Abstract
Similar to the case of the gravity-driven flow (Sisoev and Bennett 2013 Fluid Dyn. Res. 45 015503) we use the integral method to derive evolution equations modeling a pressure-driven two-layer flow of immiscible viscous fluids in a plane microchannel. It is shown that the system possesses a vast set of steady-traveling solitary and transitional waves. Analysis of the phase trajectories of the relevant dynamical system indicates the existence of families of steady-traveling periodic waves.
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