The N-rational solutions to two (2+ 1)-dimensional nonlinear evolution equations are
constructed by utilizing the long wave limit method. M-lump solutions to the two equations …

In this paper, we study abundant exact solutions including the lump and interaction solutions
to the (2+ 1)-dimensional Yu–Toda–Sasa–Fukuyama equation. With symbolic computation …

Although the equations governing fluid flow are well known, there are no analytical
expressions that describe the complexity of turbulent motion. A recent proposition is that in …

Flows through pipes and channels are the most common means to transport fluids in
practical applications and equally occur in numerous natural systems. In general, the …

The torque in turbulent Taylor–Couette flows for shear Reynolds numbers the torque
features a maximum for a stationary outer cylinder. In addition, the effective torque scaling …

Tunnel excavation in karst areas could affect natural karst hydrological processes and
runoff, resulting in groundwater drainage and even underground river cut-off. The …

Direct numerical simulation of transitional pipe flow is carried out in a long computational
domain in order to characterize the dynamics within the saddle region of phase space that …

Recent numerical studies suggest that in pipe and related shear flows, the region of phase
space separating laminar from turbulent motion is organized by a chaotic attractor, called an …

We perform the linear modal stability analysis of a pipe flow subjected to a step-like
increment in the flow rate from a steady initial flow with the flow rate, Q i, to a final flow with …

We study M-lump solutions of the (2+ 1)-dimensional generalized Calogero–Bogoyavlenskii–
Schiff (CBS) equation. The amplitude of these solutions are rational in their independent …