Article
Physics, Multidisciplinary
Shabir Ahmad, Sayed Saifullah, Arshad Khan, Mustafa Inc
Summary: This manuscript derives bright one and two soliton solutions for a nonlocal nonlinear integrable KdV equation using an improved Hirota bilinear method. The obtained results are visualized in 3D space using MATLAB, which demonstrate novel characteristics compared to the mKdV equation.
Article
Mathematics, Applied
Yu-Lan Ma, Bang-Qing Li
Summary: In this work, the nonlocal Boussinesq equations are investigated and the soliton solutions are derived using the Hirota bilinear method. The multiple solitons are classified into two types based on system parameters, and stripe-like solitons and breathers are obtained. The bifurcation behavior of solitons is found to be nonlinear, with the existence of three-and four-leaf envelopes for the breathers.
APPLIED MATHEMATICS LETTERS
(2022)
Article
Materials Science, Multidisciplinary
Shaofu Wang
Summary: The Hirota bilinear method is used to construct the new dynamics of complex N-soliton solutions for a nonlocal breaking equation. By using an auxiliary traveling wave function, different-order soliton solutions, bifurcation solutions, and lump solutions of the model are obtained. The physical phenomena and soliton propagation behavior of these solutions are explored, and the proposed soliton solutions are verified.
RESULTS IN PHYSICS
(2022)
Article
Optics
Yu-Han Deng, Xiang-Hua Meng, Gui-Min Yue, Yu-Jia Shen
Summary: This paper investigates the propagation of ultrashort femtosecond pulses in optical fibers using the Kundu-Eckhaus (KE) equation. The nonlocal KE equation, also known as the nonlocal integrable nonlinear Schrodinger equation with cubic and quintic nonlinearities, is solved using the Hirota bilinear method. The N-soliton solution is derived using symbolic calculation, and the exact solution expressions for two-soliton and three-soliton are obtained. Various propagation situations, such as periodic solitary wave evolution and collision of two parallel, perpendicular, and periodic solitary waves, are demonstrated and discussed under different parameters.
Article
Mathematics, Applied
Wen-Xin Zhang, Yaqing Liu
Summary: The paper constructs three types of reverse space, reverse time, and reverse space-time cmKdV equations, deriving diverse soliton solutions using the Hirota bilinear method. The Lax integrability of these nonlocal equations is studied through variable transformations, with figures used to describe the soliton solutions based on exact solution formulae. The solutions exhibit novel properties different from classical cmKdV equation based on their dynamical behaviors.
Article
Engineering, Mechanical
Jianping Wu
Summary: In this paper, a reduction approach is proposed for calculating multi-soliton solutions of the shifted nonlocal mKdV equation. The approach successfully reduces the N-soliton solution of the AKNS (q, r) system to three types of multi-soliton solutions of the shifted nonlocal mKdV equation, which are classified based on the spectrum configurations. Moreover, specific solutions are investigated theoretically and graphically.
NONLINEAR DYNAMICS
(2022)
Article
Physics, Multidisciplinary
Asli Pekcan
Summary: In this work, one- and two-soliton solutions of the integrable (2+1)-dimensional 3-component Maccari system are obtained using the Hirota bilinear method. Various local and nonlocal reductions of the system are represented, leading to the discovery of new integrable systems. Soliton solutions of these reduced systems are also obtained, and the solutions are illustrated by plotting their graphs for specific parameter values.
Article
Mathematics, Applied
Xuemei Xu, Yunqing Yang
Summary: This paper investigates the nonlinear dynamics of a interesting class of vector solitons in the two-component modified Korteweg-de Vries equation. Nondegenerate solitons and breather solutions of the system are constructed using a non-standard form of the Hirota direct method. The study shows that the solitons and breather solutions consist of three profiles: single-hump, double-hump, and flattop, and the collisions among solitons are always standard inelastic collisions. An explicit form of the general breather solution is presented.
APPLIED MATHEMATICS LETTERS
(2023)
Article
Engineering, Mechanical
Wen-Xin Zhang, Yaqing Liu
Summary: This paper studies the reverse space and/or time nonlocal Fokas-Lenells equation using the Hirota bilinear method. It derives the variable transformations, multisoliton and quasi-periodic solutions, and discusses the dynamical behaviors of the solutions. The paper also investigates the elastic and inelastic interactions of the solutions and discovers the infinite conservation laws of three types of nonlocal FL equations. The results obtained in this study are significant for exploring new physical phenomena in nonlinear media.
NONLINEAR DYNAMICS
(2022)
Article
Engineering, Mechanical
Xin Chen, Yaqing Liu, Jianhong Zhuang
Summary: This paper explores the exact soliton solutions of the (2+1)-dimensional generalized Hirota-Satsuma-Ito equations with time-dependent linear phase speed. The integrability condition is determined based on the Painleve integrability test of this equation. The general N-soliton solutions are then constructed using the Hirota bilinear method. The paper not only provides expressions for exact solutions and their degenerations, but also presents the spatial structures for different parameter choices, including line solitons, periodic solitons, lump solitons, and their interaction forms.
