Article
Mathematics, Interdisciplinary Applications
Lingfei Li, Yingying Xie
Summary: This work focuses on finding multi-order rogue wave solutions for the generalized (3+1)-dimensional Kadomtsev-Petviashvili equation, deriving them analytically through its bilinear form and symbolic computation. First, second and third order rogue waves are systematically analyzed, and numerical simulations are used to investigate their dynamical features. Additionally, a circular structure among the obtained rogue waves is explored.
CHAOS SOLITONS & FRACTALS
(2021)
Article
Physics, Applied
Jingwei He, Wen-Xiu Ma
Summary: This paper investigates a (2+1)-dimensional nonlinear evolution equation and its lump solutions using symbolic computation. Two classes of lump solutions are derived. For two specific examples, three-dimensional plots and density plots are used to illustrate the dynamic features of the lump solution, generated by Maple plot tools.
MODERN PHYSICS LETTERS B
(2022)
Article
Physics, Multidisciplinary
Yingying Xie, Yongsheng Yan, Lingfei Li
Summary: This paper analytically derives multi-order rogue wave solutions for a generalized (2+1)-dimensional Kadomtsev-Petviashvili (KP) equation through symbolic computation. The derived solutions consist of four independent solutions and depend on two arbitrary parameters, which can be used to shape the appearance of the wave. The study also explores the inner mechanism between the polynomial F-n and the rogue wave solution u(n).
CHINESE JOURNAL OF PHYSICS
(2022)
Article
Computer Science, Interdisciplinary Applications
Yingying Xie, Lingfei Li
Summary: This paper investigates a generalized (3+1)-dimensional Kadomtsev-Petviashvili Benjamin-Bona-Mahony equation describing fluid flow in offshore structures. Four kinds of rogue wave solutions, including a fourth order rogue wave solution, are constructed and systematically analyzed. The obtained rogue waves exhibit certain circularity structure and are shown to be stable during propagation.
MATHEMATICS AND COMPUTERS IN SIMULATION
(2022)
Article
Engineering, Mechanical
Fu-Fu Ge, Shou-Fu Tian
Summary: The study investigates the transformation of nonlinear waves in the (2+1)-dimensional generalized breaking soliton (gBS) equation by deriving N-soliton solutions and 1-order, 2-order breather wave solutions. Analytical conditions for the breather wave transformation are obtained, revealing that the 1-order breather wave can convert into various types of nonlinear waves under specific conditions. Additionally, four deformation modes of the 2-order breather wave are presented, and graphical analysis of the resulting solutions is provided to better comprehend their dynamical behaviors.
NONLINEAR DYNAMICS
(2021)
Article
Physics, Applied
Arzu Akbulut, S. M. Rayhanul Islam, Hadi Rezazadeh, Filiz Tascan
Summary: This paper obtains the exact solutions of the (1 + 1)-dimensional nonlinear dispersive modified Benjamin-Bona-Mahony (DMBBM) and the seventh-order Sawada- Kotera-Ito (S-K Ito) equations using the (w/g)-expansion method, specifically the (g'/g(2))-expansion and (g')-expansion methods. Soliton solutions in the form of hyperbolic, trigonometric, and rational functions are discovered. All solutions are verified and 3D and 2D graphs are provided and discussed.
INTERNATIONAL JOURNAL OF MODERN PHYSICS B
(2022)
Article
Engineering, Mechanical
Jiaheng Li, Junchao Chen, Biao Li
Summary: Researchers have developed a gradient optimization algorithm and proposed a new neural network structure that balances interactions between different terms in the loss function through gradient statistics to resist gradient fluctuations. When solving the complex modified KdV equation, this method effectively reproduces the dynamic behavior of data-driven solutions better than the original approach.
NONLINEAR DYNAMICS
(2022)
Article
Mathematics, Applied
Zhe Ji, Yifan Nie, Lingfei Li, Yingying Xie, Mancang Wang
Summary: This paper investigates rational solutions of an extended Camassa-Holm-Kadomtsev-Petviashvili equation and analyzes their dynamic features. Multiple order rational and generalized rational solutions are obtained, demonstrating different wave forms.
