Local-in-space blow-up criteria for a class of nonlinear dispersive wave equations
Sign Up to like & getrecommendations! Published in 2017 at "Journal of Differential Equations"
DOI: 10.1016/j.jde.2017.06.031
Abstract: Abstract This paper is concerned with blow-up phenomena for the nonlinear dispersive wave equation on the real line, u t − u x x t + [ f ( u ) ] x − [… read more here.
Keywords: space blow; blow criteria; local space; dispersive wave ... See more keywords
Non-homogeneous initial-boundary-value problem of the fifth-order Korteweg-de Vries equation with a nonlinear dispersive term
Sign Up to like & getrecommendations! Published in 2021 at "Journal of Mathematical Analysis and Applications"
DOI: 10.1016/j.jmaa.2020.124848
Abstract: Abstract We study the initial-boundary-value problem of the fifth-order KdV equation ∂ t u − ∂ x 5 u = c 1 u ∂ x u + c 2 u 2 ∂ x u +… read more here.
Keywords: term; dispersive term; fifth order; problem ... See more keywords
Nonlinear dispersive regularization of inviscid gas dynamics
Sign Up to like & getrecommendations! Published in 2020 at "AIP Advances"
DOI: 10.1063/1.5133720
Abstract: Ideal gas dynamics can develop shock-like singularities with discontinuous density. Viscosity typically regularizes such singularities and leads to a shock structure. On the other hand, in 1d, singularities in the Hopf equation can be non-dissipatively… read more here.
Keywords: gas dynamics; gas; nonlinear dispersive; regularization ... See more keywords
New lower bounds on the radius of spatial analyticity for the higher order nonlinear dispersive equation on the real line
Sign Up to like & getrecommendations! Published in 2024 at "Journal of Mathematical Physics"
DOI: 10.1063/5.0211479
Abstract: In this paper, benefited some ideas of Wang [J. Geom. Anal. 33, 18 (2023)] and Dufera et al. [J. Math. Anal. Appl. 509, 126001 (2022)], we investigate persistence of spatial analyticity for solution of the… read more here.
Keywords: higher order; analyticity; order nonlinear; dispersive equation ... See more keywords
Anomalous Correlators in Nonlinear Dispersive Wave Systems
Sign Up to like & getrecommendations! Published in 2020 at "Physical Review X"
DOI: 10.1103/physrevx.10.021043
Abstract: An extension to wave turbulence theory shows that in a system of nonlinear waves, correlations among the waves arise, causing ``ghost'' excitations that lead to coherent structures in physical space. read more here.
Keywords: wave systems; anomalous correlators; dispersive wave; nonlinear dispersive ... See more keywords
Spatiotemporal Bragg gratings forming inside a nonlinear dispersive medium.
Sign Up to like & getrecommendations! Published in 2024 at "Optics letters"
DOI: 10.1364/ol.538147
Abstract: We show that a spatiotemporal Bragg grating can be created inside a nonlinear dispersive medium (such as silica fibers) by launching a periodic train of pump pulses that travel as fundamental solitons. We develop a… read more here.
Keywords: inside nonlinear; spatiotemporal bragg; nonlinear dispersive; bragg ... See more keywords
Well-balanced finite difference scheme for solving the nonlinear dispersive shallow water equations on a moving grid
Sign Up to like & getrecommendations! Published in 2025 at "Russian Journal of Numerical Analysis and Mathematical Modelling"
DOI: 10.1515/rnam-2025-0032
Abstract: Abstract An explicit finite difference scheme well balanced on a movable grid is constructed for calculating surface waves within the framework of the one-dimensional completely nonlinear dispersive Serre–Green–Naghdi model. The property of good balance on… read more here.
Keywords: well balanced; nonlinear dispersive; finite difference; difference scheme ... See more keywords
Derivation of acoustical streaming equations for nonlinear and dispersive fluids.
Sign Up to like & getrecommendations! Published in 2023 at "Ultrasonics"
DOI: 10.2139/ssrn.4199112
Abstract: The equations of streaming generated by an acoustic mod propagating in a nonlinear dispersive medium (exhibiting absorption and dispersion of phase sound speed) are derived with an arbitrarily shaped incident acoustical field assumed. This field… read more here.
Keywords: operator; nonlinear dispersive; dispersion; derivation acoustical ... See more keywords
Temporal Reflection from Ultrashort Solitons in Nonlinear Dispersive Medium: Impact of Raman Scattering
Sign Up to like & getrecommendations! Published in 2024 at "Photonics"
DOI: 10.3390/photonics11121189
Abstract: This review focuses on phenomena such as temporal reflection, total internal reflection, and waveguiding from ultrashort solitons forming inside a nonlinear dispersive medium such as an optical fiber. The case of wider solitons, moving at… read more here.
Keywords: temporal reflection; ultrashort solitons; reflection; nonlinear dispersive ... See more keywords