Long-wave equation for a confined ferrofluid interface: periodic interfacial waves as dissipative solitons

We study the dynamics of a ferrofluid thin film confined in Hele-Shaw cell, and subjected to tilted nonuniform magnetic field. It is shown that interface between an inviscid outer fluid (air) supports traveling waves, governed by novel modified Kuramoto--Sivashinsky-type equation derived under long-wave approximation. The balance energy production dissipation this equations allows for existence dissipative solitons. These permanent waves' propagation velocity profile shape are be tunable via external A multiple-scale analysis performed obtain correction linear prediction velocity, reveal how nonlinearity arrests instability. periodic interfacial waves discovered identified as fixed points phase plane. transitions states (wave profiles) occur. explained spectral stability waves. Interestingly, multiperiodic which non-integrable analog double cnoidal wave, also found propagate model equation. solutions investigated numerically, they long-lived transients, but ultimately abruptly transition one stable identified.