Article
Mathematics, Applied
Rongqiang Tang, Shuang Yuan, Xinsong Yang, Peng Shi, Zhengrong Xiang
Summary: This paper investigates a novel method for achieving finite-time synchronization of delayed reaction-diffusion systems by designing intermittent control and weighted Lyapunov-Krasovskii functional. A general finite-time stability criterion is established, and sufficient conditions for finite-time synchronization are given. The weight factor of the Lyapunov-Krasovskii functional plays a significant role in the settling time. The usefulness and generality of the method and stability criterion are demonstrated through important corollaries.
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION
(2023)
Article
Automation & Control Systems
Md Arzoo Jamal, Rakesh Kumar, Santwana Mukhopadhyay, Subir Das
Summary: The present article investigates the fixed-time stability analysis of nonlinear dynamical systems with impulsive effects. Novel criteria are derived to achieve stability in fixed-time under stabilizing and destabilizing impulses. Theoretical results show that the estimated fixed-time in this study is less conservative and more accurate compared to existing theorems. The theoretical findings are also applied to impulsive control of general neural network systems.
JOURNAL OF THE FRANKLIN INSTITUTE-ENGINEERING AND APPLIED MATHEMATICS
(2022)
Article
Mathematics, Applied
Chenguang Xu, Minghui Jiang, Junhao Hu
Summary: This paper focuses on the mean-square finite-time synchronization (MFTS) problem of stochastic competitive neural networks with infinite time-varying discrete delays and reaction-diffusion terms (IRSCNNs). A new approach, which uses integral inequality, Gronwall-type inequality, and comparison strategy, is proposed to study MFTS. Two control schemes, a feedback control scheme and a new adaptive control strategy, are designed to achieve MFTS of IRSCNNs. The correctness of the results is verified through examples.
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION
(2023)
Article
Automation & Control Systems
Haiqi Peng, Quanxin Zhu
Summary: The aim of the article is to discuss the stochastic fixed-time (FIXT) stability of impulsive stochastic nonlinear time-varying systems. Several novel stability theorems for determining stochastic FIXT stability are established using the multiple Lyapunov method and stochastic analysis theory. The estimation of stochastic settling time is also provided. Compared with other conclusions, these results have wider applications and relaxed constraints.
INTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL
(2023)
Article
Physics, Multidisciplinary
Yiping Luo, Yuejie Yao, Zifeng Cheng, Xing Xiao, Hanyu Liu
Summary: This paper investigates finite-time synchronization in a class of coupled nonlinear reaction-diffusion complex network system using event-triggered control. Several sufficient conditions for achieving synchronization are obtained by combining distributed event-triggered control protocol with Lyapunov stability theorem, Green formula, matrix inequality, and partial differential equation theory. The upper bound of time for achieving synchronization is estimated, and numerical simulation is used to validate the theory.
PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS
(2021)
Article
Mathematics, Applied
Pei Cheng, Chengtian Lu, Ting Cai
Summary: This paper focuses on the mean square finite-time stability of uncertain impulsive stochastic delayed systems. Some sufficient conditions are established by using the Lyapunov functional, LMIs techniques, and the concept of the average impulsive interval. The main results are applied to neural networks, and two numerical examples are provided to illustrate the effectiveness of the proposed method.
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
(2022)
Article
Engineering, Multidisciplinary
Huawei Liu, Feng Zhao, Mingyu Wang, Jianlong Qiu, Xiangyong Chen
Summary: This paper mainly introduces a novel pinning impulsive controller for finite-time synchronization of stochastic complex networks with mixed delays. A uniform criterion for finite-time synchronization is derived based on average impulsive interval. The obtained results are further extended to general stochastic complex networks and networks with mixed delays under delayed impulses. The feasibility of the theory is verified by a numerical example.
APPLIED MATHEMATICAL MODELLING
(2023)
Article
Mathematics, Applied
Akbar Zada, Bakhtawar Pervaiz, Muthaiah Subramanian, Ioan-Lucian Popa
Summary: This primer article focuses on the representation of solutions and finite-time stability of impulsive first-order delay differential systems. It introduces delayed matrix function with impulses and applies variation of parameters to obtain a representation of solutions for linear systems with impulse effects. The famous classical Grownwall inequalities and properties of delayed matrix exponential with impulses are utilized to establish sufficient conditions for finite-time stability. Several examples are provided to support the results.