Article
Materials Science, Multidisciplinary
Sachin Kumar, Hassan Almusawa, Shubham Kumar Dhiman, M. S. Osman, Amit Kumar
Summary: This paper utilizes Lie symmetry analysis to explore closed-form solutions for a (2+1)-dimensional Bogoyavlenskii's breaking soliton equation, demonstrating new and diverse results in terms of multiple solitons and solitary waves. By reducing the equation into nonlinear ODEs using Lie symmetry reductions, the study confirms the efficiency and validity of the approach in obtaining various types of wave structures and their dynamics.
RESULTS IN PHYSICS
(2021)
Article
Mathematics, Applied
Yuan Zhou, Xiaojing Zhang, Chao Zhang, Junjing Jia, Wen-Xiu Ma
Summary: The aim of this paper is to demonstrate the existence of three-wave lump solutions to a (3+1)-dimensional generalized CBS (gCBS) equation. By utilizing the quadratic functions of the form f = f12 + f22 + f32 + d with nondegenerate condition and the Hirota method, the corresponding bilinear equation is solved and lump solutions to the gCBS equation are generated. Two examples of such nonlinear equations and their lump solutions are presented, along with three-dimensional plots and contour plots of three reduced lump solutions.
APPLIED MATHEMATICS LETTERS
(2023)
Article
Mathematics, Interdisciplinary Applications
S. Saravana Veni, M. S. Mani Rajan
Summary: In this study, exact two and three soliton solutions for higher-order NLS equation with variable coefficients were obtained using Darboux transformation method. The switching characteristics of two and three solitons in the attosecond regime via inelastic soliton interactions were discussed for the first time, along with an analysis of the effects of inhomogeneous coefficients on soliton propagation features. The results have potential applications in the construction of optical switching and soliton management in optical communication systems.
CHAOS SOLITONS & FRACTALS
(2021)
Article
Mathematics, Applied
Liyuan Ding, Wen-Xiu Ma, Qingxian Chen, Yehui Huang
Summary: In this study, a nonlinear partial differential equation with a third-order derivative of the time variable DxDt3 is considered. By introducing a new fourth-order derivative term, lump solutions are constructed using the Hirota bilinear method and symbolic computation. The influence of the new fourth-order derivative term on the solutions is discussed, and the dynamical behaviors of two specific lump solutions are analyzed with varying parameters.
APPLIED MATHEMATICS LETTERS
(2021)
Article
Physics, Mathematical
Colby L. Wight, Jia Zhao
Summary: This paper focuses on using deep neural networks to design an improved Physics Informed Neural Network (PINN) for automatically solving the Allen-Cahn and Cahn-Hilliard equations. Various techniques and sampling strategies are proposed to enhance the efficiency and accuracy of the PINN in solving phase field equations, allowing for a wider applicability to a broader class of PDE problems without restriction on the explicit form of the PDEs.
COMMUNICATIONS IN COMPUTATIONAL PHYSICS
(2021)
Article
Physics, Multidisciplinary
Bo Ren, Peng-Cheng Chu
Summary: This paper investigates the D'Alembert wave of a (2+1)-dimensional generalized breaking soliton equation with nonlinear terms, including the dynamics of three soliton molecules, asymmetry soliton interactions, and interactions between different types of solitons.
CHINESE JOURNAL OF PHYSICS
(2021)
Article
Physics, Multidisciplinary
Shaofu Wang
Summary: In this paper, the (2 + 1)-dimensional breaking soliton equation is studied using the multi-linear variable separation method. The authors derived a set of periodic multi-soliton solutions based on the projected Riccati equation, and described a new method for constructing Weierstrass elliptic function solutions. Different Weierstrass elliptic function solutions were also constructed and local excitations were studied.
EUROPEAN PHYSICAL JOURNAL PLUS
(2022)
Article
Engineering, Multidisciplinary
MeiYu Li, Sudao Bilige, Run-Fa Zhang, Lihui Han
Summary: In this paper, the (3 + 1)-dimensional Kadomtsev-Petviashvili-Boussinesq-like equation is used to derive exact solutions, including interaction wave solitons, cross-kink wave solitons, and bright-dark solitons, under certain constraints using the generalized bilinear form and the symbolic computation Maple. The accuracy of the solutions is ensured by a special selection of parameters and the visualization of dynamics through three-dimensional, density, and contour graphs. These solutions have applications in studying certain phenomena in physics.
