Article
Materials Science, Multidisciplinary
Haleh Tajadodi, Zareen A. Khan, Ateeq ur Rehman Irshad, J. F. Gomez-Aguilar, Aziz Khan, Hasib Khan
Summary: This article discusses how to formulate exact solutions of the time fractional DBM equation, Sinh-Gordon equation and Liouville equation using the simplest equation method in the context of conformable fractional derivatives. By transforming the original equations into nonlinear ODEs, the method provides a simple yet effective approach for solving FOPDEs.
RESULTS IN PHYSICS
(2021)
Article
Mathematics, Applied
Maciej Dunajski, Nora Gavrea
Summary: The passage discusses how radial solutions to the elliptic Sinh-Gordon and Tzitzeica equations can be interpreted as Abelian vortices on specific surfaces of revolution. These surfaces have a conical excess angle at infinity and can be globally embedded in hyperbolic space, even though they cannot be embedded in Euclidean 3-space. The existence of these hyperbolic embeddings is determined through asymptotic analysis of a Painleve III ordinary differential equation (ODE).
Article
Multidisciplinary Sciences
Rodica Cimpoiasu, Radu Constantinescu, Alina Streche Pauna
Summary: The paper explores traveling wave solutions of the Bullough-Dodd (BD) model of the scalar field using a technique based on multiple auxiliary equations. By reducing the model to a 2D-nonlinear equation and solving it through a refined version of the auxiliary equation technique, multiparametric solutions are discovered. The key idea is the degeneration of the general elliptic equation under special conditions into subequations with fewer parameters, allowing for the construction of a series of solutions for the BD equation in a unitary way, some of which are previously unreported. This technique could potentially be applied to handle other types of nonlinear equations from quantum field theory and other scientific fields.
Article
Mathematics, Applied
Wen-Rong Sun, Bernard Deconinck
Summary: By utilizing the integrability of the sinh-Gordon equation, the spectral stability of its elliptic solutions is demonstrated. A Lyapunov functional is constructed using the first three conserved quantities of the sinh-Gordon equation, showing that these elliptic solutions are orbitally stable with respect to subharmonic perturbations of arbitrary period.
JOURNAL OF NONLINEAR SCIENCE
(2021)
Article
Engineering, Mechanical
Hulya Durur, Asif Yokus, Kashif Ali Abro
Summary: Computational and traveling wave solutions were investigated for Tzitzeica and Dodd-Bullough-Mikhailov equations using the (1/G') -expansion method, resulting in different types of solutions presented in logarithmic form. The reliability and effectiveness of the method in producing hyperbolic type solutions were highlighted through graphical illustration and comparative analysis, indicating its applicability in obtaining exact solutions for nonlinear evolution equations.
NONLINEAR ENGINEERING - MODELING AND APPLICATION
(2021)
Article
Mathematics, Interdisciplinary Applications
Ji-Huan He, Yusry O. El-Dib
Summary: This paper presents a tutorial introduction to two-scale fractal calculus, discussing its compatibility with traditional differential derivatives and its applications in highly nonlinear differential equations. The use of two-scale transform to convert fractal differential equations to traditional models, along with the analysis using homotopy perturbation method, demonstrates the accuracy and applicability of the introduced formulation.
FRACTALS-COMPLEX GEOMETRY PATTERNS AND SCALING IN NATURE AND SOCIETY
(2021)
Article
Mathematics, Applied
Gordon Blower, Ian Doust
Summary: This paper discusses the scattering functions and their applications in Hankel integral operator of a linear system (-A, B, C) in continuous time t > 0. By studying the properties of algebras containing the integral operator R-infinity, solutions of the sinh-Gordon PDE are obtained. Moreover, the tau function of sinh-Gordon satisfies a particular Painleve III' nonlinear ODE and describes a random matrix model, with asymptotic distribution found by the Coulomb fluid method to be the solution of an electrostatic variational problem on an interval.
