In this talk, some mathematical and numerical aspects of the Weertman equation are discussed. This equation models steadily-moving dislocations in materials science. It involves integral operators that are simply represented by their Fourier transforms. Its solution can be interpreted as the traveling wave of an "artificial" dynamical system (a nonlinear integral reaction-advection-diffusion equation). Under reasonable hypotheses, we prove that, for any initial condition, the solutions of this dynamical system actually converge to the unique solution of the Weertman equation. This convergence provides a way of approximating numerically the solution of the Weertman equation.