Abstract
The linear and nonlinear stability of the Kelvin-Helmholtz problem for magnetic fluids with surface adsorption is studied by employing the multiple scale method. The phenomenon of nonlinear focusing or collapse is considered. It is shown that the evolution of the amplitude is governed by a two-dimensional Schrödinger equation with cubic nonlinearity. This equation gives rise to a self-focusing singularity when the velocity difference is in the subcritical regime. Also from its equation, we obtain the condition for the existence of the modulational instability. The various regions of stability and instability are indicated.
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