APPLIED MATHEMATICS AND COMPUTATION
(2022)
Article
Computer Science, Artificial Intelligence
Xiaofei Xing, Huaiqin Wu, Jinde Cao
Summary: This paper addresses the finite-time synchronization issue for fractional-order reaction-diffusion complex networks. A finite-time stability principle is developed for fractional-order nonlinear impulsive systems, and a hybrid controller, consisting of an event-triggered controller and an impulsive controller, is designed to achieve the global finite-time synchronization objective. The global synchronization conditions are expressed as algebraic inequalities using the Lyapunov stability theory and fractional calculus. Additionally, the exclusion of Zeno behavior is proved for the designed event-triggered strategy. A numerical example is provided to validate the proposed control approach and theoretical results.
Article
Automation & Control Systems
Mingzhu Wang, Shuchen Wu, Xiaodi Li
Summary: This paper investigates Lyapunov stability of general nonlinear systems using event-triggered impulsive control, considering delayed impulses. By excluding Zeno behavior, a set of sufficient conditions for uniform and asymptotic stability are obtained based on impulsive control theory in the framework of event triggering. The results depend on the event-triggering mechanism and time delays.
JOURNAL OF THE FRANKLIN INSTITUTE-ENGINEERING AND APPLIED MATHEMATICS
(2021)
Article
Computer Science, Artificial Intelligence
Tianliang Zhang, Feiqi Deng
Summary: This paper focuses on the finite-time synchronization of stochastic memristor-based neural networks with time-varying discrete and distributed delays and discontinuous nonlinear functions via the adaptive state-feedback controller. The method successfully synchronizes the neural networks by transforming the problem into finite-time stabilization and designing control gain parameters. An example is provided to verify the effectiveness of the proposed method.
Article
Computer Science, Artificial Intelligence
Xueyan Yang, Xiaodi Li
Summary: This article studies the problem of finite-time stability and finite-time contractive stability for nonlinear impulsive systems with consideration of time delay. Sufficient conditions for FTS/FTCS are constructed using Lyapunov function methods. A relationship between impulsive frequency and time delay is established to reveal the performance of FTS/FTCS. The theoretical results are applied to finite-time state estimation of neural networks. Two examples demonstrate the effectiveness and distinctiveness of the proposed delay-dependent impulsive schemes.
IEEE TRANSACTIONS ON NEURAL NETWORKS AND LEARNING SYSTEMS
(2023)
Article
Automation & Control Systems
Tao Chen, Shiguo Peng, Zhenhua Zhang
Summary: This work presents a method to achieve finite-time consensus of leader-following non-linear multi-agent systems using distributed event-triggered impulsive control, with a controller designed without sign functions to overcome chattering phenomenon. Simulations are used to demonstrate the effectiveness of the proposed control scheme.
IET CONTROL THEORY AND APPLICATIONS
(2021)
Article
Automation & Control Systems
Lirong Huang, Sheng Xu
Summary: This study addresses the rarely studied problem of input delay in impulsive control systems. By proposing a novel approach, the researchers establish Lyapunov-Razumikhin-type theorems on the exponential stability of stochastic impulsive delay systems. Based on these results, they develop a foundational theory for the impulsive stabilization of stochastic delay systems with input delay. The proposed theory offers a control design method for systems with input delay and provides an upper bound for the acceptable input delay while maintaining exponential stability for the controlled system. As future work, the researchers present event-triggered impulsive control systems that extend the classical impulsive control systems in the literature.