NONLINEAR DYNAMICS
(2023)
Article
Physics, Multidisciplinary
Shaofu Wang
Summary: This paper considers a high-dimensional wave soliton equation and constructs new soliton solutions, lump soliton solutions, breather solutions, and their combined solutions using the simple Hirota method and bilinear backlund transformation. Additionally, the paper explores the physical interaction and frontal collision phenomena of these solutions and verifies the obtained results.
Article
Mathematics, Applied
Pan Wang, Tian-Ping Ma, Feng-Hua Qi
Summary: This paper investigates the multi-soliton solutions of the CH equations and the interaction dynamics of solitons, analyzing different ways in which solitons interact and how soliton velocity can be controlled by adjusting physical parameters. Local interference between two/three solitons is observed experimentally, and the effects of parameters on the formation of peaks and holes during collisions are discussed.
APPLIED MATHEMATICS AND COMPUTATION
(2021)
Article
Mathematics
Wen-Xiu Ma
Summary: Reduced nonlocal matrix integrable modified Korteweg-de Vries (mKdV) hierarchies are obtained through two transpose-type group reductions in the matrix Ablowitz-Kaup-Newell-Segur (AKNS) spectral problems. Riemann-Hilbert problems and soliton solutions are formulated based on the reduced matrix spectral problems.
Article
Multidisciplinary Sciences
Hai Jing Xu, Song Lin Zhao
Summary: This paper examines local and nonlocal reductions of two nonisospectral Ablowitz-Kaup-Newell-Segur equations, resulting in various solutions for the modified Korteweg-de Vries equation and sine-Gordon equation, including solitons and Jordan block solutions. The dynamics of these solutions are analyzed and illustrated through asymptotic analysis.
Article
Physics, Multidisciplinary
Metin Gurses, Asli Pekcan
Summary: This study focuses on the one-and two-soliton solutions of shifted nonlocal NLS and MKdV equations. The singular structures of these soliton solutions are discussed and some graphs are presented.
Article
Physics, Multidisciplinary
Metin Gurses, Cetin Senturk
COMMUNICATIONS IN THEORETICAL PHYSICS
(2019)
Article
Physics, Particles & Fields
Metin Gurses, Yaghoub Heydarzade, Cetin Senturk
EUROPEAN PHYSICAL JOURNAL C
(2019)
Article
Mathematics, Applied
Metin Gurses, Asli Pekcan, Kostyantyn Zheltukhin
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION
(2020)
Article
Physics, Multidisciplinary
Metin Gurses, Asli Pekcan, Kostyantyn Zheltukhin
Article
Mathematics, Applied
Metin Gurses, Asli Pekcan
Summary: This study addressed the challenge of the nonexistence of Hirota formulation for AKNS(N) hierarchy for N >= 3 in (2 + 1) dimensions. The researchers overcame this difficulty for N = 3, 4 and obtained Hirota bilinear forms for these members. They explored local and nonlocal reductions of the equations and derived new integrable equations in (2 + 1) dimensions.
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION
(2021)
Article
Physics, Multidisciplinary
Metin Gurses, Asli Pekcan
Article
Physics, Multidisciplinary
Metin Gurses, Asli Pekcan
Summary: This study focuses on the one-and two-soliton solutions of shifted nonlocal NLS and MKdV equations. The singular structures of these soliton solutions are discussed and some graphs are presented.
Article
Acoustics
Metin Gurses, Asli Pekcan
Summary: We study two members of the multi-component AKNS hierarchy, namely the multi-NLS and multi-MKdV systems. The Hirota bilinear forms of these equations are derived, and soliton solutions are obtained. All possible local and nonlocal reductions of these systems of equations are found, and a prescription is given to obtain their soliton solutions. (2 + 1)-dimensional extensions of the multi-component AKNS systems are also derived.
Article
Astronomy & Astrophysics
Metin Gurses, Yaghoub Heydarzade, Cetin Senturk
Summary: In this study, we investigate the Kerr-Schild-Kundt class of metrics in generic gravity theories with Maxwell's field and prove that these metrics linearize and simplify the field equations of such theories.
Article
Physics, Multidisciplinary
Asli Pekcan
Summary: In this work, one- and two-soliton solutions of the integrable (2+1)-dimensional 3-component Maccari system are obtained using the Hirota bilinear method. Various local and nonlocal reductions of the system are represented, leading to the discovery of new integrable systems. Soliton solutions of these reduced systems are also obtained, and the solutions are illustrated by plotting their graphs for specific parameter values.
Article
Astronomy & Astrophysics
Metin Gurses, Yaghoub Heydarzade
Article
Astronomy & Astrophysics
Metin Gurses, Tahsin Cagri Sisman, Bayram Tekin
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)