Article
Mathematics
Miguel Ballesteros, Diego Iniesta, Ivan Naumkin, Clemente Pena
Summary: This paper discusses the initial-boundary value problem for the nonlinear Klein-Gordon equation in a quarter-plane with Dirichlet non zero boundary conditions. By constructing the wave and scattering operators, the influence of the boundary data on the asymptotic behavior of solutions is studied. It is demonstrated that non zero boundary conditions require a modification of the critical value of the nonlinear term.
JOURNAL OF DIFFERENTIAL EQUATIONS
(2022)
Article
Mathematics, Applied
Jie Chen, Baoxiang Wang
Summary: In this paper, we investigate the almost sure scattering for the Klein-Gordon equations with Sobolev critical power and obtain the almost sure scattering with random initial data under certain conditions. We employ the method of induction on scales and bushes argument, and utilize the mass term of the Klein-Gordon equation to control the increment of energy.
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS
(2022)
Article
Engineering, Multidisciplinary
Daniel Appelo, Fortino Garcia, Allen Alvarez Loya, Olof Runborg
Summary: This paper considers the application of the WaveHoltz iteration to time-harmonic elastic wave equations with energy conserving boundary conditions. Two time-stepping schemes, explicit and implicit, are presented to eliminate time discretization error from the WaveHoltz solution. Numerical experiments demonstrate the effectiveness of the proposed methods.
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
(2022)
Article
Mathematics, Interdisciplinary Applications
Yao Haiyang, Wang Haiyan, Zhang Zhichen, Xu Yong, Juergen Kurths
Summary: This study formulates a mathematical model to describe the complex variation of underwater propagating acoustic signals, presenting a perturb-coefficient nonlinear propagation equation and analyzing initial and boundary conditions to obtain solutions. The model is proven effective through simulations and suitable for various underwater circumstances.
CHAOS SOLITONS & FRACTALS
(2021)
Article
Mathematics, Applied
Keltoum Bouhali, Sulima Ahmed Zubair, Wiem Abedelmonem Salah Ben Khalifa, Najla ELzein AbuKaswi Osman, Khaled Zennir
Summary: This study focuses on the analysis of the propagation of m-nonlinear viscoelastic waves equations in an unbounded domain, exploring the effects of various damping terms on solution behavior and finding an energy decay rate through appropriate energy estimates.
Article
Optics
Deniu Yang
Summary: This paper investigates bifurcations and soliton solutions for the Generalized Gerdjikov-Ivanov equation using the theory of dynamical systems. Bifurcation parameter sets are presented. Under fixed parameter cases, the exact explicit parametric representations of all bounded soliton solutions are obtained and classified.
Article
Engineering, Mechanical
Mohamed R. Ali, Mahmoud A. Khattab, S. M. Mabrouk
Summary: In this paper, the integrability of the Landau-Ginzburg-Higgs (LGH) equation is proved by deriving the Lax pair through a simple modification of the Ablowitz-Kaup-Newell-Segur (AKNS) formalism. The inverse scattering transformation (IST) is then applied to obtain and graphically represent the travelling wave solutions in 2d and 3d profiles.
NONLINEAR DYNAMICS
(2023)
Article
Mathematics, Applied
Mohamed Biomy
Summary: This article discusses the impact of weak and strong damping terms on the decay rate in nonlinear m-wave equation systems with new viscoelastic structures. A novel scenario for energy decay is presented in system (3.7) by imposing a new condition on the kernel function in (2.4) using appropriate energy estimates. This result extends the findings in [18, 27] for m-equation systems inspired by the paper [1].
Article
Mathematics
Emil Novruzov, Vural Bayrak
Summary: We investigate the blow-up phenomena for the two-component generalizations of nonlinear dispersive wave equation on the real line and establish a blowup criterion for the system of coupled equations.
