COLLECTED RESULTS ON FINITE AMPLITUDE PLANE WAVES IN DEFORMED MOONEY-RIVLIN MATERIALS

1996 ◽  
pp. 1-45
Author(s):  
Ph. Boulanger ◽  
M. Hayes
Keyword(s):  
Plane Waves ◽  
Finite Amplitude

Further analysis of nonlinear, periodic, highly superluminous waves in a magnetized plasma

1982 ◽  
Vol 27 (1) ◽  
pp. 177-187 ◽  
Author(s):  
P. C. Clemmow
Keyword(s):  
Magnetic Field ◽  
Power Series ◽  
Periodic Solutions ◽  
Wave Speed ◽  
Nonlinear Differential Equations ◽  
Plane Waves ◽  
Electron Plasma ◽  
Finite Amplitude ◽  
Magnetized Plasma ◽  
Cold Electron

A perturbation method is applied to the pair of second-order, coupled, nonlinear differential equations that describe the propagation, through a cold electron plasma, of plane waves of fixed profile, with direction of propagation and electric vector perpendicular to the ambient magnetic field. The equations are expressed in terms of polar variables π, φ, and solutions are sought as power series in the small parameter n, where c/n is the wave speed. When n = 0 periodic solutions are represented in the (π,φ) plane by circles π = constant, and when n is small it is found that there are corresponding periodic solutions represented to order n2 by ellipses. It is noted that further investigation is required to relate these finite-amplitude solutions to the conventional solutions of linear theory, and to determine their behaviour in the vicinity of certain resonances that arise in the perturbation treatment.

Determination of the nonlinear parameter by propagating and modeling finite amplitude plane waves

2006 ◽  
Vol 119 (5) ◽  
pp. 2639-2644 ◽  
Author(s):  
F. Chavrier ◽  
C. Lafon ◽  
A. Birer ◽  
C. Barrière ◽  
X. Jacob ◽  
...  
Keyword(s):  
Plane Waves ◽  
Finite Amplitude ◽  
Nonlinear Parameter

scholarly journals Aerial plane waves of finite amplitude

1910 ◽  
Vol 84 (570) ◽  
pp. 247-284 ◽  
Keyword(s):  
Dynamical Equation ◽  
Plane Waves ◽  
Finite Amplitude ◽  
One Dimension ◽  
Inviscid Fluid ◽  
Elastic Fluid ◽  
Perpendicular Plane

In the investigations which follow, we are concerned with the motion of an elastic fluid in one dimension, say, parallel to x . It is implied not only that there are no component velocities perpendicular to x , but that the motion is the same in any perpendicular plane, so that it is a function of x and of the time ( t ) only. If u be the velocity at any point x, p the pressure, ρ the density, X an impressed force, the dynamical equation for an inviscid fluid is du/dt + u du/dx = X - 1/ ρ dp/dx . At the same time the "equation of continuity" takes the form dρ/dt + d (pu)/dx = 0.

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