INTERNATIONAL JOURNAL OF NONLINEAR SCIENCES AND NUMERICAL SIMULATION
(2022)
Article
Physics, Applied
Run-Fa Zhang, Ming-Chu Li, Tao Fang, Fu-Chang Zheng, Sudao Bilige
Summary: In this paper, new trial functions are constructed based on the bilinear neural networks method, and multiple solutions of the dimensionally reduced p-generalized Burgers-Kadomtsev-Petviashvili equation are solved. The dynamic properties of the solutions are analyzed with appropriate parameters and different activated functions.
MODERN PHYSICS LETTERS B
(2022)
Article
Engineering, Mechanical
Run-Fa Zhang, Ming-Chu Li
Summary: In this study, a bilinear residual network method is proposed to solve nonlinear evolution equations. The method reduces the complexity of the model and provides more interactive results. The exact analytical solution for the Caudrey-Dodd-Gibbon-Kotera-Sawada-like equation is obtained using the steps of solving through the residual network. Characteristic plots and dynamic analysis of these rogue waves are given.
NONLINEAR DYNAMICS
(2022)
Article
Computer Science, Hardware & Architecture
Mohammed Albishari, Mingchu Li, Runfa Zhang, Esmail Almosharea
Summary: This paper proposes a deep learning-based early stage detection scheme to enhance the detection capability of routing attacks in IoT. The experiments demonstrate its effectiveness and superior performance in terms of prediction accuracy and precision.
JOURNAL OF SUPERCOMPUTING
(2023)
Article
Engineering, Mechanical
Run-Fa Zhang, Ming-Chu Li, Amina Cherraf, Shashank Reddy Vadyala
Summary: In this work, the nonlinear property of neural network is utilized to investigate interference wave and bright and dark soliton solutions. The generalized broken soliton-like equation is derived through the generalized bilinear method. Three neural network models are proposed for accurately fitting explicit solutions of the generalized broken soliton-like equations and Boiti-Leon-Manna-Pempinelli-like equation. Interference wave solutions and bright and dark soliton solutions are obtained using the bilinear neural network method, and are visualized through three-dimensional plots and density plots.
NONLINEAR DYNAMICS
(2023)
Article
Engineering, Industrial
Qing Li, Mingchu Li, Yuan Tian, Jianyuan Gan
Summary: This paper presents a tri-level stochastic game-theoretic model that considers risk-averse strategies between a defender and an attacker in supply networks. The model incorporates uncertainty in facility capacity and attack effect, using Conditional-Value-at-Risk (CVaR) to control the risk associated with extreme scenarios. The goal of the model is to minimize the CVaR cost of the defender and locate facilities with capacity backups at different levels for recovery against worst-case attacks.
RELIABILITY ENGINEERING & SYSTEM SAFETY
(2023)
Article
Engineering, Mechanical
Litao Gai, Youhua Qian, Yupeng Qin, Runfa Zhang
Summary: This paper proposes a trilinear neural network method based on the trilinear form of a (3+1)-dimensional p-GBS equation, which can be used to construct new exact traveling wave solutions. By setting the hidden neurons in three types of tensor functions to specific functions, the paper successfully obtains a class of periodic bright-dark soliton solutions, two types of breather-like wave solutions, and three types of rogue wave solutions for the p-GBS equation. The dynamic characteristics are explained through the 3D and density graphs of these solutions.
NONLINEAR DYNAMICS
(2023)
Article
Engineering, Mechanical
Na Lv, Yichao Yue, Runfa Zhang, Xuegang Yuan, Ran Wang
Summary: In this paper, the authors investigate various nonlinear phenomena of two Kadomtsev-Petviashvili (KP) equations using the bilinear neural network method. They present the fission and annihilation phenomena of breather waves and rogue waves on non-zero backgrounds of a (3+1)-dimensional KP equation, and obtain three interaction solutions on nonconstant backgrounds of a (2+1)-dimensional KP equation with variable coefficients. The authors also analyze the dynamic characteristics and evolution behaviors of the obtained solutions through three-dimensional animations. This study demonstrates the effectiveness of the bilinear neural network method combined with symmetry analysis in solving high-dimensional differential equations with constant and variable coefficients.
