Some General Results for Multi-dimensional Compactonsin Generalized   N-dimensional KdV Equations
  We derive a general theorem relating the energy and momentum with the velocity of any solitary wave solution of the generalized KdV equation in $N$-dimensions that follows from an action principle. Further, we show that our $N$-dimensional Lagrangian formulation leads to a subclass of the equations discussed recently by Rosenau, Hyman and Staley. 
Fred Cooper, Avinash Khare, Avadh Saxena