  We consider the propagation of sine-Gordon kinks in a planar curved strip as
a model of nonlinear wave propagation in curved wave guides. The homogeneous
Neumann transverse boundary conditions, in the curvilinear coordinates, allow
to assume a homogeneous kink solution. Using a simple collective variable
approach based on the kink coordinate, we show that curved regions act as
potential barriers for the wave and determine the threshold velocity for the
kink to cross. The analysis is confirmed by numerical solution of the 2D
sine-Gordon equation.
