Single soliton solution to the extended KdV equation over uneven depth
  In this note we look at the influence of a shallow, uneven riverbed on a soliton. The idea consists in approximate transformation of the equation governing wave motion over uneven bottom to equation for flat one for which the exact solution exists. The calculation is one space dimensional, and so corresponding to long trenches or banks under wide rivers or else oceans. 
George Rowlands, Piotr Rozmej, Eryk Infeld, Anna Karczewska
physics.flu-dyn