IEEE TRANSACTIONS ON AUTOMATIC CONTROL
(2023)
Article
Computer Science, Theory & Methods
Zenghui Hu, Xiaowu Mu, Jingru Mu
Summary: This paper studies the finite-time impulsive control problem for stochastic T-S fuzzy systems with parameter uncertainties. To reduce the number of impulsive control and information transmission, an event-triggered impulsive control (ETIC) scheme is proposed, which involves the co-design of event-triggered mechanisms and impulsive gains to ensure stochastic finite-time stability (SFTS) of the considered systems. In the ETIC scheme, impulsive inputs are applied to the systems only at event-triggering instants, and the waiting time is introduced to avoid Zeno behavior and further save communication resources. A theoretical analysis shows that, compared with the time-triggered impulsive control, ETIC not only removes the restriction of an upper bound for impulsive intervals but also significantly reduces the number of impulsive control while ensuring the same control performance. Two examples illustrate the advantages and validity of the ETIC scheme.
FUZZY SETS AND SYSTEMS
(2023)
Article
Automation & Control Systems
Kamal Mammadov, Cheng-Chew Lim, Peng Shi
Summary: In this manuscript, we formulate the general Target-Attacker-Defender differential game in both continuous-time and discrete-time turn-based variants in n-dimensional Euclidean space. The objective of the Attackers is to get as close as possible to the Target before collision with the Defender, while the Target and Defender coordinate to achieve the opposite. We consider the most general setting for this zero-sum differential game, where the agents can move at different speeds, and prove the Nash equilibrium strategies in the discrete-time turn-based variant.
INTERNATIONAL JOURNAL OF CONTROL
(2022)
Article
Automation & Control Systems
Kai-Ning Wu, Wei-Jie Zhou, Xiao-Zhen Liu
Summary: This paper investigates the passivity-based boundary control problem of reaction-diffusion systems with time-varying delay and boundary input-output. By employing the Lyapunov functional method and inequality techniques, sufficient conditions for input strict passivity and output strict passivity of the systems are derived. In the presence of parameter uncertainties, sufficient conditions for robust passivity are presented. Moreover, the theoretical results are applied to the synchronization problem of coupled reaction-diffusion systems with delay, and a criterion for asymptotic synchronization is obtained. Numerical simulations are provided to validate the effectiveness of the theoretical results.
JOURNAL OF THE FRANKLIN INSTITUTE-ENGINEERING AND APPLIED MATHEMATICS
(2022)
Article
Engineering, Mechanical
Shuang Liang, Kai-Ning Wu
Summary: The boundary control problem for stochastic Korteweg-de Vries-Burgers equations is investigated, with proposed criteria for mean square exponential stability, robust mean square exponential stability, and mean square H-infinity performance, in the presence of uncertainties in system parameters and additive noises. Numerical examples validate the theoretical results.
NONLINEAR DYNAMICS
(2022)
Article
Computer Science, Artificial Intelligence
Xing-Yu Li, Qing-Ling Fan, Xiao-Zhen Liu, Kai-Ning Wu
Summary: This article investigates the exponential stability of delay reaction-diffusion cellular neural networks (DRDCNNs) in two cases: when the state information is fully available and when it is not fully available. Aperiodically intermittent boundary controllers are designed to stabilize the controlled system when the state information is fully available, and observer-based aperiodically intermittent boundary controllers are proposed when the state information is not fully available. By utilizing the Lyapunov functional method and Poincare's inequality, a criterion for achieving exponential stabilization of DRDCNNs is obtained. The influence of diffusion coefficient matrix, control gains, time-delays, and control proportion on stability is studied based on the obtained results. Numerical examples are presented to illustrate the effectiveness of the theoretical results.
NEURAL COMPUTING & APPLICATIONS
(2022)
Article
Automation & Control Systems
Wei-Jie Zhou, Min Long, Xiao-Zhen Liu, Kai-Ning Wu
Summary: This paper investigates the passivity-based boundary control problem for stochastic delay reaction-diffusion systems with boundary input-output. Delay-dependent sufficient conditions are obtained to ensure the stability and robustness of the system using Lyapunov functional method and stochastic inequality techniques. Numerical simulations are provided to validate the effectiveness of the proposed theoretical results.
