A Discourse on the Benney Equation
  It is shown that the Benney system is equivalent to a one body classical dynamical problem in which the interaction potential is a functional of the action function. The general solution of this equation is responsible for the general solution of the Benney system. Some particular solutions of the selfconsistent Hamilton-Jacobi equation arising in this investigation are presented in explicit form. 
A.N. Leznov and J. Sanchez Mondragon