Article
Mechanics
Zhenyong Lu, Shun Zhong, Huizheng Chen, Xiaodong Wang, Jiajie Han, Chao Wang
Summary: This study focuses on the nonlinear behaviors of a dual-rotor system supported by a rolling element bearing, discussing the time-varying stiffness and primary resonance behaviors affected by the ball bearing parameters. The results show that the mean values of the equivalent stiffness of the system and the rotation speed for forced resonance decrease as the clearance of the ball bearing increases.
INTERNATIONAL JOURNAL OF NON-LINEAR MECHANICS
(2021)
Article
Engineering, Mechanical
Shuai Gao, Steven Chatterton, Lorenzo Naldi, Paolo Pennacchi
Summary: Rolling elements in rolling element bearings should continuously roll on raceways for pure rolling, but skidding or over-skidding may occur with improper loading and lubrication, especially in low-load roller bearings. An empirical study shows the inaccuracy of theoretical values for determining slipping of rolling elements, and proposes a more accurate KH-THD model that considers thermal effects for large-scale industrial bearings.
MECHANICAL SYSTEMS AND SIGNAL PROCESSING
(2021)
Article
Engineering, Aerospace
Xinxing Ma, Hui Ma, Haiqin Qin, Xumin Guo, Chenguang Zhao, Mingyue Yu
Summary: The study focuses on the influence of SFD on the nonlinear dynamic behavior of a dual-rotor system supported by rolling bearings. It is found that SFD can effectively suppress amplitude jumps in the system, but improper parameters may worsen vibration. The ball bearing clearance, unbalance, centralizing spring stiffness, and oil film clearance of SFD all have effects on the system's steady-state vibration responses.
CHINESE JOURNAL OF AERONAUTICS
(2021)
Article
Engineering, Multidisciplinary
Xuan Xie, Ming Li, Xiaolei Du
Summary: This study establishes a mathematical model for the nonlinear dynamic behavior of a marine rotor-bearing system coupled with vibration isolation structure under ship rolling motion, and analyzes the dynamic steady-state response of the system through numerical methods. The effects of rotor speed and ship rolling on the system are studied, with results showing significant nonlinear behaviors due to the influence of nonlinear oil film force and ship rolling motion.
APPLIED MATHEMATICAL MODELLING
(2022)
Article
Acoustics
Tianzhu Wang, Qian Ding
Summary: This paper investigates the modal balancing method for a rotor-bearing system based on nonlinear normal modes (NNMs). The proposed algorithm includes three steps: computing NNMs and expressing nonlinear modal shapes using complex Fourier series, describing unbalance response as a complex amplitude with higher harmonics, and estimating correction coefficients for each harmonic to obtain total unbalance corrections. Hertz contact force and different radial internal clearances of the ball bearings are considered in the balancing simulation. The accuracy and effectiveness of the proposed method are demonstrated by comparing the responses after balancing with NNMs and the linear modal method.
JOURNAL OF SOUND AND VIBRATION
(2023)
Article
Engineering, Multidisciplinary
Yaofeng Liu, Changfeng Yan, Jianxiong Kang, Zonggang Wang, Lixiao Wu
Summary: In the rotor-bearing system, vibration interaction between supporting bearings can cause a vibration response on a healthy bearing that resembles a faulty one, leading to a false positive fault diagnosis. To address this issue, a dynamic model of the RBS was developed, considering the effects of vibration interactions and verified through experimentation. The vibration characteristics of supporting bearings under typical types of vibration interactions were analyzed, and the amplitudes of characteristic frequencies for true and false positive faults were discussed. Based on this analysis, a fault diagnosis criterion was established to eliminate the impact of characteristic frequency amplitude and identify false positive faults. The criterion was successfully applied to experimental data.
Article
Acoustics
Shaojie Guo, Changqing Bai
Summary: This article investigates the coupling effects of unbalanced magnetic pull and ball bearing on the nonlinear vibration of a three-phase asynchronous motor using experimental and numerical methods. The results obtained from experiments and numerical analysis show that the unbalanced magnetic pull and ball bearing forces significantly interact and nonlinearly influence the rotor dynamic characteristics. The effects of rotational speed and rotor mass eccentricity are also discussed, and it is found that the magnetic pull gradually increases the amplitude of the ball bearing-rotor system, with its effect decreasing as the rotational speed and mass eccentricity increase.
