The evolution of a nonlinear wave train on the background of a stratified shear flow that is losing stability

The effects arising during the loss of stability of a shear flow in an ideal incompressible stratified fluid are investigated using the approximation of weak nonlinearity. A nonlinear evolutionary equation is obtained for the amplitude of the wave train which consists of almost neutral harmonics. It is shown that the coefficient for the nonlinear term in this equation is purely imaginary and that the role of the nonlinearity amounts to a frequency shift.