  Topological insulators are unique physical structures that are insulators in
their bulk, but support currents at their edges which can be unidirectional and
topologically protected from scattering on disorder and inhomogeneities.
Photonic topological insulators can be crafted in materials that exhibit a
strong nonlinear response, thus opening the door to the exploration of the
interplay between nonlinearity and topological effects. Among the fascinating
new phenomena arising from this interplay is the formation of topological edge
solitons -- hybrid asymmetric states localized across and along the interface
due to different physical mechanisms. Such solitons have so far been studied
only in materials with Kerr-type, or cubic, nonlinearity. Here the first
example of the topological edge soliton supported by parametric interactions in
$\chi^{(2)}$ nonlinear media is presented. Such solitons exist in Floquet
topological insulators realized in arrays of helical waveguides made of a
phase-matchable $\chi^{(2)}$ material. Floquet edge solitons bifurcate from
topological edge states in the spectrum of the fundamental frequency wave and
remain localized over propagation distances drastically exceeding the helix
period, while travelling along the edge of the structure. A theory of such
states is developed. It is shown that multicolor solitons in a Floquet system
exists in the vicinity of (formally infinite) set of linear resonances
determined by the Floquet phase matching conditions. Away from resonance,
soliton envelopes can be described by a period-averaged single nonlinear
Schr\"odinger equation with an effective cubic nonlinear coefficient whose
magnitude and sign depend on the overall phase-mismatch between the fundamental
frequency and second harmonic waves.
