  We study the existence of monotone heteroclinic traveling waves for the
$1$-dimensional reaction-diffusion equation $$ u_t = (| u_x |^{p-2} u_x + | u_x
|^{q-2} u_x)_x + f(u), $$ where the non-homogeneous operator appearing on the
right-hand side is known as $(p, q)$-Laplacian. Here we assume that $2 \leq q <
p$ and $f$ is a nonlinearity of Fisher type, namely it is always positive out
of its zeros. We give an estimate of the critical speed and we comment on the
roles of $p$ and $q$ in the dynamics, providing some numerical simulations.
