Persistence of travelling fronts of KdV–Burgers–Kuramoto equation

We study the travelling fronts of KdV–Burgers–Kuramoto equation from geometric singular perturbation point of view. Motivated by the analogue between travelling fronts and heteroclinic orbits of the corresponding ordinary differential equations, we prove the persistence of these waves for sufficiently small dissipation. The result of numerical investigation also establishes our analysis.