  We investigate wave propagation in rotationally symmetric tubes with a
periodic spatial modulation of cross section. Using an asymptotic perturbation
analysis, the governing quasi two-dimensional reaction-diffusion equation can
be reduced into a one-dimensional reaction-diffusion-advection equation.
Assuming a weak perturbation by the advection term and using projection method,
in a second step, an equation of motion for traveling waves within such tubes
can be derived. Both methods predict properly the nonlinear dependence of the
propagation velocity on the ratio of the modulation period of the geometry to
the intrinsic width of the front, or pulse. As a main feature, we can observe
finite intervals of propagation failure of waves induced by the tube's
modulation. In addition, using the Fick-Jacobs approach for the highly
diffusive limit we show that wave velocities within tubes are governed by an
effective diffusion coefficient. Furthermore, we discuss the effects of a
single bottleneck on the period of pulse trains within tubes. We observe period
changes by integer fractions dependent on the bottleneck width and the period
of the entering pulse train.
