scholarly journals The relativity theory of divergent waves

1929 ◽  
Vol 123 (791) ◽  
pp. 119-133 ◽  
Keyword(s):  
Electromagnetic Wave ◽  
Transverse Wave ◽  
Small Amplitude ◽  
Plane Electromagnetic Wave ◽  
Plane Waves ◽  
Finite Amplitude ◽  
Relativity Theory ◽  
Wave Form ◽  
Infinite Plane ◽  
Special Case

Einstein investigated the problem of the propagation of gravitational waves in 1916 and 1918. The special case of plane waves of small amplitude was considered by Weyl, who showed that such waves may be regarded as the result of superposing weaves of three types. Eddington found that of these only one, the transverse-transverse, is real, and identified a particular type of electromagnetic transverse-transverse wave with light. The gravitational potentials in his solution, however, contain an aperiodic term which increases without limit, from which it is inferred that light cannot be propagated indefinitely either in space or time. We considered the case of plane waves of finite amplitude and came to the conclusion that an infinite plane electromagnetic wave cannot be propagated without change of wave-form, and suggested that the relativity theory of light must be approached by way of the study of divergent waves. The present discussion is confined to waves of a purely gravitational nature.

Solitary Filaments of Coupled Electromagnetic Wave and Finite Amplitude Ion Fluctuations

1976 ◽  
Vol 31 (12) ◽  
pp. 1517-1519 ◽  
Author(s):  
P. K. Shukla ◽  
M. Y. Yu ◽  
S. G. Tagare
Keyword(s):  
Electromagnetic Wave ◽  
Electromagnetic Radiation ◽  
Plasma Density ◽  
Large Amplitude ◽  
Small Amplitude ◽  
Finite Amplitude ◽  
Nonlinear Coupling ◽  
Incoming Radiation

Abstract We show analytically that the nonlinear coupling of a large amplitude electromagnetic wave with finite amplitude ion fluctuations leads to filamentation. The latter consists of striations of the electromagnetic radiation trapped in depressions of the plasma density. The filamentation is found to be either standing or moving normal to the direction of the incoming radiation. Criteria for the existence of localized filaments are obtained. Small amplitude results are discussed.

scholarly journals The relativity theory of plane waves

1926 ◽  
Vol 111 (757) ◽  
pp. 95-104 ◽  
Keyword(s):  
Gravitational Field ◽  
Electromagnetic Waves ◽  
Small Amplitude ◽  
Plane Waves ◽  
Cumulative Effect ◽  
Relativity Theory ◽  
Transverse Waves ◽  
Propagation Of Light ◽  
Cumulative Change ◽  
The Waves

Weyl has shown that any gravitational wave of small amplitude may be regarded as the result of the superposition of waves of three types, viz.: (i) longitudinal-longitudinal; (ii) longitudinal-transverse; (iii) transverse-transverse. Eddington carried the matter much further by showing that waves of the first two types are spurious; they are “merely sinuosities in the co­ordinate system,” and they disappear on the adoption of an appropriate co-ordinate system. The only physically significant waves are transverse-transverse waves, and these are propagated with the velocity of light. He further considers electromagnetic waves and identifies light with a particular type of transverse-transverse wave. There is, however, a difficulty about the solution as left by Eddington. In its gravitational aspect light is not periodic. The gravitational potentials contain, in addition to periodic terms, an aperiodic term which increases without limit and which seems to indicate that light cannot be propagated indefinitely either in space or time. This is, of course, explained by noting that the propagation of light implies a transfer of energy, and that the consequent change in the distribution of energy will be reflected in a cumulative change in the gravitational field. But, if light cannot be propagated indefinitely, the fact itself is important, whatever be its explana­tion, for the propagation of light over very great distances is one of the primary facts which the relativity theory or any like theory must meet. In endeavouring to throw further light on this question, it seemed desirable to avoid the assumption that the amplitudes of the waves are small; terms neglected on this ground might well have a cumulative effect. All the solu­tions discussed in this paper are exact.

Capillary–gravity waves of solitary type and envelope solitons on deep water

1993 ◽  
Vol 252 ◽  
pp. 703-711 ◽  
Author(s):  
Michael S. Longuet-Higgins
Keyword(s):  
Surface Tension ◽  
Dispersion Relation ◽  
Gravity Waves ◽  
Deep Water ◽  
Small Amplitude ◽  
Finite Amplitude ◽  
Surface Slope ◽  
Carrier Wave ◽  
Envelope Solitons ◽  
Special Case

The existence of steady solitary waves on deep water was suggested on physical grounds by Longuet-Higgins (1988) and later confirmed by numerical computation (Longuet-Higgins 1989; Vanden-Broeck & Dias 1992). Their numerical methods are accurate only for waves of finite amplitude. In this paper we show that solitary capillary-gravity waves of small amplitude are in fact a special case of envelope solitons, namely those having a carrier wave of length 2π(T/ρg)1½2 (g = gravity, T = surface tension, ρ = density). The dispersion relation $c^2 = 2(1-\frac{11}{32}\alpha^2_{\max)$ between the speed c and the maximum surface slope αmax is derived from the nonlinear Schrödinger equation for deep-water solitons (Djordjevik & Redekopp 1977) and is found to provide a good asymptote for the numerical calculations.

Multiple scattering of a plane electromagnetic wave by hemispherical bosses on an infinite plane

1996 ◽  
Vol 74 (3-4) ◽  
pp. 108-113 ◽  
Author(s):  
A.-K. Hamid
Keyword(s):  
Electromagnetic Wave ◽  
Plane Wave ◽  
Plane Electromagnetic Wave ◽  
Ground Plane ◽  
Image Plane ◽  
Angle Of Incidence ◽  
Infinite Plane ◽  
Incident Plane ◽  
Section Versus ◽  
The Given

An analytic solution to the problem of scattering of a plane electromagnetic wave by a system of hemispherical bosses on a perfectly conducting ground plane is obtained using the solution of scattering by a system of full spheres and the method of images. The system considered is replaced by a system of complete spheres in the absence of the ground plane, but with the given incident plane wave and also a supplement, image plane wave, chosen such that the boundary conditions for the total field are satisfied at all points where the ground plane is located in the original problem. Numerical results for a different system of simulations are presented for the normalized backscattering cross section versus the angle of incidence.

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