JOURNAL OF VIBRATION AND CONTROL
(2022)
Article
Engineering, Mechanical
Hang Zhang, Miaomiao Cheng, Xiang Zhou, Libo Feng, Kai Feng
Summary: This study demonstrates that hybrid foil magnetic bearings can optimize the dynamic performance and improve the stability of the rotor system by adjusting the working mode and load sharing ratio. The results show that an appropriate load sharing ratio with hybrid mode can effectively improve the rotordynamic performance of the HFMBs-rotor system, while increasing the load can also significantly improve the stability of the system.
NONLINEAR DYNAMICS
(2023)
Article
Engineering, Mechanical
Duzhou Zhang, Dengyun Wu, Qinkai Han, Hong Wang
Summary: This paper investigates the dynamic force transmissibility of an aerospace flywheel rotor system supported by angular contact ball bearings. The study establishes a lateral vibration model for the system and uses harmonic balance method and arc length continuation to solve the DFT, discussing the effects of rotor unbalance excitation, axial preload, and rotor damping on the system performance. The results provide important insights for dynamic performance evaluation and vibration isolation device design in aerospace flywheel rotor systems.
NONLINEAR DYNAMICS
(2021)
Article
Engineering, Mechanical
Pengfei Wang, Hongyang Xu, Yang Yang, Hui Ma, Duo He, Xiang Zhao
Summary: The rotor misalignment fault is a common fault in rotating machinery systems, which has a significant impact on the dynamic characteristics of the system, especially in the low-speed range. Bearing misalignment should not be ignored and needs to be considered in modeling. Misalignment causes periodic changes in bearing contact angle, radial clearance, and ball rotational speed, as well as increasing the critical speed and axial vibration of the system.
NONLINEAR DYNAMICS
(2022)
Article
Engineering, Mechanical
Jianbo Zhang, Dongjiang Han, Zhongliang Xie, Chao Huang, Zhushi Rao, Mingbo Song, Zhimin Su
Summary: In this paper, a dynamic model of the aerostatic bearing-rotor system is established to investigate the influences of rotational speed, unbalance, rotor mass, and supply pressure on the nonlinear behaviors of the system. The results demonstrate various nonlinear phenomena, including periodic and quasi-periodic motions. Additionally, it is found that proper adjustments of the unbalance, rotor mass, and supply pressure can control the nonlinear vibration and enhance system stability.
TRIBOLOGY INTERNATIONAL
(2022)
Article
Mathematics, Applied
Bin Fang, Jinhua Zhang, Ke Yan, Jun Hong
Summary: In this paper, a novel mathematical model is established to study the VC parameter vibration responses of the ball bearing-rotor system based on the restoring force coupling method. The study considers both the rotor radial and tilting motions. The results show multiple resonant responses and complex internal resonance phenomenon in the rotor parametric vibration.
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION
(2023)
Article
Mechanics
Yaoyu Han, Lihua Yang, Tengfei Xu
Summary: This paper investigates the influence of changes in rolling element position on radial stiffness in bearing-rotor systems. Mathematical modeling based on Hertz elastic contact theory is used to study the differences in radial stiffness under two boundary positions and the oscillation of rotor center displacement. The results show significant fluctuations in radial stiffness and oscillations in rotor center position during system operation.
ARCHIVE OF APPLIED MECHANICS
(2021)
Article
Engineering, Multidisciplinary
Zeyuan Chang, Lei Hou, Yushu Chen
Summary: This paper investigates the nonlinear dynamics and thermal bidirectional coupling characteristics of a rotor-ball bearing system. The motion equations of the rotor system are formulated considering the thermal effects on the radial clearance of the ball bearing. A heat transfer model, incorporating the frictional heat generation induced by the ball bearing's dynamic load, is established and coupled with the motion equations. The results demonstrate that the thermal expansion of the ball bearing affects the dynamics and thermal characteristics of the system, while the nonlinear dynamic response of the rotor leads to nonlinear thermal characteristics of the ball bearing.
APPLIED MATHEMATICAL MODELLING
(2023)
Article
Engineering, Mechanical
Song Deng, Xianlin Zhu, Dongsheng Qian, Shaofeng Jiang, Lin Hua
Summary: This paper proposes a nonlinear dynamic model for studying angular contact ball bearings with waviness and cage whirl motion. The interactions between balls, cage, and bearing rings are investigated, and the impact of waviness on the dynamic behavior of the system is analyzed. The study shows that sparse waviness with tiny amplitude can improve the stability of the bearing system.
NONLINEAR DYNAMICS
(2022)
Article
Mechanics
Pawan Kumar, S. P. Harsha
Summary: In this study, the vibration response of porous functionally graded piezoelectric plates with electro-thermal loading was investigated using finite element formulations. The results showed that the material's unevenness and porosity distribution have an impact on the frequency, and the frequency decreases with an increase in the a/h ratio.
