scholarly journals Time-independent harmonics dispersion relation for time-evolving nonlinear waves

2021 ◽  
Vol 7 (50) ◽  
Author(s):  
Romik Khajehtourian ◽  
Mahmoud I. Hussein
Keyword(s):  
Dispersion Relation ◽  
Nonlinear Waves

Stability of strong electromagnetic waves in overdense plasmas against long-wavelength perturbations

1985 ◽  
Vol 33 (2) ◽  
pp. 285-301 ◽  
Author(s):  
F. J. Romeiras ◽  
G. Rowlands
Keyword(s):  
Dispersion Relation ◽  
Nonlinear Waves ◽  
Electromagnetic Waves ◽  
Modulation Depth ◽  
Longitudinal Direction ◽  
Transverse Component ◽  
Ion Density ◽  
Long Wavelength ◽  
The Stability ◽  
Two Parameters

We consider the stability against long-wavelength small parallel perturbations of a class of exact standing wave solutions of the equations that describe an unmagnetized relativistic overdense cold electron plasma. The main feature of these nonlinear waves is a circularly polarized transverse component of the electric field periodically modulated in the longitudinal direction. Using an analytical method developed by Rowlands we obtain a dispersion relation valid for long-wavelength perturbations. This dispersion relation is a biquadratic equation in the phase velocity of the perturbations whose coefficients are very complicated functions of the two parameters used to define the nonlinear waves: the normalized ion density and a quantity related to the modulation depth. This dispersion relation is discussed for the whole range of the two parameters revealing, in particular, the existence of a region in parameter space where the nonlinear waves are stable.

The dispersion relation for nonlinear waves in a developing process

1986 ◽  
Vol 4 (3) ◽  
pp. 256-277 ◽  
Author(s):  
Gu Daifang ◽  
Yuan Yeli
Keyword(s):  
Dispersion Relation ◽  
Nonlinear Waves

THE ANISOTROPIC CHARACTERS IN TWO-DIMENSIONAL LATTICE

2013 ◽  
Vol 27 (07) ◽  
pp. 1361010
Author(s):  
YANG YANG ◽  
MAI-MAI LIN ◽  
WEN-SHAN DUAN
Keyword(s):  
Dispersion Relation ◽  
Nonlinear Waves ◽  
Particle Displacement ◽  
Transverse Waves ◽  
Compressional Waves ◽  
Cubic Lattice ◽  
Simple Cubic ◽  
Simple Cubic Lattice ◽  
Special Cases ◽  
Linear And Nonlinear

The anisotropic characters of simple cubic lattice are investigated in this paper. Both the linear and nonlinear wave propagating in this lattice have been studied. The dispersion relation has been studied numerically. It is shown that the dispersion relation strongly depends on the directions of wave propagation. Generally, the direction of waves has the inclination angle α with respect to particle displacement. There are compressional waves α = 0 or transverse waves α = π/2 only for some special cases. The nonlinear waves in this lattice have also been studied. The anisotropic characters of this lattice for the nonlinear waves have also been shown. The compressional and transverse nonlinear solitons have also been studied. The characters of both solitons, such as amplitude and width, have been investigated.

Dispersion relation for nonlinear waves in a fluid with gas bubbles

1989 ◽  
Vol 29 (5) ◽  
pp. 688-690
Author(s):  
S. I. Plaksin
Keyword(s):  
Dispersion Relation ◽  
Nonlinear Waves ◽  
Gas Bubbles

scholarly journals Nonlinear waves on the surface of a fluid covered by an elastic sheet

2013 ◽  
Vol 733 ◽  
pp. 394-413 ◽  
Author(s):  
Luc Deike ◽  
Jean-Claude Bacri ◽  
Eric Falcon
Keyword(s):  
Dispersion Relation ◽  
Wave Field ◽  
Nonlinear Waves ◽  
Random Noise ◽  
Finite Size ◽  
Wave Turbulence ◽  
Transverse Motion ◽  
Elastic Sheet ◽  
Theoretical Hypothesis ◽  
Noise Forcing

AbstractWe experimentally study linear and nonlinear waves on the surface of a fluid covered by an elastic sheet where both tension and flexural waves occur. An optical method is used to obtain the full space–time wave field, and the dispersion relation of the waves. When the forcing is increased, a significant nonlinear shift of the dispersion relation is observed. We show that this shift is due to an additional tension of the sheet induced by the transverse motion of a fundamental mode of the sheet. When the system is subjected to a random-noise forcing at large scales, a regime of hydroelastic wave turbulence is observed with a power-law spectrum of the scale, in disagreement with the wave turbulence prediction. We show that the separation between relevant time scales is well satisfied at each scale of the turbulent cascade as expected theoretically. The wave field anisotropy, and finite size effects are also quantified and are not at the origin of the discrepancy. Finally, the dissipation is found to occur at all scales of the cascade, contrary to the theoretical hypothesis, and could thus explain this disagreement.

Nonlinear Waves, Solitons and Chaos

2000 ◽  
Author(s):  
Eryk Infeld ◽  
George Rowlands
Keyword(s):  
Nonlinear Waves

Nonlinear Waves and Inverse Scattering

1992 ◽  
Author(s):  
Mark J. Ablowitz
Keyword(s):  
Inverse Scattering ◽  
Nonlinear Waves

Nonlinear Waves, Dynamical Systems and Other Applied Mathematics Programs

1991 ◽  
Author(s):  
Jr. Miller ◽  
Friedman Willard ◽  
Avner
Keyword(s):  
Dynamical Systems ◽  
Nonlinear Waves ◽  
Applied Mathematics
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