  We investigate traveling wave solutions for a nonlinear system of two coupled
reaction-diffusion equations characterized by double degenerate diffusivity:
\[n_t= -f(n,b), \quad b_t=[g(n)h(b)b_x]_x+f(n,b).\] These systems mainly appear
in modeling spatial-temporal patterns during bacterial growth. Central to our
study is the diffusion term $g(n)h(b)$, which degenerates at $n=0$ and $b=0$;
and the reaction term $f(n,b)$, which is positive, except for $n=0$ or $b=0$.
Specifically, the existence of traveling wave solutions composed by a couple of
strictly monotone functions for every wave speed in a closed half-line is
proved, and some threshold speed estimates are given. Moreover, the regularity
of the traveling wave solutions is discussed in connection with the wave speed.
