Interacting Weakly Nonlinear Hyperbolic and Dispersive Waves

1991 ◽  
pp. 83-111 ◽  
Author(s):  
John K. Hunter
Keyword(s):  
Dispersive Waves ◽  
Weakly Nonlinear

Weakly nonlinear dispersive waves: group velocity

1982 ◽  
Vol 27 (3) ◽  
pp. 507-514
Author(s):  
Bhimsen K. Shivamoggi
Keyword(s):  
Group Velocity ◽  
Acoustic Waves ◽  
Specific Problem ◽  
Electron Plasma ◽  
Hot Electron ◽  
Ion Acoustic Waves ◽  
Dispersive Waves ◽  
Weakly Nonlinear ◽  
Longitudinal Waves ◽  
Wave Trains

For slowly varying wave trains in a linear system, it is known that a quantity proportional to the square of the amplitude propagates with the group velocity. It is shown here, by considering a specific problem of longitudinal waves in a hot electron-plasma and using an asymptotic analysis, that this result continues to be valid even when weak nonlinearities are introduced into the system provided they produce slowly varying wave trains. The method of analysis fails, however, for weakly nonlinear ion-acoustic waves.

Higher harmonics of electron plasma waves

1977 ◽  
Vol 17 (3) ◽  
pp. 357-368 ◽  
Author(s):  
E. Märk ◽  
N. Sato
Keyword(s):  
Harmonic Wave ◽  
Collisionless Plasma ◽  
Plasma Waves ◽  
Electron Plasma ◽  
Excited Electron ◽  
Harmonic Waves ◽  
Dispersive Waves ◽  
Weakly Nonlinear ◽  
Nonlinear Mixing ◽  
Higher Harmonic

A model based on nonlinear mixing of dispersive waves is used to predict higher harmonic waves generated by weakly nonlinear electron plasma waves. The total harmonic wave is given by superposition of modes which lie at different points (with the same frequency) in the dispersion diagram. The model well explains the experimental results concerning the harmonic waves produced by externally excited electron plasma waves propagating along a collisionless plasma column.

Nonlinear Wave Modulation in Nanorods Using Nonlocal Elasticity Theory

2018 ◽  
Vol 19 (7-8) ◽  
pp. 709-719 ◽  
Author(s):  
Guler Gaygusuzoglu ◽  
Metin Aydogdu ◽  
Ufuk Gul
Keyword(s):  
Elasticity Theory ◽  
Nonlinear Equations ◽  
Nonlinear Wave ◽  
Nonlocal Elasticity ◽  
Nonlocal Elasticity Theory ◽  
Reductive Perturbation Method ◽  
Nls Equation ◽  
Dispersive Waves ◽  
Weakly Nonlinear ◽  
Wave Modulation

AbstractIn this study, nonlinear wave modulation in nanorods is examined on the basis of nonlocal elasticity theory. Eringen's nonlocal elasticity theory is employed to derive nonlinear equations for the motion of nanorods. The analysis of the modulation of axial waves in nonlocal elastic media is performed, and the reductive perturbation method is used for the solution of the nonlinear equations. The propagation of weakly nonlinear and strongly dispersive waves is investigated, and the nonlinear Schrödinger (NLS) equation is acquired as an evolution equation. For the purpose of a numerical investigation of the nonlocal impacts on the NLS equation, it has been investigated whether envelope solitary wave solutions exist by utilizing the physical and geometric features of the carbon nanotubes. Amplitude dependent wave frequencies, phase and group velocities have been obtained and they have compared for the linear local, the linear nonlocal, the nonlinear local and the nonlinear nonlocal cases.

Weakly Nonlinear Dispersive Waves under Parametric Resonance Perturbation

2010 ◽  
Vol 124 (1) ◽  
pp. 19-37 ◽  
Author(s):  
Sergei Glebov ◽  
Oleg Kiselev ◽  
Nikolai Tarkhanov
Keyword(s):  
Parametric Resonance ◽  
Dispersive Waves ◽  
Weakly Nonlinear

An evaluation of a model equation for water waves

1981 ◽  
Vol 302 (1471) ◽  
pp. 457-510 ◽  
Keyword(s):  
Theoretical Model ◽  
Initial Value Problem ◽  
Water Waves ◽  
Laboratory Experiments ◽  
Initial Conditions ◽  
Initial Value ◽  
Dispersive Waves ◽  
Weakly Nonlinear ◽  
Spatial Periodicity ◽  
Long Channel

This study assesses a particular model for the unidirectional propagation of water waves, comparing its predictions with the results of a set of laboratory experiments. The equation to be tested is a one-dimensional representation of weakly nonlinear, dispersive waves in shallow water. A model for such flows was proposed by Korteweg & de Vries (1895) and this has provided the theoretical basis for a number of laboratory experiments. Some recent studies that have been made in the area are those of Zabusky & Galvin (1971), Hammack (1973) and Hammack & Segur (1974). In each case the theoretical model gave a good qualitative account of the experiments, but the quantitative comparisons were not very extensive. One of the purposes of this paper is to provide a more detailed quantitative assessment of a particular model than has been given to date. An important aspect of the formulation of the theoretical model is the specification of the initial conditions and the boundary conditions for the equation. Zabusky & Galvin (1971) considered an initial-value problem having spatial periodicity, whereas Hammack (1973) and Hammack & Segur (1974) considered an initial-value problem posed on the real line. In contrast, we shall consider an initial-value problem posed on the half line with boundary data specified at the origin. This problem was chosen to correspond with an experiment in which waves were generated at one end of a long channel, and obviates certain difficulties inherent in the other formulations.

Turbulence of one-dimensional weakly nonlinear dispersive waves

2001 ◽  
pp. 107-116 ◽  
Author(s):  
V. E. Zakharov ◽  
P. Guyenne ◽  
A. N. Pushkarev ◽  
F. Dias
Keyword(s):  
Dispersive Waves ◽  
Weakly Nonlinear ◽  
One Dimensional

scholarly journals On the Propagation of Weakly Nonlinear Random Dispersive Waves

2014 ◽  
Vol 212 (3) ◽  
pp. 849-874 ◽  
Author(s):  
Anne-Sophie de Suzzoni ◽  
Nikolay Tzvetkov
Keyword(s):  
Dispersive Waves ◽  
Weakly Nonlinear
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