memory delay and nonlocal interaction. The nonlocal interaction, characterized by the given Green function, leads to inhomogeneous steady states with any modes. The joint effect of nonlocal interaction and memory delay can result in spatially inhomogeneous Hopf bifurcation and Turing-Hopf bifurcation.
APPLIED MATHEMATICS LETTERS
(2024)
Article
Mathematics, Applied
Baoquan Zhou, Ningzhong Shi
Summary: This paper develops a stochastic SEIS epidemic model perturbed by Black-Karasinski process and investigates the impact of random fluctuations on disease outbreak. The results show that random fluctuations facilitate disease outbreak, and a sufficient condition for disease persistence is established.
APPLIED MATHEMATICS LETTERS
(2024)
