Behavior of periodic solutions of viscous conservation laws under localized and nonlocalized perturbations
We establish nonlinear stability and asymptotic behavior of traveling periodic waves of
viscous conservation laws under localized perturbations or nonlocalized perturbations …
viscous conservation laws under localized perturbations or nonlocalized perturbations …
Modulational instability in equations of KdV type
It is a matter of experience that nonlinear waves in a dispersive medium, propagating
primarily in one direction, may appear periodic in small space and time scales, but their …
primarily in one direction, may appear periodic in small space and time scales, but their …
Nonlinear modulational stability of periodic traveling-wave solutions of the generalized Kuramoto–Sivashinsky equation
In this paper we consider the spectral and nonlinear stabilities of periodic traveling wave
solutions of a generalized Kuramoto–Sivashinsky equation. In particular, we resolve the …
solutions of a generalized Kuramoto–Sivashinsky equation. In particular, we resolve the …
Stability of small periodic waves in fractional KdV-type equations
MA Johnson - SIAM Journal on Mathematical Analysis, 2013 - SIAM
We consider the effects of varying dispersion and nonlinearity on the stability of periodic
traveling wave solutions of nonlinear PDEs of KdV type, including generalized KdV and …
traveling wave solutions of nonlinear PDEs of KdV type, including generalized KdV and …
On the Exponential Stability of a Nonlinear Kuramoto–Sivashinsky–Korteweg-de Vries Equation with Finite Memory
B Chentouf - Mediterranean Journal of Mathematics, 2022 - Springer
The aim of this paper is to investigate the stability problem for a nonlinear dispersive
equation with memory. More precisely, the equation under consideration combines the well …
equation with memory. More precisely, the equation under consideration combines the well …
Spectral stability of inviscid roll waves
We carry out a systematic analytical and numerical study of spectral stability of
discontinuous roll wave solutions of the inviscid Saint-Venant equations, based on a …
discontinuous roll wave solutions of the inviscid Saint-Venant equations, based on a …
Viscous film flow coating the interior of a vertical tube. Part 1. Gravity-driven flow
R Camassa, HR Ogrosky, J Olander - Journal of fluid mechanics, 2014 - cambridge.org
The gravity-driven flow of a viscous liquid film coating the inside of a tube is studied both
theoretically and experimentally. As the film moves downward, small perturbations to the …
theoretically and experimentally. As the film moves downward, small perturbations to the …
[PDF][PDF] Small-amplitude finite-depth Stokes waves are transversally unstable
arxiv:2409.01663v1 [math.AP] 3 Sep 2024 Page 1 arxiv:2409.01663v1 [math.AP] 3 Sep 2024
SMALL-AMPLITUDE FINITE-DEPTH STOKES WAVES ARE TRANSVERSALLY UNSTABLE …
SMALL-AMPLITUDE FINITE-DEPTH STOKES WAVES ARE TRANSVERSALLY UNSTABLE …
Stability of viscous St. Venant roll waves: from onset to infinite Froude number limit
We study the spectral stability of roll wave solutions of the viscous St. Venant equations
modeling inclined shallow water flow, both at onset in the small Froude number or “weakly …
modeling inclined shallow water flow, both at onset in the small Froude number or “weakly …
[HTML][HTML] Numerical proof of stability of roll waves in the small-amplitude limit for inclined thin film flow
B Barker - Journal of Differential Equations, 2014 - Elsevier
We present a rigorous numerical proof based on interval arithmetic computations
categorizing the linearized and nonlinear stability of periodic viscous roll waves of the KdV …
categorizing the linearized and nonlinear stability of periodic viscous roll waves of the KdV …