Solitary and transitional waves in gravity-driven two-layer microchannel flow

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.