Attractors and transients for a perturbed periodic KdV equation: A nonlinear spectral analysis

1993 ◽  
Vol 3 (1) ◽  
pp. 477-539 ◽  
Author(s):  
N. M. Ercolani ◽  
D. W. McLaughlin ◽  
H. Roitner
Keyword(s):  
Spectral Analysis ◽  
Kdv Equation ◽  
Nonlinear Spectral Analysis ◽  
Perturbed Periodic

scholarly journals Multiscale Segmentation via Bregman Distances and Nonlinear Spectral Analysis

2017 ◽  
Vol 10 (1) ◽  
pp. 111-146 ◽  
Author(s):  
Leonie Zeune ◽  
Guus van Dalum ◽  
Leon W.M.M. Terstappen ◽  
Stephan A. van Gils ◽  
Christoph Brune
Keyword(s):  
Spectral Analysis ◽  
Bregman Distances ◽  
Multiscale Segmentation ◽  
Nonlinear Spectral Analysis

scholarly journals Internal gravity waves: Analysis using the periodic, inverse scattering transform

1999 ◽  
Vol 6 (1) ◽  
pp. 11-26 ◽  
Author(s):  
W. B. Zimmerman ◽  
G. W. Haarlemmer
Keyword(s):  
Spectral Analysis ◽  
Inverse Scattering ◽  
Gravity Waves ◽  
Water Waves ◽  
Nonlinear Filtering ◽  
Kdv Equation ◽  
Internal Gravity Waves ◽  
Inverse Scattering Transform ◽  
Linear Superposition ◽  
Scattering Transform

Abstract. The discrete periodic inverse scattering transform (DPIST) has been shown to provide the salient features of nonlinear Fourier analysis for surface shallow water waves whose dynamics are governed by the Korteweg-de Vries (KdV) equation - (1) linear superposition of components with power spectra that are invariants of the motion of nonlinear dispersive waves and (2) nonlinear filtering. As it is well known that internal gravity waves also approximately satisfy the KdV equation in shallow stratified layers, this paper investigates the degree to which DPIST provides a useful nonlinear spectral analysis of internal waves by application to simulations and wave tank experiments of internal wave propagation from localized dense disturbances. It is found that DPIST analysis is sensitive to the quantity λ = (r/6s) * (ε/μ2), where the first factor depends parametrically on the Richardson number and the background shear and density profiles and the second factor is the Ursell number-the ratio of the dimensionless wave amplitude to the dimensionless squared wavenumber. Each separate wave component of the decomposition of the initial disturbance can have a different value, and thus there is usually just one component which is an invariant of the motion found by DPIST analysis. However, as the physical applications, e.g. accidental toxic gas releases, are usually concerned with the propagation of the longest wavenumber disturbance, this is still useful information. In cases where only long, monochromatic solitary waves are triggered or selected by the waveguide, the entire DPIST spectral analysis is useful.

Wavelet basis analysis in perturbed periodic KdV equation

1998 ◽  
Vol 19 (11) ◽  
pp. 1053-1058 ◽  
Author(s):  
Lu Dianchen ◽  
Tian Lixin ◽  
Liu Zengrong
Keyword(s):  
Kdv Equation ◽  
Wavelet Basis ◽  
Perturbed Periodic
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