Modulational instability in thin liquid film flowing down an inclined uniformly heated plate

The modulational instability properties regarding the evolution of interfacial disturbances flow a thin liquid film down an inclined uniformly heated plate subject to thermal Marangoni (thermocapillary) effects are investigated under framework linear stability analysis. investigation has been performed both analytically and numerically using complex cubic Ginzburg–Landau equation without driving term provide comprehensive pictures influence nonlinearity, dissipation, dispersion on disturbance generation evolution. It is shown that when interplay between nonlinear relatively important, evolve as superposition groups traveling periodic waves with different amplitudes, smooth modulations. Furthermore, dynamic modes these become aperiodic. Conversely, instabilities influenced by strong saturates, situations lead possible modulated wavy structures, caused dispersive dissipative effects. Moreover, appearance spatial temporal profiles amplitude term. Here, based our investigation, two cases highlighted. In first case, which corresponds very small disturbances, from solitary wave patterns. second increasing rapid, therefore, we can observe development modulationally marginal-like stable patterns or nonuniform profiles.