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 [2], 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 [65]--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 [9].

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 [17].

Dispersion equation 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

[18] 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