Figure 3 shows, in long wave approximation, the soft branches of the dispersion relation
for [[GAMMA] = 1 in the absence of intermolecular forces ([PHI] = 0) and for [PHI] = 0.
According to the dispersion relation, coastal-trapped waves in the low-frequency range propagate with the shallower water on their right.
Also the dispersion relation of the coastal-trapped waves supports our hypothesis that these rather strong current oscillations, observed in June 1995 in the Irbe Strait, are coastal-trapped waves propagating northwards along the eastern coast of the Baltic Proper.
Next, having studied the dispersion relation for the eastern Baltic Proper, we present the first derivative in the series as
This is the dispersion relation reduces in the simple form to give
We find that in the longitudinal mode of propagation the dispersion relation is modified due to the pressure of neutral particles, thermal conductivity and arbitrary radiative heat-loss functions.
The dispersion relation (14) shows the combined influence of thermal conductivity and arbitrary radiative heat-loss functions on the self gravitational instability of a two components of the partially-ionized plasmas we find that in this dispersion relation the terms due to the arbitrary radiative heat-loss function with thermal conductivity have entered through the factor [[OMEGA].
6) gives rise to the asymptotic expression of the dispersion relation
The leading order part of the dispersion relation corresponds to the case of plane waves that was studied in detail in .
The linearized discrete equations are used to define a small parameter, responsible for the weak transverse effect while dispersion relation has the same form as for the plane waves.
We may calculate the dispersion relation of a one-dimensional plane wave in the small strain approximation in order to check some consequences of the above stress-strain relation.
We calculated also a one-dimensional dispersion relation and concluded that it was similar to the dispersion relation of some microstructured materials as one could expect in the case of higher grade solids (see e.