NONLINEAR DYNAMICS
(2023)
Article
Automation & Control Systems
Yang Zhang, Run-Fa Zhang, Ka-Veng Yuen
Summary: This paper proposes a neural network-based method for obtaining the analytical solution of the Fokker-Planck equation. The method uses the explicit model of neural networks as the trial function and converts the equation solving into the calculation of weights and biases.
ENGINEERING APPLICATIONS OF ARTIFICIAL INTELLIGENCE
(2023)
Proceedings Paper
Computer Science, Artificial Intelligence
Xiao Zheng, Syed Bilal Hussain Shah, Liqaa Nawaf, Omer F. Rana, Yuanyuan Zhu, Jianyuan Gan
Summary: An online auction-based strategy is proposed in the paper, allowing users and mobile devices to interact dynamically with the system, optimizing the long-term utility effectively. Experimental results demonstrate the effectiveness of this strategy.
WIRELESS ALGORITHMS, SYSTEMS, AND APPLICATIONS, PT III
(2022)
Proceedings Paper
Computer Science, Artificial Intelligence
Esmail Almosharea, Mingchu Li, Runfa Zhang, Mohammed Albishari, Ikhlas Al-Hammadi, Gehad Abdullah Amran, Ebraheem Farea
Summary: Unmanned Aerial Vehicles (UAV) supported by 5G networks can provide aerial-aerial/aerial-ground computing services to remote and isolated areas at a low cost. This study proposes an aerial-aerialground network (AAGN) computing architecture using High Altitude Unmanned Aerial Vehicle (HAU) and Mini-Drones (MDs) based on Mobile Edge Computing (MEC) services. The proposed framework aims to reduce energy consumption and processing delay, optimize HAU mobility and MDs scheduling, and enhance task offloading efficiency.
WIRELESS ALGORITHMS, SYSTEMS, AND APPLICATIONS, PT III
(2022)
Article
Physics, Multidisciplinary
Y. Y. Feng, S. D. Bilige, R. F. Zhang
Summary: This paper studies the multiple rogue wave solutions of the (2+1)-dimensional Sharma-Tasso-Olver equation using the bilinear neural network method. Various types of solutions were obtained using the introduced NMM and 3-2-4 NNM models, with detailed analysis of rogue wave solutions centered at the origin or with a fixed center. The results significantly enrich the exact solutions of the equation and enhance our understanding of nonlinear dynamic systems.
INDIAN JOURNAL OF PHYSICS
(2022)
Article
Mathematics, Interdisciplinary Applications
Bo Li, Tian Huang
Summary: This paper proposes an approximate optimal strategy based on a piecewise parameterization and optimization (PPAO) method for solving optimization problems in stochastic control systems. The method obtains a piecewise parameter control by solving first-order differential equations, which simplifies the control form and ensures a small model error.
CHAOS SOLITONS & FRACTALS
(2024)
Article
Mathematics, Interdisciplinary Applications
Guram Mikaberidze, Sayantan Nag Chowdhury, Alan Hastings, Raissa M. D'Souza
Summary: This study explores the collective behavior of interacting entities, focusing on the co-evolution of diverse mobile agents in a heterogeneous environment network. Increasing agent density, introducing heterogeneity, and designing the network structure intelligently can promote agent cohesion.
CHAOS SOLITONS & FRACTALS
(2024)
Article
Mathematics, Interdisciplinary Applications
Gengxiang Wang, Yang Liu, Caishan Liu
Summary: This investigation studies the impact behavior of a contact body in a fluidic environment. A dissipated coefficient is introduced to describe the energy dissipation caused by hydrodynamic forces. A new fluid damping factor is derived to depict the coupling between liquid and solid, as well as the coupling between solid and solid. A new coefficient of restitution (CoR) is proposed to determine the actual physical impact. A new contact force model with a fluid damping factor tailored for immersed collision events is proposed.
CHAOS SOLITONS & FRACTALS
(2024)
