  The propagation of localized edge modes in photonic honeycomb lattices,
formed from an array of adiabatically varying periodic helical waveguides, is
considered. Asymptotic analysis leads to an explicit description of the
underlying dynamics. Depending on parameters, edge states can exist over an
entire period or only part of a period; in the latter case an edge mode can
effectively disintegrate and scatter into the bulk. In the presence of
nonlinearity, a `time'-dependent one-dimensional nonlinear Schr\"odinger (NLS)
equation describes the envelope dynamics of edge modes. When the average of the
`time varying' coefficients yields a focusing NLS equation, soliton propagation
is exhibited. For both linear and nonlinear systems, certain long lived
traveling modes with minimal backscattering are found; they exhibit properties
of topologically protected states.
