Nonlinear Analysis and Solitary Waves for Interfacial Waves Propagating between Two Ideal Fluids

A. M. Abourabia；M. A. Mahmoud；G. M. Khedr

Chinese Journal of Physics

48卷6期（2010 / 12 / 01）

783 - 795

英文

We present the nonlinear analysis and solutions of the nonlinear Schrödinger (NLS) equation for waves propagating at the interface between two ideal fluids. The method of multiple scale expansion is employed in order to obtain a dispersion relation for the first-order problem and an NLS equation for the higher-order problem. The dispersion relation of the model NLS equation is studied. The solutions of the NLS equation are derived analytically by using the complex tanh-function method. We observe that the elevation of the interface is in the form of traveling solitary waves, which increase in amplitude as the density ratio increases and decrease in amplitude as the wave number increases. Also, we find that the wave number has a stabilizing effect, while the density ratio has a destabilizing effect. We observe that the slip velocities also bring in nonlinear solitary and periodic characters. Finally, we find that the conservation of power is in the form of traveling waves. Also, as the wave number increases and the density ratio decreases, the conservation of power more accurately fluctuates around zero.