A mode parabolic equations method with the resonant mode interaction
  A mode parabolic equation method for resonantly interacted modes was developed. The flow of acoustic energy is conserved for the derived equations with an accuracy adequate to the used approximation. The testing calculations were done for ASA wedge benchmark and proved excellent agreement with COUPLE program. 
M.Yu. Trofimov, S.B. Kozitskiy, A.D. Zakharenko
physics.class-ph