Linearly Implicit and High-Order Energy-Conserving Schemes for Nonlinear Wave Equations
Sign Up to like & getrecommendations! Published in 2020 at "Journal of Scientific Computing"
DOI: 10.1007/s10915-020-01245-6
Abstract: A key issue in developing efficient numerical schemes for nonlinear wave equations is the energy-conserving. Most existing schemes of the energy-conserving are fully implicit and the schemes require an extra iteration at each time step… read more here.
Keywords: energy; energy conserving; high order; wave equations ... See more keywords
A study on fully nonlinear wave load effects on floating wind turbine
Sign Up to like & getrecommendations! Published in 2019 at "Journal of Fluids and Structures"
DOI: 10.1016/j.jfluidstructs.2019.05.008
Abstract: Abstract The influence of fully nonlinear wave effects on floating wind turbine has been studied in this paper by comparing both floater motions and structural responses of tower base and mooring lines exposed to linear… read more here.
Keywords: nonlinear wave; fully nonlinear; wind turbine; floating wind ... See more keywords
Bragg scattering of nonlinear surface waves by sinusoidal sandbars
Sign Up to like & getrecommendations! Published in 2024 at "Journal of Fluid Mechanics"
DOI: 10.1017/jfm.2023.1005
Abstract: Abstract Based on the multiple-scale expansion technique, a new set of extended nonlinear Schrödinger (ENLS) equations up to the third order is derived to account for the additional high-order bottom and dispersion effects as well… read more here.
Keywords: bragg scattering; effect; nonlinear wave; sandbar ... See more keywords
Nonlinear wave propagation governed by a fractional derivative
Sign Up to like & getrecommendations! Published in 2025 at "Nature Communications"
DOI: 10.1038/s41467-025-60625-4
Abstract: The idea of fractional derivatives has a long history that dates back centuries. Apart from their intriguing mathematical properties, fractional derivatives have been studied widely in physics, for example in quantum mechanics and generally in… read more here.
Keywords: governed fractional; propagation governed; fractional derivatives; nonlinear wave ... See more keywords
Photonic reservoir computing based on nonlinear wave dynamics at microscale
Sign Up to like & getrecommendations! Published in 2019 at "Scientific Reports"
DOI: 10.1038/s41598-019-55247-y
Abstract: High-dimensional nonlinear dynamical systems, including neural networks, can be utilized as computational resources for information processing. In this sense, nonlinear wave systems are good candidates for such computational resources. Here, we propose and numerically demonstrate… read more here.
Keywords: based nonlinear; reservoir; wave dynamics; information processing ... See more keywords
Invariant conservation law-preserving discretizations of linear and nonlinear wave equations
Sign Up to like & getrecommendations! Published in 2020 at "Journal of Mathematical Physics"
DOI: 10.1063/5.0004372
Abstract: Symmetry- and conservation law-preserving finite difference discretizations are obtained for linear and nonlinear one-dimensional wave equations on five- and nine-point stencils using the theory of Lie point symmetries of difference equations and the discrete direct… read more here.
Keywords: conservation law; conservation; point; wave equations ... See more keywords
Basic fractional nonlinear-wave models and solitons.
Sign Up to like & getrecommendations! Published in 2024 at "Chaos"
DOI: 10.1063/5.0190039
Abstract: This review article provides a concise summary of one- and two-dimensional models for the propagation of linear and nonlinear waves in fractional media. The basic models, which originate from Laskin's fractional quantum mechanics and more… read more here.
Keywords: models solitons; nonlinear wave; basic fractional; fractional nonlinear ... See more keywords
Simulation of nonlinear wave phenomena in Saturn's magnetosphere: Overtaking collisions of multisolitons at critical compositions
Sign Up to like & getrecommendations! Published in 2025 at "Physics of Plasmas"
DOI: 10.1063/5.0263626
Abstract: The excitation and overtaking collisions (OCs) of ion-acoustic solitons (IASs) are simulated in a plasma containing light and heavy ions, as well as cold and hot superthermal electrons, along with stationary charged dust grains. A… read more here.
Keywords: phenomena saturn; saturn magnetosphere; wave phenomena; nonlinear wave ... See more keywords
NLS approximation for wavepackets in periodic cubically nonlinear wave problems in ℝd
Sign Up to like & getrecommendations! Published in 2018 at "Applicable Analysis"
DOI: 10.1080/00036811.2018.1544620
Abstract: ABSTRACT The dynamics of single carrier wavepackets in nonlinear wave problems over periodic structures can be often formally approximated by the constant coefficient nonlinear Schrödinger equation as an effective model for the wavepacket envelope. We… read more here.
Keywords: periodic coefficients; approximation; nls approximation; approximation wavepackets ... See more keywords
Local well-posedness and small data scattering for energy super-critical nonlinear wave equations
Sign Up to like & getrecommendations! Published in 2019 at "Applicable Analysis"
DOI: 10.1080/00036811.2019.1616084
Abstract: In this work, we consider the following nonlinear wave equations We prove that when and The Cauchy problem is locally well-posed in with . Moreover, the small data theory holds under the same restriction. read more here.
Keywords: posedness small; well posedness; local well; small data ... See more keywords
Variational methods for breather solutions of nonlinear wave equations
Sign Up to like & getrecommendations! Published in 2021 at "Nonlinearity"
DOI: 10.1088/1361-6544/abed38
Abstract: We construct infinitely many real-valued, time-periodic breather solutions of the nonlinear wave equation ∂ttU−ΔU=Q(x)|U|p−2UonT×RN with suitable N ⩾ 2, p > 2 and localized nonnegative Q. These solutions are obtained from critical points of a… read more here.
Keywords: solutions nonlinear; methods breather; variational methods; breather solutions ... See more keywords