Table 2.

Stationary points of the upper dispersion surface for $0<\tilde{\alpha }<1/3$.

point	$({\tilde{k}}_1,{\tilde{k}}_2)$	${\tilde{\omega }}_2$	type
A	$(\pi ,{\displaystyle \frac{\pi }{\sqrt{3}}})$	$\sqrt{{\displaystyle \frac{6}{2-\sqrt{1+3{\tilde{\alpha }}^2}}}}$	maximum
D	$({\displaystyle \frac{4\pi }{3}},0)$	$\sqrt{{\displaystyle \frac{9}{2(1-\tilde{\alpha })}}}$	minimum
F	$(4\arccos \left[{\displaystyle \frac{\sqrt{7-27{\tilde{\alpha }}^2}}{4}}\right],0)$	${\displaystyle \frac{9\sqrt{1+3{\tilde{\alpha }}^2}}{4}}$	saddle point