  We investigate wavefront solutions in a nonlinear system of two coupled
reaction-diffusion equations with degenerate diffusivity: \[n_t = n_{xx} - nb,
\quad b_t = [D nbb_x]_x + nb,\] where $t\geq0,$ $x\in\mathbb{R}$, and $D$ is a
positive diffusion coefficient. This model, introduced by Kawasaki et al. (J.
Theor. Biol. 188, 1997), describes the spatial-temporal dynamics of bacterial
colonies $b=b(x,t)$ and nutrients $n=n(x,t)$ on agar plates. Kawasaki et al.
provided numerical evidence for wavefronts, leaving the analytical confirmation
of these solutions an open problem. We prove the existence of an infinite
family of wavefronts parameterized by their wave speed, which varies on a
closed positive half-line. We provide an upper bound for the threshold speed
and a lower bound for it when $D$ is sufficiently large. The proofs are based
on several analytical tools, including the shooting method and the fixed-point
theory in Fr\'echet spaces, to establish existence, and the central manifold
theorem to ascertain uniqueness.
