  Qualitatively new aspects of the (linear and non-linear) stability of sheared
relativistic (slab) jets are analyzed. The linear problem has been solved for a
wide range of jet models well inside the ultrarelativistic domain (flow Lorentz
factors up to 20; specific internal energies $\approx 60c^2$). As a distinct
feature of our work, we have combined the analytical linear approach with
high-resolution relativistic hydrodynamical simulations, which has allowed us
i) to identify, in the linear regime, resonant modes specific to the
relativistic shear layer ii) to confirm the result of the linear analysis with
numerical simulations and, iii) more interestingly, to follow the instability
development through the non-linear regime. We find that very high-order
reflection modes with dominant growth rates can modify the global, long-term
stability of the relativistic flow. We discuss the dependence of these resonant
modes on the jet flow Lorentz factor and specific internal energy, and on the
shear layer thickness. The results could have potential applications in the
field of extragalactic relativistic jets.