INTERNATIONAL JOURNAL OF SYSTEMS SCIENCE
(2023)
Article
Mathematics, Applied
Run-Jie Zhang, Liming Wang, Kai-Ning Wu
Summary: This paper investigates the boundary finite-time stabilization of fractional reaction-diffusion systems (FRDSs). Sufficient conditions are obtained to ensure the finite-time stability (FTS) of FRDSs under the designed controller. The effect of diffusion term of FRDSs on the FTS is also investigated. Both Neumann and mixed boundary conditions are considered. Moreover, the robust finite-time stabilization of uncertain FRDSs is studied when there are uncertainties in the system's coefficients. Numerical examples are presented to verify the effectiveness of the theoretical results.
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
(2023)
Article
Mathematics, Applied
Shuang Liang, Kai-Ning Wu, Ming-Xin He
Summary: The research focuses on the finite-time boundary stabilization of the Korteweg-de Vries-Burgers (KdVB) equations. A distributed controller and a boundary controller design are proposed to ensure stability. The effectiveness of the proposed methods is verified through theoretical analysis and numerical examples.
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION
(2023)
Article
Mathematics, Applied
Shuang Liang, Deqiong Ding, Kai-Ning Wu
Summary: The exponential input-to-state stability (EISS) for delay Korteweg-de Vries-Burgers (DKdVB) equations is investigated in this paper. By using the Lyapunov-Krasovskii functional method and inequality techniques, a sufficient condition is established to ensure the EISS for DKdVB equations. This condition shows the effect of both time delay and diffusion term on the EISS. Robust EISS of uncertain DKdVB equations is also studied in the presence of uncertainties of system's coefficients, and a criterion is obtained to guarantee the EISS for the uncertain DKdVB equation. Numerical simulation examples are provided to demonstrate the validity of the derived results.
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION
(2023)
Article
Computer Science, Information Systems
Yuan Sun, Bing Yan, Peng Shi, Cheng-Chew Lim
Summary: An adaptive leader-follower consensus controller is designed in this article for a class of nonlinear multiagent systems with time-varying asymmetric output constraints and unknown control directions. A new state transformation approach is introduced to convert the output into an equivalent unconstrained state. By integrating different control methods, including an adaptive neural network-based backstepping control method and a Nussbaum function approach, the controller compensates for the unknown control directions and guarantees the convergence of the consensus tracking error to a small compact set.
IEEE SYSTEMS JOURNAL
(2023)
Article
Automation & Control Systems
Zhi Lian, Peng Shi, Cheng-Chew Lim, Xin Yuan
Summary: This article addresses the problem of lateral control for networked-based autonomous vehicle systems. A novel solution is proposed using fuzzy-model-based system and asynchronous resilient event-triggered scheme. The proposed control design techniques enable the vehicles to smoothly follow the planned path under external disturbances and network-induced issues.
IEEE TRANSACTIONS ON CYBERNETICS
(2023)
Article
Automation & Control Systems
Xiao-Zhen Liu, Kai-Ning Wu, Choon Ki Ahn
Summary: This article studies the synchronization problem of coupled fractional delayed reaction-diffusion neural networks with boundary controllers. The study presents both time-continuous and time-discontinuous controllers and analyzes the effects of control parameters on system performance.
IEEE TRANSACTIONS ON SYSTEMS MAN CYBERNETICS-SYSTEMS
(2023)
Article
Mathematics, Applied
Xing -Yu Li, Kai-Ning Wu, Xiao-Zhen Liu
Summary: In this study, the Mittag-Leffler stabilization of short memory fractional reaction-diffusion systems (SMFRDSs) is investigated using a designed intermittent boundary controller. By employing the Lyapunov functional method and various inequalities, a sufficient criterion is derived to ensure the Mittag-Leffler stability of SMFRDSs. The robust Mittag-Leffler stability is also considered in the presence of uncertainties in SMFRDSs. Furthermore, the influence of control gains and diffusion coefficient matrix on stability is analyzed. Numerical simulations are conducted to validate the proposed approach based on the obtained results.
APPLIED MATHEMATICS AND COMPUTATION
(2023)
Article
Computer Science, Artificial Intelligence
Yang Fei, Peng Shi, Cheng-Chew Lim
Summary: This article investigates the collision-free cooperative formation control problem for second-order multiagent systems with unknown velocity, dynamics uncertainties, and limited reference information. It proposes an observer-based sliding mode control law to ensure convergence of the system's tracking error and boundedness of the relative distance between each pair of agents. Potential fields and a time-varying topology are introduced to achieve collision-free motion.
