The linear form of BBM equation (1) which describes dispersive effect to the equation yields
dispersion relation stating the relation between the wavenumber k and frequency w; the
dispersion relation reads [omega] = k/(1 + [k.sup.2]).
In this case, the deformed energy-momentum
dispersion relation equation (1) will go back to classical one when the energy of the test particle is much lower than [E.sub.p].
By means of the solutions to (5) in both media, one can find the corresponding expressions for [[xi].sub.r], and after merging these solutions, together with those for [p.sub.tot], through appropriate boundary conditions at the interface r = a, one can derive the
dispersion relation of the normal modes propagating in the moving magnetic flux tube.
Considering the nondimensionalized linear
dispersion relation [9] for deep water with a current, we think that the initial estimation of the nonlinear
dispersion relation satisfies
Besides, the
dispersion relations of TE waves and TM waves are dual (according to (4) and (8)), so we can get the other
dispersion relation by exchanging the elements of [??] and [??] in either relation ([[micro].sub.x], [[micro].sub.y], and [[epsilon].sub.z] exchange with [[epsilon].sub.x], [[epsilon].sub.y], and [[micro].sub.z]).
Slinky-whistler
dispersion relation from 'scaling'.
7a using the linear
dispersion relation (13) are denoted by [[lambda].sub.l], and they are given in Fig.
On the
dispersion relation of random gravity waves, 1, (58) 2 (59)
This phase change can be derived from K-K
dispersion relation [16].