for long locsiton wavelengths can be obtained by taking a Taylor series expansion of Eq. (20) at q → 0. By only retaining terms up to the order of q 2 and calculating all the necessary sums and products of trigonometric functions, we find that Eqs. (17) and (18) still hold in the NNA. It is sufficient to find locsitons with q lying within the first Brillouin zone of the reciprocal lattice, because any solutions with q lying outside the first Brillouin zone are physically equivalent to them due to the discrete nature of our system. The dispersion relation D NNA 2 ( q ) in Eq. (20) also has the required symmetry and periodicity. It is common to use high- symmetry points in the first Brillouin zone to denote most interesting directions in the lattice [see Fig. 1(b)]. Note that in terms of u$_{K}$ we may write ΓK ‖ u$_{K}$ and ΓM ⊥ u$_{K}$ . The dispersion dependence δ/δ$_{LL}$ = D NNA 2 ( q ) in the case of | δ$_{LL}$ | ≫ 1 is shown in Fig. 2(b,c) for two different orientations of E$_{in}$ with respect to the lattice: in Fig. 2(b) θ$_{0}$ = 0 (i. e., E$_{in}$ ‖ ΓK), while in Fig. 2(c) θ$_{0}$ = π/ 2 (i. e., E$_{in}$ ‖ ΓM). The x axis on the plots is aligned with the external field E$_{in}$ ; the hexagonal boundaries of the first Brillouin zones are shown with thicker dashed lines. The central parts of all three plots in Fig. 2 are very similar, which reflects our finding that Eqs. (17) and (18) hold for long locsiton wavelengths within both NRA and NNA. At the same time, significant differences accumulate closer to the boundaries of the first Brillouin zone. Fig. 2(b,c) also show that for both orientations of E$_{in}$ the maxima and minima of D NNA 2 ( q ) are attained at the zone boundaries, specifically, at different M points. To facilitate the comparison of the three plots in Fig. 2 and finding the edges of the locsiton band, the NNA dispersion dependencies for two high-symmetry directions are presented in Fig. 3 and compared to the the NRA result. For both longitudinal and transverse locsitons, Fig. 3 shows corresponding cross-sections of the three plots of Fig. 2. As we already noted earlier in this paper, the NRA result is only meaningful for q up to ∼ π ; Fig. 3 suggests that it is a good approximation for the NNA result at q < ∼ π/ 2, regardless of the orientation of E$_{in}$ with respect to the lattice. It is instructive to give explicit analytic expressions for each of the four NNA-based dependencies in Fig. 3. The respective dispersion relations derived from Eq. (20) and the corresponding ranges for δ/δ$_{LL}$ , obtained in the assumption that | δ$_{LL}$ | ≫ 1, are as follows: 15