Variational Method for Studying Solitons in the KdV equation
  We use a class of trial wave functions which are generalizations of gaussians to study single soliton approximate analytic solutions to the KdV equations. The variational parameters obey a Hamiltonian dynamics obtained from the Principle of Least Action. We get extremely accurate approximate single soliton solutions including their time dependence using this method. 
F.Cooper, C.Lucheroni, H.Shepard and P. Sodano