IEEE TRANSACTIONS ON NEURAL NETWORKS AND LEARNING SYSTEMS
(2023)
Article
Automation & Control Systems
Xin-Xin Han, Kai-Ning Wu, Yugang Niu
Summary: This article presents an asynchronous boundary control design for a class of MJRDNNs, establishes a sufficient criterion for ensuring the stochastic finite-time boundedness of the considered MJRDNNs, and provides a numerical example to illustrate the effectiveness of the proposed design method.
IEEE TRANSACTIONS ON CYBERNETICS
(2023)
Article
Mathematics, Applied
Hao Liu, Yuzhe Li
Summary: This paper investigates the finite-time stealthy covert attack on reference tracking systems with unknown-but-bounded noises. It proposes a novel finite-time covert attack method that can steer the system state into a target set within a finite time interval while being undetectable.
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION
(2024)
Article
Mathematics, Applied
Nikolay A. Kudryashov, Aleksandr A. Kutukov, Sofia F. Lavrova
Summary: The Chavy-Waddy-Kolokolnikov model with dispersion is analyzed, and new properties of the model are studied. It is shown that dispersion can be used as a control mechanism for bacterial colonies.
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION
(2024)
Article
Mathematics, Applied
Qiang Ma, Jianxin Lv, Lin Bi
Summary: This paper introduces a linear stability equation based on the Boltzmann equation and establishes the relationship between small perturbations and macroscopic variables. The numerical solutions of the linear stability equations based on the Boltzmann equation and the Navier-Stokes equations are the same under the continuum assumption, providing a theoretical foundation for stability research.
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION
(2024)
Article
Mathematics, Applied
Samuel W. Akingbade, Marian Gidea, Matteo Manzi, Vahid Nateghi
Summary: This paper presents a heuristic argument for the capacity of Topological Data Analysis (TDA) to detect critical transitions in financial time series. The argument is based on the Log-Periodic Power Law Singularity (LPPLS) model, which characterizes financial bubbles as super-exponential growth (or decay) with increasing oscillations approaching a tipping point. The study shows that whenever the LPPLS model fits the data, TDA generates early warning signals. As an application, the approach is illustrated using positive and negative bubbles in the Bitcoin historical price.
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION
(2024)
Article
Mathematics, Applied
Xavier Antoine, Jeremie Gaidamour, Emmanuel Lorin
Summary: This paper is interested in computing the ground state of nonlinear Schrodinger/Gross-Pitaevskii equations using gradient flow type methods. The authors derived and analyzed Fractional Normalized Gradient Flow methods, which involve fractional derivatives and generalize the well-known Normalized Gradient Flow method proposed by Bao and Du in 2004. Several experiments are proposed to illustrate the convergence properties of the developed algorithms.
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION
(2024)
Article
Mathematics, Applied
Lianwen Wang, Xingyu Wang, Zhijun Liu, Yating Wang
Summary: This contribution presents a delayed diffusive SEIVS epidemic model that can predict and quantify the transmission dynamics of slowly progressive diseases. The model is applied to fit pulmonary tuberculosis case data in China and provides predictions of its spread trend and effectiveness of interventions.
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION
(2024)
Article
Mathematics, Applied
Shuangxi Huang, Feng-Fei Jin
Summary: This paper investigates the error feedback regulator problem for a 1-D wave equation with velocity recirculation. By introducing an invertible transformation and an adaptive error-based observer, an observer-based error feedback controller is constructed to regulate the tracking error to zero asymptotically and ensure bounded internal signals.
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION
(2024)
Article
Mathematics, Applied
Weimin Liu, Shiqi Gao, Feng Xu, Yandong Zhao, Yuanqing Xia, Jinkun Liu
Summary: This paper studies the modeling and consensus control of flexible wings with bending and torsion deformation, considering the vibration suppression as well. Unlike most existing multi-agent control theories, the agent system in this study is a distributed parameter system. By considering the mutual coupling between the wing's deformation and rotation angle, the dynamics model of each agent is expressed using sets of partial differential equations (PDEs) and ordinary differential equations (ODEs). Boundary control algorithms are designed to achieve control objectives, and it is proven that the closed-loop system is asymptotically stable. Numerical simulation is conducted to demonstrate the effectiveness of the proposed control scheme.
