Whitham method for Benjamin-Ono-Burgers equation and dispersive shocks   in internal waves in deep fluid
  The Whitham modulation equations for the parameters of a periodic solution are derived using the generalized Lagrangian approach for the case of damped Benjamin-Ono equation. The structure of the dispersive shock in internal wave in deep water is considered by this method. 
Y. Matsuno, V.S. Shchesnovich, A.M. Kamchatnov, R.A. Kraenkel