  Dyakonov surface waves are a well-known example of surface electromagnetic
waves propagating along a plane interface between isotropic and anisotropic
dielectric media. Here, we investigate the spectrum and radiative losses of
Dyakonov waves at the curved interface considering both cases of "positive" and
"negative" curvature of anisotropic medium. We demonstrate how Dyakonov waves
at a plane interface continuously transform to the leaky or guided modes of an
anisotropic cylindrical waveguide and simple derive asymptotic equation for
radiative losses. All analytical results are confirmed by solving exact
dispersion equation numerically. We believe that our work extends the potential
practical application of Dyakonov waves in optics and photonics devices.
