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 sm
all parameter. The test calculations with the COUPLE program give an excellent agreement.
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 b
enchmark and proved excellent agreement with COUPLE program.
Three dimensional roll-type double-diffusive convection in a horizontally infinite layer of an uncompressible liquid is considered in the neighborhood of Hopf bifurcation points. A system of amplitude equations for the variations of convective rolls
amplitude is derived by multiple-scaled method. An attention is paid to an interaction of convection and horizontal vortex. Different cases of the derived equations are discussed.