MECHANICS BASED DESIGN OF STRUCTURES AND MACHINES
(2023)
Article
Mechanics
Bikramjit Singh, R. S. Mulik, S. P. Harsha
Summary: In this study, static and vibration analyses of functionally graded gears (FGGs) were conducted using a numerical method. The results were compared with bi-material gears and steel gears to evaluate the performance differences.
MECHANICS BASED DESIGN OF STRUCTURES AND MACHINES
(2023)
Article
Engineering, Civil
V. Kumar, S. J. Singh, V. H. Saran, S. P. Harsha
Summary: This paper investigates the vibration response of a porous Functionally Graded Material (FGM) plate with variable thickness. Mathematical modeling is used to describe the plate resting on different types of elastic foundations. The effects of variable foundation and porosity distribution on the plate's behavior are analyzed and compared to that of a homogeneous plate.
INTERNATIONAL JOURNAL OF STRUCTURAL STABILITY AND DYNAMICS
(2023)
Article
Materials Science, Multidisciplinary
Bikramjit Singh, R. S. Mulik, S. P. Harsha
Summary: This study conducted a dynamic response analysis of functionally graded gears (FGGs) using a 6-degree of freedom dynamic model. Results showed that FGGs exhibited lower mesh stiffness and weight compared to steel gears within the considered range of gradient index (GI).
PROCEEDINGS OF THE INSTITUTION OF MECHANICAL ENGINEERS PART L-JOURNAL OF MATERIALS-DESIGN AND APPLICATIONS
(2023)
Article
Engineering, Mechanical
Rajesh Govindan, V. Huzur Saran, Suraj Prakash Harsha
Summary: This study investigates the transmissibility responses of 14 male subjects exposed to vertical sinusoidal vibration at different frequencies and magnitudes. The results show that the resonance frequency decreases with increasing vibration magnitude for the sternum, abdomen, thigh, and leg. Higher vibration magnitudes result in greater segmental transmissibility at frequencies lower than the resonance frequency. The abdomen exhibits the highest vibration transmissibility, followed by the thigh, sternum, and head.
PROCEEDINGS OF THE INSTITUTION OF MECHANICAL ENGINEERS PART C-JOURNAL OF MECHANICAL ENGINEERING SCIENCE
(2023)
Article
Engineering, Mechanical
Vikas Tiwari, Satish C. Sharma, S. P. Harsha
Summary: This paper investigates the performance of suspension systems of high-speed passenger vehicles in a deflated state. A dynamic model with 13 degrees of freedom is developed and the influence of vibration on ride comfort and quality is assessed using Sperling's ride index method. The study focuses on the modelling of the air spring with a laminated rubber isolator. It is concluded that the vehicle should move at a slower speed when the air spring is deflated to maintain passenger comfort.
VEHICLE SYSTEM DYNAMICS
(2023)
Article
Engineering, Mechanical
Maan Singh Rathore, S. P. Harsha
Summary: The proposed framework of VAEGAN-RDCNN is used for bearing fault diagnosis based on nonlinear vibration responses. Imbalanced data augmentation is solved using VAEGAN, and residual deep convolutional neural network (RDCNN) is used to characterize the 2D patterns. Experimental results demonstrate that the proposed method achieves superior results in terms of generated sample quality and performance evaluation compared to conventional methods.
JOURNAL OF VIBRATION ENGINEERING & TECHNOLOGIES
(2023)
Article
Engineering, Multidisciplinary
Maan Singh Rathore, S. P. Harsha
Summary: Rotating machinery failure analysis requires signal preprocessing to extract fault-related information. This paper proposes a method using Gaussian Mixture Models (GMM) and t-distributed stochastic neighbor embedding (t-SNE) techniques for intelligent instance annotation, and a one-dimensional convolutional neural network (1DCNN) for automatic feature extraction and selection. Experimental results show that this method achieves higher accuracy in classifying bearing lifetime data.
JOURNAL OF FAILURE ANALYSIS AND PREVENTION
(2022)
Article
Engineering, Civil
Vikas Tiwari, Satish C. Sharma, S. P. Harsha
Summary: In a railroad wagon, air springs are used to restrict abnormal vibrations caused by track irregularities and improve traveler comfort. However, when air springs deflate, excessive vibrations occur and the ride becomes less comfortable. To alleviate this, a laminated rubber spring can act as a temporary emergency spring to reduce dynamic load. This study examines the effect of deflated air springs on passengers' ride comfort and proposes accurate prediction models. It also finds that the presence of a laminated rubber spring increases the dynamic stiffness of the air spring at higher frequencies and reducing the diameter of the surge pipe decreases its stiffness at lower frequencies. In order to maintain passenger comfort, vehicle speed should be reduced when the air spring is deflated.
