Monotone wave fronts for $(p, q)$-Laplacian driven reaction-diffusion equations

We study the existence of monotone heteroclinic traveling waves for the 1-dimensional reaction-diffusion equation u_t = (|u_x|^(p-2)u_x)_x +(|u_x|^(q-2)u_x)_x + f(u), t is an element of R, x is an element of R,where the non-homogeneous operator appearing on the right-hand side is of (p, q)-Laplacian type. Here we assume that 2 <= q < p and f is a nonlinearity of Fisher type on [0, 1], namely f(0) = 0 = f(1) and f > 0 on ]0,1[. 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.