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
(2023)
Article
Physics, Multidisciplinary
T. Aydemir
Summary: In this paper, we discuss the unified method to find more general wave solutions of the Tzitzeica equation, the Dodd-Bullough-Mikhailov equation, and the Tzitzeica-Dodd-Bullough equation, with physical applications. The unified method provides straightforward solutions with free parameters, without the need for extra hardware support. The solutions are plotted using Maple to better understand the physical structure of the wave solutions. Diverse types of geometrically structured solitons are produced by using arbitrary parameters.
THEORETICAL AND MATHEMATICAL PHYSICS
(2023)
Article
Engineering, Mechanical
Leiqiang Bai, Jianming Qi, Yiqun Sun
Summary: The main novelty of this paper includes the first application of the modified (G'/G(2))-expansion method, the discussion of wave obliqueness effects in NQSGE, the investigation of phase portraits and bifurcation behaviors in NQSGE using Hamiltonian systems, the analysis of sensitivity to initial values and chaotic behavior in NQSGE, and the comparison of different fractional-order derivatives in NQSGE.
NONLINEAR DYNAMICS
(2023)
Article
Mathematics, Applied
Nauman Raza, Farwa Salman, Asma Rashid Butt, Maria Luz Gandarias
Summary: In this manuscript, the Lie point symmetries, conservation laws, and traveling wave reductions have been derived, and new forms of soliton solutions of the generalized q-deformed equation have been extracted via a unified method. The study has analyzed various solutions and demonstrated their statistical data through illustrations. This research is important for modeling complex processes.
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION
(2023)
Article
Astronomy & Astrophysics
S. Miraboutalebi, F. Ahmadi, A. Jahangiri
Summary: In this study, we investigate the nonlinear Klein-Gordon field with phi(4) self-interaction within the framework of the relativistic generalized uncertainty principle (RGUP). By applying the generalized tanh-method, we obtain more general solutions and analyze the energy spectrum of each solution. The modification parameter of the corresponding RGUP is estimated using the rest energy of the mass of the Higgs boson.
Article
Mathematics
Lewa' Alzaleq, Du'a Al-zaleq, Suboh Alkhushayni
Summary: The sinh-Gordon equation is widely used in various scientific fields to describe the dynamics of strings and multi-strings. In this paper, a generalized sinh-Gordon equation with variable coefficients is studied, and it is found that its traveling wave solutions can be derived from the known solutions of the standard sinh-Gordon equation. These solutions are valuable for studying the balance between dispersion and nonlinearity in real-life phenomena.
Article
Materials Science, Multidisciplinary
Da Shi, Zhao Li
Summary: This article studies and constructs new optical soliton solutions for the (������+1)-dimensional time fractional order Sinh-Gordon equation. The differential equation is transformed into an ordinary differential equation connected with a quartic polynomial using traveling wave transformation. Classification of the roots of the fourth degree polynomial is done using the polynomial complete discrimination system, and specific expressions of optical soliton solutions are given. The characteristics of some exact solutions are visualized using 3D, 2D, and contour graphs, providing a deeper understanding of the physical characteristics corresponding to the discussed model.
RESULTS IN PHYSICS
(2023)
Article
Mathematics, Applied
Abdullahi Yusuf, Tukur A. Sulaiman, Mustafa Inc, Sayed Abdel-Khalek, K. H. Mahmoud
Summary: This study investigates the nonlinear Hamiltonian amplitude equation using two analytical techniques and successfully constructs important wave solutions, depicting the clear dynamical behavior of the results. All acquired solutions satisfy the original equation.
Article
Materials Science, Multidisciplinary
A. Safaei Bezgabadi, M. A. Bolorizadeh
Summary: This paper presents the analytic solutions of the generalized nonlinear Schrodinger equation (GNLSE) by implementing the extended SinhGordon equation expansion method (ShGEEM), which includes effects such as dispersion, waveguide's loss, Kerr Effect, self-steepening and Raman Effect. The obtained solutions represent bright, dark and combined bright-dark solitons, and constraint conditions for valid solutions are provided. New solutions are graphically shown for pulse propagation along a photonic crystal fiber.
RESULTS IN PHYSICS
(2021)
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)
