An energy flux conserving one-way coupled mode propagation model
  A pure analytic one-way coupled mode propagation model for resonant interacting modes is obtained by the multiscale expansion method. It is proved that the acoustic energy flux is conserved in this model up to the first degree of the corresponding small parameter. The test calculations with the COUPLE program give an excellent agreement. 
M.Yu. Trofimov, S.B. Kozitskiy, A.D. Zakharenko
physics.ao-ph