From Maxwell's equations, the dispersion relation of space charge mode is strictly deduced, and the field pattern is studied.
The dispersion is related to the wave vector and similar to the dispersion relation of the isotropic dielectric.
The imaginary parts of the polarization and correlation contributions are calculated analytically and the real parts of them are obtained by means of dispersion relation.
The phonon dispersion relations of magnesium aluminium spinel MgAl2O4are calculated by using frozen phonon method.
The second example is the asymptotic periodic solution and the dispersion relation of weakly non-linear waves in a self-gravitating medium.
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