Article
Multidisciplinary Sciences
Attilio Maccari
Summary: This paper investigates the perturbative approach for the double sine-Gordon equation, which yields a set of differential equations that demonstrate the amplitude and phase modulation of the approximate solution. The well-known perturbation theory for the sine-Gordon equation is obtained when ? = 0. A phase-locked solution with the same frequency as the linear case is derived for a special value of ? = -1/8. Both coherent solutions (solitary waves, lumps, etc.) and fractal solutions are obtained in general. The presence of envelope wobbling solitary waves is demonstrated using symmetry considerations, highlighting the relationship between phase modulation, solution amplitude, and position. The main conclusion is that focusing solely on coherent solutions is overly simplistic due to the rich behavior of the double sine-Gordon equation, which includes wobbling chaotic and fractal solutions resulting from an arbitrary function in its solution.
Article
Engineering, Marine
Md Rezwan Ahamed Fahim, Purobi Rani Kundu, Md Ekramul Islam, M. Ali Akbar, M. S. Osman
Summary: The (3+ 1)-dimensional Kadomtsev-Petviashvili and the modified KdV-Zakharov-Kuznetsov equations have significant impact in modern science, and this article analyzes their effects on wave contours and extracts different standard wave configurations. Wave solutions are obtained using the sine-Gordon expansion method, and the efficiency of this approach in solving high-dimensional nonlinear evolution equations is established. The study provides closed-form solutions and discusses them through diagrams.
JOURNAL OF OCEAN ENGINEERING AND SCIENCE
(2022)
Article
Materials Science, Multidisciplinary
Zhiming Xue, Ganbin Chen, Changguo Wang, Rui Huang
Summary: The study investigates the peeling and sliding behaviors of graphene nanoribbons on a graphene substrate, revealing rich dynamics in adhesion, friction, and deformation patterns. Different types of strain solitons are identified during the stick-slip sliding process, depending on the ribbon structure. The study also highlights the influence of constrained displacements on the sliding force and the quasi-linear relationship between ribbon width and sliding friction.
JOURNAL OF THE MECHANICS AND PHYSICS OF SOLIDS
(2022)
Article
Engineering, Mechanical
O. Nikan, Z. Avazzadeh, M. N. Rasoulizadeh
Summary: This paper presents an efficient and accurate localized meshless collocation method for solving the nonlinear sine-Gordon equation with Neumann boundary conditions, demonstrating stability and convergence. The proposed LRBF-PU technique shows advantages in computational efficiency and well-conditioned linear systems compared to global collocation methods. Numerical results validate the method's effectiveness in capturing ring and line solitons of circular and elliptic shapes, with good agreement compared to existing literature.
NONLINEAR DYNAMICS
(2021)
Article
Mathematics, Applied
Timur Mashkin
Summary: The study focuses on the perturbed sine-Gordon equation with an assumed analytic perturbation F in ε. An invariant manifold adjusted to the perturbation F is implicitly constructed, with the initial value problem having a unique solution following a trajectory on the manifold. The trajectory is described by specific ODEs determined by two parameters.
Article
Mathematics, Applied
Yibo Wang, Rui Du, Zhenhua Chai
Summary: In this paper, a lattice Boltzmann model with BGK operator (LBGK) is proposed for solving time-fractional nonlinear wave equations in Caputo sense. The model approximates the Caputo fractional derivative using a fast evolution algorithm and demonstrates second-order accuracy in space through numerical examples.
ADVANCES IN APPLIED MATHEMATICS AND MECHANICS
(2022)
Article
Mathematics
Jiong Weng, Xiaojing Liu, Youhe Zhou, Jizeng Wang
Summary: The proposed method converts nonlinear wave equations into a system of ODEs and achieves a complete decoupling between spatial and temporal discretization. Numerical solutions to benchmark problems show that the wavelet algorithm has higher accuracy and faster convergence compared to existing methods. The accuracy of the method remains consistent across different equations and nonlinearities, indicating independence from equation order and nonlinearity.
Article
Mathematics, Applied
Huiyang Zhang, Yonghui Xia
Summary: Based on the geometric singular perturbation theory and the Melnikov method, this article studies the persistence of kink and anti-kink wave solutions in the perturbed double sine-Gordon equation. The explicit expression of the Melnikov function is provided. Furthermore, the monotonicity of the period function for the unperturbed double sine-Gordon equation is investigated.
APPLIED MATHEMATICS LETTERS
(2023)
Article
Mathematics, Interdisciplinary Applications
J. E. Macias-Diaz
Summary: This study provides computational evidence of nonlinear supratransmission in time-fractional sine-Gordon equations with damping for the first time. The presence of nonlinear supratransmission gradually diminishes as the order alpha decreases from 2 to 1, with bifurcation diagrams illustrating the relationship between driving amplitude and frequency triggering supratransmission.
CHAOS SOLITONS & FRACTALS
(2021)
Article
Engineering, Electrical & Electronic
Nauman Raza, Saima Arshed, Melike Kaplan, Asma Rashid Butt
Summary: This article investigates the propagation of pulses in optical fiber using the nonlinear partial differential equation (NPDE). Two analytical techniques, the Sine-Gordon expansion (SGE) procedure and the modified auxiliary equation (MAE) method, are used to study the proposed model. Trigonometric, hyperbolic, and rational function solutions are obtained from these methods. The obtained results are demonstrated with 3D graphs to show their physical significance and dynamic behaviors with different parameter values.
