Solutions of the dispersion relation, Eq. (39), for the Alfvén wave case. Left and right panels present the real and imaginary parts of the wave frequency ω, respectively, as a function of the wavenumber k. The axes are scaled in the nondimensional units: C and D, defined in Eq. (40) for better visualization. Three solutions are marked with different colors and line styles: red solid for solution 1, orange dashed for solution 2, and green dotted for solution 3. The values of k for which we compare the analytical and numerical solutions using the values of ω, corresponding to solution 3 (green dots), are marked in the panels: pink triangle (k = 61.8 m⁻¹), green triangle (k = 6.18 m⁻¹), orange star (k = 6.18 × 10⁻² m⁻¹), and black triangle (k = 6.18 × 10⁻⁶ m⁻¹).