  We consider the "convection-diffussion" equation $u_t=J*u-u-uu_x,$ where $J$
is a probability density. We supplement this equation with step-like initial
conditions and prove a convergence of corresponding solution towards a
rarefaction wave, i.e. a unique entropy solution of the Riemann problem for the
nonviscous Burgers equation. Methods and tools used in this paper are inspired
by those used in [Karch, Miao and Xu, SIAM J. Math. Anal. {\bf 39} (2008), no.
5, 1536--1549.], where the fractal Burgers equation was studied.
