Hurtovyy Y. Propagation of weakly nonlinear wave packets in a two-fluid system

The Thesis is devoted to the problem of propagation of weakly nonlinear wave packets at the interface of two layers with different density. The solution and nonlinear evolutional Schr?dinger equation are obtained using the method of multiple scales. Condition of modulational instability is found and numerically investigated taking into account influence of surface tension. Geometrical and physical parameters of two fluid systems in which unstable solution leads to creation of envelope solitons are investigated. Areas where the second-harmonic resonance of internal wave packets appears that leads to the asymmetry of crest and bottom are found. The case of wave-packets propagation at wave number near cut-off leads to another equation which contains first as well as second derivatives in time. This equation is valid for all wave numbers. Results allow to define conditions of propagation and evolution of weak nonlinear internal wave packets in the dispersive stratified fluids and they can be used in oceanology and in the new technologies with the usage of two immiscible fluid systems.