A connection between the shallow-water equations and the   Euler-Poincar\'e equations
  The Euler-Poincar\'e differential (EPDiff) equations and the shallow water (SW) equations share similar wave characteristics. Using the Hamiltonian structure of the SW equations with flat bottom topography, we establish a connection between the EPDiff equations and the SW equations in one and multi-dimensions. Additionally, we show that the EPDiff equations can be recast in a curl formulation. 
Roberto Camassa and Long Lee
math-ph math.MP