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION
(2024)
Article
Mathematics, Applied
Gourav Mandal, Lakshmi Narayan Guin, Santabrata Chakravarty
Summary: The ecological framework investigates the dynamical complexity of a system influenced by prey refuge and alternative food sources for predators. This study provides a thorough investigation of the stability-instability phenomena, system parameters sensitivity, and the occurrence of bifurcations. The bubbling phenomenon, which indicates a change in the amplitudes of successive cycles, is observed in the current two-dimensional continuous system. The controlling system parameter for the bubbling phenomena is found to be the most sensitive. The prediction and identification of bifurcations in the dynamical system are crucial for theoretical and field researchers.
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION
(2024)
Article
Mathematics, Applied
Damian Trofimowicz, Tomasz P. Stefanski, Jacek Gulgowski, Tomasz Talaska
Summary: This paper presents the application of control engineering methods in modeling and simulating signal propagation in time-fractional electrodynamics. By simulating signal propagation in electromagnetic media using Maxwell's equations with fractional-order constitutive relations in the time domain, the equations in time-fractional electrodynamics can be considered as a continuous-time system of state-space equations in control engineering. Analytical solutions are derived for electromagnetic-wave propagation in the time-fractional media based on state-transition matrices, and discrete time zero-order-hold equivalent models are developed and their analytical solutions are derived. The proposed models yield the same results as other reference methods, but are more flexible in terms of the number of simulation scenarios that can be tackled due to the application of the finite-difference scheme.
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION
(2024)
Article
Mathematics, Applied
Yuhao Zhao, Fanhao Guo, Deshui Xu
Summary: This study develops a vibration analysis model of a nonlinear coupling-layered soft-core beam system and finds that nonlinear coupling layers are responsible for the nonlinear phenomena in the system. By using reasonable parameters for the nonlinear coupling layers, vibrations in the resonance regions can be reduced and effective control of the vibration energy of the soft-core beam system can be achieved.
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION
(2024)
Article
Mathematics, Applied
S. Kumar, H. Roy, A. Mitra, K. Ganguly
Summary: This study investigates the nonlinear dynamic behavior of bidirectional functionally graded plates (BFG) and unidirectional functionally graded plates (UFG). Two different methods, namely the whole domain method and the finite element method, are used to formulate the dynamic problem. The results show that all three plates exhibit hardening type nonlinearity, with the effect of material gradation parameters being more pronounced in simply supported plates.
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION
(2024)
Article
Mathematics, Applied
Isaac A. Garcia, Susanna Maza
Summary: This paper analyzes the role of non-autonomous inverse Jacobi multipliers in the problem of nonexistence, existence, localization, and hyperbolic nature of periodic orbits of planar vector fields. It extends and generalizes previous results that focused only on the autonomous or periodic case, providing novel applications of inverse Jacobi multipliers.
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION
(2024)
Article
Mathematics, Applied
Yongjian Liu, Yasi Lu, Calogero Vetro
Summary: This paper introduces a new double phase elliptic inclusion problem (DPEI) involving a nonlinear and nonhomogeneous partial differential operator. It establishes the existence and extremality results to the elliptic inclusion problem and provides definitions for weak solutions, subsolutions, and supersolutions.
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION
(2024)
Article
Mathematics, Applied
Shangshuai Li, Da-jun Zhang
Summary: In this paper, the Cauchy matrix structure of the spin-1 Gross-Pitaevskii equations is investigated. A 2 x 2 matrix nonlinear Schrodinger equation is derived using the Cauchy matrix approach, serving as an unreduced model for the spin-1 BEC system with explicit solutions. Suitable constraints are provided to obtain reductions for the classical and nonlocal spin-1 GP equations and their solutions, including one-soliton solution, two-soliton solution, and double-pole solution.
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION
(2024)
