Graphical investigation of the dispersion equation for . The solid lines show the graph of function Y = f(ϖ), while the dashed-dotted lines have equations Y = 4/(ζ − 1). The upper dashed-dotted line corresponding to ζ> 1 does not intersect the solid lines, which implies that there are no propagating wave modes when . Depending on the value of ζ< 1, the lower dashed-dotted line intersects the solid lines either at two or at four points, so there are up to four positive roots of the dispersion equation. However, only one of them satisfies the condition ϖ< | κ |. The vertical dotted line indicates the root satisfying the condition ϖ< | κ |.