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
Photonic reservoir computing based on nonlinear wave dynamics at microscale
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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
NLS approximation for wavepackets in periodic cubically nonlinear wave problems in ℝd
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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
On the Nonlinear Wave Equation with Time-periodic Potential
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DOI: 10.1093/imrn/rnz014
Abstract: It is known that for some time-periodic potentials $q(t, x) \geq 0$ having compact support with respect to $x$ some solutions of the Cauchy problem for the wave equation $\partial _t^2 u - \Delta _x… read more here.
Keywords: nonlinear wave; time periodic; wave equation; equation ... See more keywords
Strongly nonlinear wave dynamics of continuum phononic materials with periodic rough contacts.
Sign Up to like & getrecommendations! Published in 2022 at "Physical review. E"
DOI: 10.1103/physreve.105.024201
Abstract: We investigate strongly nonlinear wave dynamics of continuum phononic material with discrete nonlinearity. The studied phononic material is a layered medium such that the elastic layers are connected through contact interfaces with rough surfaces. These… read more here.
Keywords: wave dynamics; continuum phononic; dynamics continuum; strongly nonlinear ... See more keywords
Hermitian Nonlinear Wave Mixing Controlled by a PT-Symmetric Phase Transition.
Sign Up to like & getrecommendations! Published in 2022 at "Physical review letters"
DOI: 10.1103/physrevlett.129.153901
Abstract: While non-Hermitian systems are normally constructed through incoherent coupling to a larger environment, recent works have shown that under certain conditions coherent couplings can be used to similar effect. We show that this new paradigm… read more here.
Keywords: non hermitian; nonlinear wave; wave mixing; symmetric phase ... See more keywords
Dynamical behavior of nonlinear wave solutions of the generalized Newell–Whitehead–Segel equation
Sign Up to like & getrecommendations! Published in 2020 at "International Journal of Modern Physics C"
DOI: 10.1142/s012918312050059x
Abstract: Dynamical behavior of nonlinear wave solutions of the perturbed and unperturbed generalized Newell–Whitehead–Segel (GNWS) equation is studied via analytical and computational approaches for the fir... read more here.
Keywords: wave solutions; generalized newell; dynamical behavior; behavior nonlinear ... See more keywords