m = 0 and m = -1 harmonics have the greatest contribution to the summation of the spatial harmonics, and the dispersion equation
of the unperturbed structure converges quickly.
Roop, "Variational formulation for the stationary fractional advection dispersion equation
," Numerical Methods for Partial Differential Equations, vol.
and we obtain exactly the same dispersion equation
and cutoff frequencies as reported in , where [OMEGA] = w x a[square root of [[epsilon].sub.0][[mu].sub.0] [??] [OMEGA]/2[pi] = f * a/[square root of [[epsilon].sub.0][[mu].sub.0]] is the normalized frequency.
This dispersion equation
is similar to the dispersion equation
of normal MHD modes in a twisted flux tube surrounded by incompressible plasma --the only difference is that, there in (10), [K.sub.e] = [m.sub.0e] - [k.sub.z].
On the other hand, one can show that, for a P medium, the dispersion Equation
(8) is actually an identity which is satisfied by any one-form v .
This is the dispersion equation
of Love-type wave in a electrically open circuit piezoelectric layer over a non-homogeneous half-space.
and the first two exact solutions of the Pochhammer-Chree dispersion equation
for an elastic cylinder .
that governs the propagation of elastic-concentration waves has been derived by solving a system of coupled partial differential equations.
Expressing the constant [C.sub.2] from the first and second equations of the system and equating the resulting expressions, we obtain a dispersion equation
of the form
 obtained the analytical solution for the space Riesz fractional reaction dispersion equation
, and they also constructed an explicit finite difference scheme for it.
The relationship between wave velocity and frequency (wave number and frequency) is represented by dispersion equation
(1) and dispersion curve.
Using a well-known dispersion equation
[D.sub.m](f, [k.sub.z]) = 0 for the m-th order azimuthal mode in an infinite cylinder with nonuniform axial field specified above [2,18], we can define the functions