JOURNAL OF FUNCTIONAL ANALYSIS
(2022)
Article
Mechanics
D. Z. Ning, S. B. Zhang, L. F. Chen, H. -W. Liu, B. Teng
Summary: This study investigates the Bragg scattering of nonlinear surface waves over a wavy bottom using two-dimensional fully nonlinear numerical wave tanks. The results show the existence of classic Bragg resonances as well as newly captured resonances, and demonstrate the opposite roles of surface wave and bottom nonlinearities in shifting the resonance conditions.
JOURNAL OF FLUID MECHANICS
(2022)
Article
Crystallography
Hongcheng Ni, Yuangang Lu, Zelin Zhang, Jianqin Peng, Wei Geng, Biao Dong, Jian Huang
Summary: A novel nonlinear optical limiter based on stimulated Brillouin scattering in highly nonlinear fiber was proposed and experimentally demonstrated. The limiting effects of the highly nonlinear fiber were characterized and verified theoretically and experimentally. The proof-of-concept experiment showed that the proposed limiter has excellent performance due to its small effective area and high Brillouin gain coefficient.
Article
Physics, Fluids & Plasmas
G. Sary, L. Gremillet
Summary: In this paper, a novel 2D reduced numerical model for stimulated Raman scattering (SRS) in laser fusion plasmas is presented. It couples envelope equations for electromagnetic fields with a hybrid description of the electron species. The model accurately reproduces linear Landau damping and trapped-particle instabilities, and shows good agreement with experimental data.
PHYSICS OF PLASMAS
(2022)
Article
Physics, Multidisciplinary
Ya Guo, Hiroaki Nakajima, Wenbin Lin
Summary: The effective one-body method allows for the application of black hole perturbation theory to binary systems with comparable masses. In this study, we investigate the gravitational-wave equation for a spinless binary in the background of the effective one-body system, which is applicable to spherically symmetric backgrounds. We derive gauge conditions for the decoupled wave equation and provide solutions in terms of metric perturbations for a specific case, expanding upon the findings of Jing et al. (Sci. China-Phys. Mech. Astron. 65, 260411 (2022)). Ultimately, we obtain the gravitational-wave equation as a generalization of the Teukolsky equation.
SCIENCE CHINA-PHYSICS MECHANICS & ASTRONOMY
(2023)
Article
Optics
Binyu Rao, Xin Tian, Meng Wang, Xiaoming Xi, Chongwei Wang, Hao Lia, Zefeng Wang
Summary: This paper demonstrates an effective method to mitigate the Raman noise induced after long fiber transmission of oscillator laser by intensifying the four-wave mixing (FWM) process. Experimental results show that the oscillator with a wider bandwidth of the high reflection (HR) grating is easier to inspire the FWM process during laser transmission and tends to have a lower Raman ratio at the output. The observed SRS suppression is more than 15 dB. This work should have significant reference for SRS suppression during the power scaling of high-power fiber amplifiers by the master-oscillator power-amplifier (MOPA) structure.
OPTICS AND LASER TECHNOLOGY
(2023)
Article
Optics
M. T. Darvishi, Mohammad Najafi, Lanre Akinyemi, Hadi Rezazadeh
Summary: In this study, three well-known PDEs are extended to logarithmic nonlinearities with and without attenuation terms. The logarithmic unstable nonlinear Schrodinger (UNLS), logarithmic Hamiltonian amplitude, and logarithmic extended UNLS equations are investigated to find their Gaussian solitary wave solutions. It is shown that these logarithmic models can be distinguished by Gaussian solitary wave solutions. These logarithmic extensions and their Gaussian solutions will be helpful in finding logarithmic extensions of other PDEs.
JOURNAL OF NONLINEAR OPTICAL PHYSICS & MATERIALS
(2023)
Article
Physics, Multidisciplinary
Tinggui Chen, Baizhan Xia, Dejie Yu, Chuanxing Bi
Summary: This study proposes a gradient phononic crystal structure for enhanced acoustic sensing. By breaking the symmetry of the PC structure, topologically protected edge states are introduced, resulting in topological acoustic rainbow trapping. The robustness and enhancement properties are verified numerically and experimentally.