OPTICAL AND QUANTUM ELECTRONICS
(2022)
Article
Materials Science, Multidisciplinary
Md Abdul Kayum, Shamim Ara, M. S. Osman, M. Ali Akbar, Khaled A. Gepreel
Summary: Stable soliton solutions for the nonlinear Klein-Gordon equation have been established using the sine-Gordon expansion procedure, resulting in various new types of solitary wave solutions. The procedure is proven to be an efficient and straightforward mathematical tool for exact solitary wave solutions, with potential applications in optics, quantum mechanics, mathematical physics, and engineering.
RESULTS IN PHYSICS
(2021)
Article
Multidisciplinary Sciences
Purobi Rani Kundu, Md. Rezwan Ahamed Fahim, Md. Ekramul Islam, M. Ali Akbar
Summary: The EMC equation and the RW equation are important mathematical models in various fields, with the SGE method being developed to study higher-dimensional NLEEs. The extended SGE method successfully found multiple soliton solutions for these equations, showing that the solutions' characteristics are influenced by parameter choices. This study may have significant implications for analyzing higher-dimensional NLEEs.
Article
Mathematics, Applied
Shundong Zhu, Shanshan Yin, Xin Li
Summary: In this study, the degenerate solutions of the modified KdV-SG system were investigated through the bilinear method. The dynamic properties of these solutions were visually displayed and accurately described by specific mathematical expressions. Additionally, the paper intuitively demonstrated the derivation of higher-order degenerate solutions from the N-soliton solution.
APPLIED MATHEMATICS LETTERS
(2022)
Article
Mathematics
A. Paiva
Summary: The paper explores the interaction of Dirac delta-waves in models governed by the nonlinear Klein-Gordon equation, establishing that in certain cases they behave like classical solitons in the sine-Gordon equation. By examining the phi-four equation and the sine-Gordon equation, the study delves deeper into this phenomenon.
JOURNAL OF DIFFERENTIAL EQUATIONS
(2021)
Article
Physics, Multidisciplinary
Jun Li, Yong Chen
Summary: The paper introduces a new architecture that combines deep residual neural networks with underlying physical laws to address unresolved issues in solving nonlinear evolution equations. By utilizing the sine-Gordon equation as a case study, the model demonstrates good numerical results and robustness against small perturbations.
COMMUNICATIONS IN THEORETICAL PHYSICS
(2021)
Article
Geochemistry & Geophysics
S. V. Trofimenko, V. G. Bykov, T. V. Merkulova
JOURNAL OF VOLCANOLOGY AND SEISMOLOGY
(2015)
Article
Geochemistry & Geophysics
S. V. Trofimenko, V. G. Bykov, T. V. Merkulova
JOURNAL OF SEISMOLOGY
(2017)
Article
Geosciences, Multidisciplinary
Sergey V. Trofimenko, Victor G. Bykov, Nikolay V. Shestakov, Nikolay N. Grib, Hiroaki Takahashi
FRONTIERS OF EARTH SCIENCE
(2016)
Article
Geochemistry & Geophysics
S. V. Trofimenko, V. G. Bykov
JOURNAL OF VOLCANOLOGY AND SEISMOLOGY
(2017)
Article
Geosciences, Multidisciplinary
N. V. Shestakov, M. Ohzono, H. Takahashi, M. D. Gerasimenko, V. G. Bykov, E. I. Gordeev, V. N. Chebrov, N. N. Titkov, S. S. Serovetnikov, N. F. Vasilenko, A. S. Prytkov, A. A. Sorokin, M. A. Serov, M. N. Kondratyev, V. V. Pupatenko
DOKLADY EARTH SCIENCES
(2014)
Article
Geochemistry & Geophysics
Victor G. Bykov
JOURNAL OF SEISMOLOGY
(2014)
Article
Geosciences, Multidisciplinary
S. V. Trofimenko, V. G. Bykov
RUSSIAN JOURNAL OF PACIFIC GEOLOGY
(2014)
Article
Geosciences, Multidisciplinary
V. G. Bykov, T. Merkulova
RUSSIAN JOURNAL OF PACIFIC GEOLOGY
(2020)
Article
Geosciences, Multidisciplinary
V. G. Bykov, T. Merkulova
Summary: An analysis of earthquake data from different tectonic zones demonstrates their impact on the Amurian plate and surrounding structures. The study also reveals the migration patterns of earthquakes and highlights the insufficient research on the influence of the Western Pacific subduction on the deformation field in mainland Asia.
RUSSIAN JOURNAL OF PACIFIC GEOLOGY
(2021)
Article
Geochemistry & Geophysics
V. G. Bykov, T. Merkulova, M. Y. Andreeva
Summary: This paper explores the impact of Western Pacific subduction on the geodynamics of the Asian continent. The data on migration of slow strain and earthquakes from the Western Pacific subduction zone are analyzed, and the velocities of earthquake migration are calculated for different profiles.
PURE AND APPLIED GEOPHYSICS
(2022)
Article
Mechanics
V. G. Bykov
PHYSICAL MESOMECHANICS
(2020)
Article
Geochemistry & Geophysics
S. V. Trofimenko, V. G. Bykov, N. N. Grib
GEODYNAMICS & TECTONOPHYSICS
(2018)
Article
Geosciences, Multidisciplinary
Victor G. Bykov, Sergey V. Trofimenko
NONLINEAR PROCESSES IN GEOPHYSICS
(2016)
Review
Geochemistry & Geophysics
V. G. Bykov
GEODYNAMICS & TECTONOPHYSICS
(2018)