We investigate the KP-Burgers flow in the background of the shock profile solution of the KdV-Burgers equation. We show that the KdV-Burgers shock profile is stable and asymptotically stable under the KPB-I flow with respect to small perturbations in some spaces close to the energy space.
"On the stability of line-shock profiles for Kadomtsev-Petviashvili-Burgers equations." Adv. Differential Equations 15 (1/2) 99 - 136, January/February 2010.