THE ONSET OF STOCHASTIC PULSATIONS AT THE EARLY NONLINEAR STAGE OF THE DEVELOPMENT OF PERTURBATIONS IN THE JET OF AN INCOMPRESSIBLE FLUID PROPAGATING ALONG A WALL

The Korteweg-De Vries equation, which describes the non-linear propaga tion of perturbations in a jet of incompressible fluid emanating from a slit in a planar screen and propagating along a wall is considered. When account is taken of the natural vibrations of the wall, the equat ion becomes inhomogeneous. If an external action is specified in the f orm of a running wave, the particular solution of the inhomogeneous eq uation may be sought in an analogous form. As a result, the simplest p roblem in the theory of dynamical systems in the Hamiltonian formulati on arises. As usual, the existence of a homoclinic structure in the ne ighbourhood of the separatrices is deduced from an analysis of a Poinc are transformation. Among the trajectories belonging to the homoclinic structure in the secant plane, there are some with properties which a re formulated in terms of determinate chaos. A fundamentally important conclusion concerning the dual role of solitons at the non-linear sta ge of the wave motion of the fluid follows: on the one hand, they serv e as the nuclei of large-scale coherent structures and. on the other h and, they are responsible for the onset of stochastic pulsations.