INTERNATIONAL JOURNAL OF STRUCTURAL STABILITY AND DYNAMICS
(2023)
Article
Materials Science, Multidisciplinary
Pawan Kumar, Suraj P. Harsha
Summary: This paper analyzes the vibration and buckling responses of the smart porous core sandwich plate (SPCSP) under thermoelectric and thermomechanical loading. The plate has both conventional and unconventional boundary conditions. The thermo-mechanical properties of the plate vary through the thickness direction, and the plate considers geometrical nonlinearity and assumes a quadratic electric potential function. The formulation is derived using the Hamilton principle and the first-order shear deformation theory (FSDT) displacement field, and the governing equation is solved computationally using a modified Newton-Raphson scheme.
JOURNAL OF INTELLIGENT MATERIAL SYSTEMS AND STRUCTURES
(2023)
Article
Engineering, Mechanical
Maan Singh Rathore, S. P. Harsha
Summary: This paper proposes a data augmentation model SAE-WGAN to address the data imbalance issue in bearing fault diagnosis. The model utilizes Wasserstein distance and informative noise vectors to improve the quality of generated samples for stable training. Metrics such as normalized cross-correlation and Kullback-Leibler divergence are employed for quantitative evaluation. Experimental validation and comparisons demonstrate the effectiveness of the proposed model, achieving improvements compared to state-of-the-art methods. The utilization of one-dimensional convolutional neural network further enhances fault classification performance under limited faulty data, as indicated by receiver operating characteristic curve and area under curve values.
JOURNAL OF THE BRAZILIAN SOCIETY OF MECHANICAL SCIENCES AND ENGINEERING
(2023)
Article
Mechanics
V. Kumar, S. J. Singh, V. H. Saran, S. P. Harsha
Summary: This manuscript focuses on the analysis of free and forced vibration considering porosity and orthotropic foundation effect. It presents an exact solution for a variable thickness functionally graded material (FGM) plate resting on an orthotropic foundation using the first-order shear deformation plate theory (FSDT) model. Mathematical modeling takes into account three types of microstructural defects and the effect of the orthotropic Pasternak foundation. The differential equation is derived using a variational approach and solved through the Galerkin method, with results compared and validated against existing literature.
MECHANICS BASED DESIGN OF STRUCTURES AND MACHINES
(2023)
Article
Automation & Control Systems
Amit Mathur, Pradeep Kumar, S. P. Harsha
Summary: This article presents a data-driven fault diagnosis method for rolling element bearing under different operating conditions. Filter-type feature selection algorithms are incorporated to rank the time-domain statistical features extracted from vibration data of various bearing defect conditions. The results show that the neighborhood component analysis algorithm achieves the highest accuracies for bearing fault detection with both the support vector machine and artificial neural network. The effective feature ranking before fault classification can lead to efficient and reliable bearing fault diagnosis.
PROCEEDINGS OF THE INSTITUTION OF MECHANICAL ENGINEERS PART I-JOURNAL OF SYSTEMS AND CONTROL ENGINEERING
(2023)
Article
Engineering, Mechanical
Anand Prakash, Pawan Kumar, V. H. Saran, S. P. Harsha
Summary: In this study, thermoelastic static and vibration analysis of a thin functionally graded sigmoidal porous plate using higher-order NURBS-based Isogeometric analysis has been conducted. The material properties of the plate vary according to a modified power and sigmoid law. The mathematical model is formulated based on the Kirchhoff-Love theory, virtual work principle, and high-order continuity of NURBS basis functions. The analysis investigates the effects of porosity index, material gradient index, boundary conditions, thermal loading, and geometry on deflection, vibration frequency, and mode shapes.
INTERNATIONAL JOURNAL OF MECHANICS AND MATERIALS IN DESIGN
(2023)
Article
Engineering, Civil
V. Kumar, S. J. Singh, V. H. Saran, S. P. Harsha
Summary: This work investigates the buckling response of a porous plate made of functionally graded materials. It considers a tapered FGM plate under uniaxial and biaxial loading with various boundary conditions. The effects of Pasternak foundation and different porosity patterns on the buckling response are studied. The study utilizes the first order-shear deformation theory and the Galerkin's-Vlasov method to derive the effective equations of motion for buckling analysis.
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)
