  The dynamics of two component coupled Airy beams is investigated. In the
linear propagation regime a complete analytic solution describes breather like
propagation of the two components featuring non-diffracting self-accelerating
Airy behavior. The superposition of two beams with different input properties
opens the possibility to design more complex non-diffracting propagation
scenarios. In the strongly nonlinear regime the dynamics remains qualitatively
robust as is revealed by direct numerical simulations. Due to the Kerr effect
the two beams emit solitonic breathers, whose coupling period is compatible
with the remaining Airy-like beams. The results of this study are relevant for
the description of photonic and plasmonic beams propagating in coupled planar
waveguides as well as for birefrigent or multi-wavelengths beams.
