Magnetically induced solitons in a Hele-Shaw cell

We study the development of propagating solitons on the interface separating two viscous fluids flowing in parallel in a vertical Hele-Shaw cell. One of the fluids is a ferrofluid and a uniform magnetic field is applied in the plane of the cell, making an angle with the initially undisturbed interface. We derive a Korteweg-de Vries equation for long waves at this confined geometry which predicts the possibility of controlling the speed of the solitons by magnetic means. The influence of the tilted magnetic field on the velocity and on the shape of the solitary waves is investigated.